Arabic Origins Of Cryptolog Vol. 4

Series on Arabic Origins of Cryptology Volume Four

ibn Dunaynir's Book: Expositive Chapters on Cryptanalysis (Maq id al-Fu l al-Mutar ima an all at-Tar ama)

Series Editors M. Mrayati, Ph.D. Y. Meer Alam, Ph.D.

M. H. at-Tayyan, Ph.D.

Published by KFCRIS & KACST

Acknowledgments The editors of this series greatly appreciate the encouragement they had from Dr. Yahya Mahmoud Ben Jonayd, Secretary General of King Faisal Center for Research and Islamic Studies, to publish this Series. We are also in the debt to Dr. Saleh Athel, the president of King Abdulaziz City for Science and Technology (KACST), for supporting the project of translating this series to English. Many thanks to Dr. Daham Ismail Alani, the Secretary General of the Scientific Council of KACST, for all his efforts to make this publication possible. The typesetting of this bilingual version of the series was realized with skill and dedication by Mr. Ousama Rajab; we offer hearty thanks to him. Finally, we would like to mention our recognition to the many who had previously contributed to the Arabic version of this series, and particularly to Dr. Wathek Shaheed, Dr. Shaker al-Faham, the late Prof. Rateb an-Naffakh, and Dr. Fouad Sezgin.

Series on Arabic Origins of Cryptology Volume 4

Translated by Said M. al-Asaad

Revised by Mohammed I. al-Suwaiyel, Ph.D. Ibrahim A. al-Kadi, Ph.D. Marwan al-Bawab

Contents List of Figures .…........................................................................... vii List of Tables ......…….................................................................... viii Transliterating Arabic words ....................................................... ix Preface ............................................................................................ xi

Section 1: Analytical Study of ibn Dunayn r’s Book: Expositive Chapters on Cryptanalysis ....................... 1 1.1. Biography of ibn Dunayn r ......................…........................... 3 1.2. Study and Analysis of ibn Dunayn r’s Book .......................... 5 1.2.1. ibn Dunayn r’s Sources .................................................... 5 1.2.2. ibn Dunayn r’s Cryptological Practice ............................. 8 1.3. Structure of the Book .............................................................10 1.3.1. Cryptanalysis of Prose Ciphers ...................................... 11 1.3.1.1. Principles and Tools of Cryptanalysis ...............… 11 1.3.1.2. Types of Encipherment .........................…............. 13 1.3.1.3. Algorithms of Cryptanalysis ….............................. 15 1.3.1.4. Composite Encipherment ....................................... 32 1.3.2. Cryptanalysis of Poetry Ciphers .................................... 47 1.3.2.1. Tools for Cryptanalysing Poetry Ciphers .............. 48 1.3.2.2. On Prosody (Metrics) ............................…............ 49 1.3.2.3. On Rhymes ....................….................................... 49 1.3.2.4. Insight into Writing Knack ...…............................. 50 1.3.2.5. Other Useful Observations .................................... 53 1.3.2.6. Practical Examples .................…........................... 54 1.3.2.7. Conclusion ............................................................. 56 1.4. Originality of ibn Dunayn r .................................................. 58

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Section 2: ibn Dunayn r’s Edited Book: Expositive Chapters on Cryptanalysis ...................... 60 2.1. Editing Methodology .............................................................62 2.2. Description of the Manuscript ...............................................63 2.3. ibn Dunayn r’s Book (Original Arabic Text and English Translation) ............................................................................ 67 PART ONE. Cryptanalysis of Prose Ciphers ........................... 70  Principles and Tools of Cryptanalysis (Chapters 1-2) .....72  Types of Encipherment - Simple (Chapters 3-5) ............................................... 76 - Composite (Chapter 6) .............................................. 82  Algorithms of Cryptanalysis (Chapters 7-35) ................ 84 PART TWO. Cryptanalysis of Poetry Ciphers ........................142  Tools for Cryptanalysing Poetry Ciphers (Chapters 36-37) ......................................................... 142  On Prosody (Chapters 38-40) ........................................ 144  On Rhymes (Chapter 41) ............................................... 148  Writing Knack (Chapters 42-52) ................................... 154  Other Useful Observations (Chapters 53-59) ................ 168 - Comment on an important cipher method from The Two Essays (Chapter 60) ................................... 176  Practical Examples (Chapters 61-62) ............................ 178  Conclusion (Chapters 63-66) .........................................184

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List of Figures 1.1. ibn Dunayn r's types of encipherment ........................................ 14 1.2. Encipherment by numerical processing using ADWNA .......... . 40 2.1. A photocopy of the first sheet of ibn Dunayn r's book ...............64 2.2. A photocopy of the second sheet of ibn Dunayn r's book ......... 65 2.3. A photocopy of the last sheet of ibn Dunayn r's book ........….. 66

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List of Tables 1.1. ibn Dunayn r's work on the orders of letter frequency (statistical cryptanalysis) .......................................................... 18 1.2. Noncombinable letters (in texts) as observed by ibn Dunayn r (without repetition) .................................................................. 22 1.3. Noncombinable letters (in texts) according to ibn Dunayn r, arranged alphabetically (with repetition) ................................. 23 1.4. Noncombinable letters as demonstrated in our statistical analysis of Arabic roots ........................................................... 24 1.5. Table of noncombinable letters as observed by al-Kind ......... 25 1.6. Numerical values of letters ....................................................... 36 1.7. Finger-spelling using ADWNA ................................................ 38 1.8. The first of ibn Dunayn r's two practical examples .................. 55 1.9. The second of ibn Dunayn r's two practical examples ............. 56

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Transliterating Arabic words For transliterating Arabic words (names, titles, etc.) we have adopted the International System for the Transliteration of Arabic characters, devised by the International Standards Organization (ISO). The system constitutes ISO Recommendation R233 (December 1961). Given below is this system, with some additional explanations found to be necessary.

Vowels: Arabic characters

Short Vowels

Transliteration

Examples

(fat a)

a

as u in cup.

( amma)

u

(kasra)

i

as o in rock, and u in put. as e in red, and i in big. As a in last.

Long Vowels

ٚ (preceded by

)

as oo in moon.

ٞ (preceded by

)

as ee in sheet.

Consonants: Arabic characters

Transliteration

'

Examples (e.g. 'amr, 'ibr h m, fu' d, kis ' , t '). as a in add (e.g. ' dam, qur' n).

‫ة‬ ‫د‬ ‫س‬ ‫ط‬ ‫ػ‬ ‫ؿ‬ ‫ك‬ ‫م‬ ‫ه‬

b t

as b in back. as t in tea. as th in thin. as g in logic.

d

(e.g.

tim).

(e.g.

lid).

as d in day. as th in then.

r

as r in red.

ix

‫ى‬ ً ُ ‫ص‬ ‫ض‬ ‫ط‬ ‫ظ‬ ‫ع‬ ‫ؽ‬ ‫ف‬ ‫ق‬ ‫ن‬ ‫ي‬ َ ْ ‫٘ـ‬ ٚ ٞ

z s

as z in zoo. as s in soon. as sh in show. (e.g. mi r). (e.g. ir r). (e.g. riq). (e.g.

fir).

(e.g. Abb s). (e.g.

f q k l m n h w y

lib).

as f in few. (e.g. qur' n). as k in key. as l in led. as m in sum. as n in sun. as h in hot. as w in wet (e.g. wahab, nawfal). as ie in orient (e.g. y q t, dunayn r).

Notes: (t ' marb a): In the absolute state, ignored in transliteration (e.g. mad na); in the construct state, rendered by (t) (mad nat annab ). (suk n): Ignored in transliteration. ( adda): Rendered by doubling the consonant.

x

Preface This is the fourth book of The Arabic Origins of Cryptology series, which addresses the cryptological contributions of the Arabs, and translates a number of treatises by Arab cryptologists. An individual book is dedicated to each treatise. The first book was devoted to the oldest ever found treatise on cryptanalysis, written by the well-known Arab philosopher al-Kind about 1200 years ago. The second book of the series tackles ibn Adl n's treatise al-mu'allaf lilmalik al-'A raf (The manual written for King al-A raf). The third book deals with ibn ad-Durayhim's treatise Mift al-Kun z f alMarm z (Key to treasures on clarifying ciphers), while the fourth book (this one) covers ibn Dunayn r's work. For the time being, nine books are envisaged, unless more manuscripts are discovered. In Book One we have devoted a full chapter to study and analyse the birth of cryptology by the Arab civilization. This would highlight important aspects and prove useful for understanding the whole series.

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This book is divided into two sections. Section 1 is an analytical study of the edited book of ibn Dunayn r. It aims at introducing the book and elucidating difficult or vague points, spotting particular features and, more remarkably, highlighting aspects of originality and innovation in ibn Dunayn r's book. This section is divided into four sub-sections: one gives a brief biography of ibn Dunayn r, another provides an account of his sources and cryptological practice, a third details the structure of the book as regards cryptanalysis of both prose and poetry ciphers, and a fourth sub-section summing up the analytical study of the book, exposing ibn Dunayn r's cryptological contributions and aspects of originality. Section 2 comprises an English translation of the original Arabic text of ibn Dunayn r's edited book. It opens with a statement outlining the editing methodology adopted, which basically conforms to that commonly used by the scientific community. The edited book is xi

preceded by a brief description of the manuscript, followed by sample photocopies of selected pages from the original. The task of editing the manuscript text was a challenge indeed. Special care has been taken to present the text in due form. The English translation appears on the left-hand (even) pages, and the original Arabic text on the right-hand (odd) pages. No effort has been spared correcting the mistakes and clearing the ambiguities. For ease of reference, individual chapters have been assigned numbers (by the editors). Wherever appropriate, lead-in headings have been introduced.

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Damascus, May 2005

Dr. M. Mrayati Dr. Y. Meer Alam

Dr. M. H. Tayyan

xii

Section 1

Analytical Study of ibn Dunayn r's Book: Expositive Chapters on Cryptanalysis (Maq id al-Fu l al-Mutar ima an all at-Tar ama)

2

1.1. Biography of ibn Dunaynir He is 'Ibr h m ibn Mu ammad ibn 'Ibr h m ibn Al ibn Hibat 1 All h ibn Y suf ibn Na r ibn 'A mad, alias ibn Dunayn r al-La m , son of King Q b s ibn al-Mun ir ibn M ' as-Sam '. Born in Mosul in AH 583/ AD 1187, he lived during the reign of King a - hir z, son of Sultan Saladin, and governor of Aleppo and its administrative districts (d. AH 613/ AD 1216). He was in the employ of Prince Asad ad-D n A mad ibn Abdull h al-Muhr n on whom he made panegyrics. He was then reported to have worked for N ir ad-D n Mu ammad ibn 'Ayy b, king of Egypt (d. AH 635/AD 1238). ibn Dunayn r journeyed between Greater Syria and Egypt and lauded a number of kings and notobilities there. His life ended at the hands of King al- Az z U m n ibn al-Malik al- dil, who crucified him in as-Subayta Fort near Banyas in the year AH 627/ AD 1229.

His works According to his biographies, ibn Dunayn r wrote primarily in the following two fields: a) Poetry, in which he wrote two books, i.e. his own poetical collection (divan), and al-K f ilm al-qaw f (Sufficiency in the science of rhymes), which is still missing. b) Cryptology, the science in which he excelled and was particularly well-known. a - afad [a biographer and historian, d. AH 764/ AD 1363] has mentioned two books on cryptology by ibn Dunayn r, i.e. 1. a - ih b an-n im f ilm wa at-tar im (The shooting star in the science of making ciphers), also numbered among the missing compilations. ibn Dunayn r, however, refers to it in 2 Maq id al-fu l.

1 2

Diminutive of dinar ‫ـــ‬a unit of currency. See p.98.

3

2. Maq id al-fu l al-mutar ima

an all at-tar ama (Expositive chapters on cryptanalysis) ‫ـــ‬the subject of this volume of the series.

4

1.2. Study and Analysis of ibn Dunaynir's Book This study involves a general review of ibn Dunayn r's Maq id al-Fu l al-Mutar ima an all at-Tar ama, along the same lines as in the previous treatises. Thus, the book is to be analysed according to the order of topics that it covers. It has been found useful to add, in square brackets, explicatory headings to the already numbered chapters of the edited text. This would make life easier for the reader, and mark the sequence of ideas. A full analysis of every chapter is provided, along with illustrative examples where necessary, to rule out any possibility of ambiguity that might be encountered especially by nonprofessionals. It is only natural, on our part, to highlight ibn Dunayn r's novel additions to the contributions of his predecessors, and point out his refinements of already existing ideas. A brief appraisal is also given for each of the chapters of his book, then to conclude with a statement manifesting the aspects of ibn Dunayn r's originality.

1.2.1. ibn Dunaynir's Sources In his book, ibn Dunayn r has attained a high degree of excellence as regards his extensive knowledge, precise methodology, and wellorganized access to both cryptography and cryptanalysis. His sound systematic approach is in fact an outcome of a broad personal knowledge of the work of his predecessors in this art; he manages to make full use of their efforts, to set straight their mistakes, to redress their omissions, as well as to add his own new contributions. ibn Dunayn r's scientific method is reflected in that he considers cryptography and cryptanalysis as separate sciences, each having its own set of principles and concepts. He demonstrates this distinction particularly in the designation of two of his compilations, namely a ih b an-n im f ilm wa at-tar im, which is dedicated to cryptography, and Maq id al-fu l al-mutar ima an all attar ama, devoted to cryptanalysis ‫ـــ‬a fact revealing his insistence on treating them as separate sciences. In this respect he precedes ibn adDurayhim (d. AH 762/ AD 1361) who states in his treatise Mift alkun z f ' al-marm z, describing the cryptologue's tools: "It is

5

necessary for one experiencing cryptanalysis to develop a thorough 3 knowledge…" ibn Dunayn r seems keen to glean and marshal whatever earlier manuscripts he has run down of this science. He does proclaim that he quoted from al-Kind , and from "the Author of the Two Essays", as well as from Ab al- asan ibn ab ab (d. AH 322/ AD 934). It is also likely that he tapped the works of ibn Wahab al-K tib and the author of the book Adab a - u ar ' (The art of poets), among other great figures of this art who lived between the third and sixth centuries of the Hegira (9th - 12th AD). This is so because ibn Dunayn r's professional scientific life began in the early part of the seventh century of the Hegira. But his main source is really al-Kind 's treatise on cryptanalysis (Volume One of this series). He leans heavily on it and quotes much of its contents, yet he has been shrewd enough to adjust and modify what he takes, bidding fair to succeed at times, and falling wide of the mark at other times. He does well in explaining the points summed up by al-Kind , while he misses the mark in overlooking some things that al-Kind mentions. In this context, ibn Dunayn r's citations are not a slavish indiscriminate repetition, but a leisurely premeditated practice based on verification and experimentation. For example, he does not only cite al-Kind 's computation of letter frequency of occurrence and the resultant orders, but also emulates him in reckoning the letters of texts that appear in some sheets, and setting the letters in order, as per his own calculations, and in substantiation of al-Kind 's results. At the beginning of Chapter 8 of his book, ibn Dunayn r says: "I have considered the orders of letter frequencies according to the reckoning of Ya q b al-Kind , peace be on his soul. He said he had turned to seven parchments and counted all the orders of letter frequency of occurrence in them … It so occurred to me to take up [other] written sheets myself and count the letter frequency orders in them … So it came home to me the validity of the statement of Ya q b ibn 'Is q, 4 peace be on his soul." The fact that ibn Dunayn r adapts his quotations from al-Kind is maintained by his own statement: "and I abridged that considerably 3 4

See his treatise, Volume Three of this series, p.52. See his book, p.86.

6

such that my version should suffice instead of al-Kind 's treatise and 5 its long-winded prolixity." This very account, however, remains a moot point, since al-Kind 's treatise is, by rights, a typical example of conciseness, concentration and richness ‫ـــ‬a fact which denies the claim of any substitute that can do duty for it, and which refutes any redundance in it, with the exception perhaps of some repetition marking his treatment of letter non-combination. ibn Dunayn r's enlargement on al-Kind 's text, and also his acquaintance with the bulk of material written on the subject, are evident in his discussion of composite encipherment. He says that al-Kind did not in the least touch upon it, and that those who dealt with it later fumbled and disarranged things. He adds: "But I mentioned a good few of them [i.e. composite ciphers] to serve as a guideline in deciding on unmentioned cases, if any. al-Kind never attended to composite encipherment except incidentally [without dwelling on details]. Whoever attempted to deal with it, other than 6 al-Kind , certainly raved and went astray on that score…". By the same token, ibn Dunayn r proposes novel ideas overlooked by his predecessors for some reason. For example his approach to encipherment by utilizing the chessboard to communicate with someone who is present, and his notion of the possibility of developing it so as to convey a cipher message to an absent person. As he puts it: "It [chessboard encipherment] may be employed to address 7 an absent person in a way I shall tell you without precedent." Among those whom ibn Dunayn r proclaims to have drawn on and quoted is the Author of the Two Essays. This is manifested in his own words: "Towards the end of his Second Essay, the Author of the Two Essays on cryptanalysis states that we are destined to follow an 8 intricate path." This is the second of ibn Dunayn r's sources. The third reference is Ab al- asan ibn ab ab 's Treatise on Cryptanalysis. ibn Dunayn r writes: "I have [herein] adduced something novel that none else had ever broached before, because 5

See his book, p.94. Ibid., p.108. 7 Ibid., p.120. 8 Ibid., p.176. 6

7

al-Kind 's book [treatise] tackles prose simple encipherment only; and Ab al- asan's book treats poetry encipherment. Both failed to 9 develop the topic exhaustively in either case." This shows that ibn Dunayn r is keen to explicitly bring his own new and original views to notice, insomuch that he asserts that none had ever before him taken the lead in introducing them. His keenness is all-often associated with observing the concepts that his predecessors overlooked, or imperfectly handled, or those that eluded their attention. It seems that he opts to cite some of his references especially to point out any one of these implications. Upon comparing ibn Dunayn r's work with that of the author of Adab a - u ar ' (in his treatise on cryptanalysis of poetry), one realizes that the latter is not only extensively quoted by ibn Dunayn r, but is sometimes literally copied in many places.

1.2.2. ibn Dunaynir's Cryptological Practice In addition to his mastery of cryptography and cryptanalysis, ibn Dunayn r attained high practical expertise. This is evident in the works he left and the nature of activity he pursued. He says, for instance, concluding his discussion of the encipherment implemented by adding insignificant letters (nulls): "I was asked to cryptanalyse a ciphered message, but found it incompatible with any of the [simple encipherment] divisions. I pondered on it, sorted out its characters… and by the good assistance of the Almighty, I managed to solve it 10 straightway." A similar picture of ibn Dunayn r's practical knowledge lies in his statement, closing his argument about composite encipherment: "And we have straightforward methods out of composites… This method is within easy reach of the enlightened 11 people of this profession, who consider it carefully." It goes without saying that the last quotation above reflects ibn Dunayn r's conviction of the fact that cryptography is an established science based on rules

9

His book, p.184. Ibid., p.104. 11 Ibid., p.136. 10

8

and regulations, and exercised by qualified professionals, just like other sciences. ibn Dunayn r practiced encipherment and cryptanalysis by virtue of his personal contacts with a number of Ayyubid kings and princes of his time, and his approaches to gain their favour in Egypt and Greater Syria. Considering, as stated earlier, that he was in the employ of King N ir ad-D n Mu ammad ibn 'Ayy b of Egypt, and Prince Asad adD n 'A amad ibn Abdull h al-Muhr n , it is all-probable that he has written this treatise at the behest of one of the sovereigns of the time. There are reasons to believe that, after the fashion of many cryptologists, he may have made mention of the assignment in the introduction, which was left out by the scribe for some reason. This is testified right from the outset of the treatise: "He [ibn Dunayn r] said, following the honorific opening statement in praise of God and the 12 introduction: This book is divided into two parts…". We live in hope of time to come and reveal the original of this copy so as to set right our assumptions once and for all.

12

ibn Dunayn r's book, p.70.

9

1.3. Structure of the Book ibn Dunayn r's book is characterized by its rich content and inclusive coverage of the requisites for those engaged in cryptanalysis. It covers quantitative and qualitative data and a variety of algorithms for cryptanalysis, arranged in a way similar to the arrangement of the compilations of cryptology today. ibn Dunayn r divides his book into two broad parts: The first part (1.3.1.) treats of cryptanalysis of prose ciphers, featuring the main principles and tools thereof, and surveying, among other things, the techniques utilized in cryptanalysing the various types of encipherment, including what he calls "composite" encipherment. In addition to his use of statistical techniques in cryptanalysis pioneered earlier by al-Kind , ibn Dunayn r was the first to describe an arithmetical cipher using the decimal numerical alphabet. The other part (1.3.2.) addresses algorithms peculiar to the cryptanalysis of poetical ciphers, considering the topics of prosody, rhyme, meter, word-patterns, and principles regulating proper writing skills. ibn Dunayn r also explores snags that can possibly hamper the cryptologue's endeavour towards cryptanalysis. He winds up with a couple of practical illustrative examples, followed by verses intended, he says, for sustained mental exertion in pursuit of solution. This is a bird's eye view of ibn Dunayn r's book in its totality. A systematic analysis of the work follows; organized in conformity with the order of chapters in the edited text, so as to help the reader navigate and keep step, with a view to appreciate the author's ultimate objectives. We shall augment our analysis with illustrative examples as often as necessary, highlighting in the meanwhile the scientific value of ibn Dunayn r's achievement in the light of the past from which he has drawn, and the sophisticated present to which we belong.

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1.3.1. Cryptanalysis of Prose Ciphers 1.3.1.1. Principles and Tools of Cryptanalysis ibn Dunayn r establishes, right from the beginning, the significant fact that cryptanalysis is actually based on conjecture, or what is known in today's terminology as "tentative assumption". This conjecture is by no means arbitrary, but measured according to fixed rules and principles "so that what is assumed by the cryptanalyst is an 13 outcome of reasoning and argument by analogy" . ibn Dunayn r 14 limits the rules and principles in two aspects and one "instrument" . The first aspect is the conversancy with letter frequency count; the other is the knowledge of variety contact of letters; and the instrument is the familiarity with the methods of encipherment. He then enumerates the personal attributes characteristic of the person involved in this science, i.e. intelligence, observation, tenacity, insightful delicacy (which helps comprehend underlying obscurity), keen intuition, equanimity of mind, proper flair and apt conjecture. Chapters 1 & 2 The Quantitative Methods ibn Dunayn r expands on the two aspects of cryptanalysis, using al-Kind 's term of quantitative and qualitative expedients. By the quantitative expedients he means the utilization of letter frequency of occurrence (or frequency count) in the cipher text, and matching it against the order of letter frequency in the given language. ibn Dunayn r indicates that vowel letters have the highest frequency of occurrence in the Arabic language. In this respect, however, his coverage probably falls short of al-Kind 's splendid comprehensiveness and precision of treatment. First and foremost, he fails to be on a level with al-Kind , who gives the exact meaning of vowels as including the three long (or major) vowels [i.e. the letters: ‫ا‬, ٚ and ٞ], as well as the three short (or minor) ones [i.e. the diacritical 13 14

See ibn Dunayn r's book, p.70. Ibid., p.72.

11

15

marks in Arabic: fat a, amma and kasra] . This is an important phonetic question of which former linguists were fully conscious. Then came a time when it was neglected and remained under wraps, so much so that it was unfortunately attributed to more recent phoneticians rather than to its real originators. ibn Dunayn r maintains that the most frequently occurring letters in Arabic are the vowels; but adds the two consonant letters of ‫( ي‬l) and َ (m), so that the order of the highly-frequent letters, according to him, is: ‫( ا‬a), ‫( ي‬l), َ (m), ٚ (w) and ٞ (y). Nevertheless, he considers the vowels to "have the highest frequency among all letters in all 16 tongues" . Other letters vary in their frequency from one language to another. Here ibn Dunayn r reviews some of the languages prevalent there and then, such as Latin, in which the letter ً (s) is 17 highly frequent ; Seljuk Turkish and Mongol, in both of which the letter ْ (n) has high frequency. But then one wonders why French is not among these languages, although the Crusades were peaking up at the time of ibn Dunayn r. Considering that ibn ad-Durayhim does 18 refer to French in the context of citing calligraphs and alphabet sizes , one finds no good reason why it has slipped ibn Dunayn r's mind. In fact this question remains to be answered. The last lines of Chapter 2 indicate knowledge, on the part of the author, of these different tongues, suggesting a certain degree of cryptanalytical practice in them: "If we set out to describe the algorithms of cryptanalysis in each tongue, the book would grow 19 larger…" .

15

See al-Kind 's treatise, p.170. See his book, p.74. This fact has been established by al-Kind before; see his treatise (Volume One of this series), p.122. 17 This notion has also been mentioned earlier by al-Kind (see his treatise, p.122), and confirmed by ibn ad-Durayhim later (see his treatise, p.52). 18 See ibn ad-Durayhim's treatise, p.19 and p.54. 19 See ibn Dunayn r's book, p.74. 16

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1.3.1.2. Types of Encipherment ibn Dunayn r discusses the types of encipherment on almost the same lines as al-Kind , starting from Chapter 3 through Chapter 6. We have summed up his citation in a tree-diagram similar to that of 20 al-Kind . A quick comparison between the two diagrams shows that ibn Dunayn r’s drops the encipherment method No. 13., probably inadvertently due to scribing omission or a scribe’s oversight. This possibility is supported by the fact that he does mention this method later when he tackles cryptanalysis. In fact there is nothing particularly novel in ibn Dunayn r’s discussion of the types of encipherment except his separating up composite encipherment into two divisions, which will be explored in detail later in this study, in the course of handling algorithms of cryptanalysis. It is worthy to note that these divisions of encipherment include the three established conventional divisions adopted to date of this science. These are: 1. Concealment Cipher This includes all the cases pertaining to encipherment by changing letters with conceptual relationship and diffusion. It is done by choosing words for each letter, with a relation of some kind between them. The true letters are replaced by words, chosen such as to form a plausible-sounding plaintext in which it is impossible to suspect the existence of a secret message. This method is customarily attributed to the German Trithemius (1462-1516); modern findings, however, confirm, beyond a doubt, that it was documented by the Arabs several centuries before. 2. Transposition Cipher This involves all the cases that belong to the encipherment by retaining the forms (identities) of letters, by changing their relative positions.

3. Substitution Cipher This embraces all the cases that fall under encipherment by changing the forms (identities) of letters without relationship and diffusion.

20

See al-Kind ’s treatise (Volume One of this series), p.87 and p.144.

13

Figure 1.1.

ibn Dunayn r’s Types of Encipherment Composite (or Super-) Encipherment

Corollaries of combining simple methods

Simple Encipherment

Combining simple methods

Letters retain their forms

Some letters

Separating linked letters

Some letters

Some letters All letters

Repetition of letters

All letters

All letters

Merging letters Some letters

With relationship and diffusion

Without relationship and diffusion

Quantitative

Qualitative Linking separate letters

Letters change their forms

Transposition

Addition or omission

All letters

nulls

One null

Simple Transposition

No nulls

Several nulls

14

Species

Simple substitution

Transposition (word or line)

?

Cipher alphabet of devised shapes or symbols

Polygraphic

Transposition (letter)

Polyword

Monographic

Genus

Polyword

Monoword

Monoword

1.3.1.3. Algorithms of Cryptanalysis ibn Dunayn r elaborates, in eleven chapters (i.e. Chapters 7 through 17), the different cryptanalysis algorithms related to simple encipherment methods, outlining the quantitative (statistical) and qualitative (textural) methods. In the next seventeen chapters (i.e. Chapters 18-35) he turns to discuss composite encipherment, its methods and algorithms of cryptanalysis. The following table depicts some of the algorithms for cryptanalysing individual cipher methods, identified by their numbers 21 in al-Kind 's tree diagram against their corresponding chapter numbers in ibn Dunayn r’s book: Cryptanalysis of cipher method no. 14 Cryptanalysis of cipher method no. 15 Cryptanalysis of cipher method no. 13 Cryptanalysis of cipher method no. 14 Cryptanalysis of cipher method no. 19 Cryptanalysis of composite cipher method no. (15+19) Cryptanalysis of cipher method no. 20 Cryptanalysis of cipher method no. 21 Cryptanalysis of cipher method no. 22 Cryptanalysis of cipher method no. 22 Cryptanalysis of cipher method no. 7 and 8

Chapter 7 Chapter 7 Chapter 11 Chapter 12 Chapter 13 Chapter 13 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17

Next, each chapter will be examined individually as follows: Chapter 7 22 Cryptanalysis of Simple Substitution Cipher This method is known, in today's terminology, as the monoalphabetic simple substitution. In this method "every letter is 23 represented by a symbol that is unique to it," ibn Dunayn r says. The cryptanalysis is accomplished according to the following steps: 21

See Volume One (of this series ), p.87. Methods Nos. 14 and 15. 23 See his book, p.84. 22

15

1. Counting the enciphered forms (symbols), and arranging them in a list. 2. Establishing the frequency of occurrence of each form, and affixing the frequency numbers to the respective forms. 3. Disposing the forms in descending order of frequency. 4. Writing down the language letters, conformably with their order of frequency, against the corresponding forms in cipher. 5. Maneuvering for correct combination of letters and intelligible articulateness of words. 6.Turning over intractable forms again and over again, assuming all possible alternatives and combinations, and using fair conjecture, until the cipher makes sense. ibn Dunayn r then goes to mention the orders of the letters of highest frequency of occurrence in the Arabic language. These are: ‫ا‬, ‫ي‬, ٚ, َ, ‫٘ـ‬, ٞ, and ْ. Perhaps his full awareness of the importance of this group of letters makes him reiterate them elsewhere, but with the 24 slight difference where the letter َ comes before the letter ٚ. Chapter 8 Orders of Arabic Letters, or the Quantitative Method The application of the approach described in Chapter 7 demands a knowledge of the orders of Arabic letter frequency of occurrence in typical clear texts. ibn Dunayn r states that he has come to know these orders from al-Kind 's treatise, and that he has conducted his own count of letter frequency in a three-sheet Arabic text. As he puts it: "It so occurred to me to take up [other] written sheets myself and count the letter frequency orders in them. Thus I took three sheets of prose epistolary texts and I calculated the frequency of the letter ‫( ا‬alif); it turned out to be… So it came home to me the validity of the 25 statement of Ya q b ibn Is q [al-Kind ], peace be on his soul." ibn Dunayn r's statement bespeaks an exquisite scientific technique that is worthy of note: He begins by studying the works of his predecessors, then he systematically verifies his results, through the independent 24 25

See his book, p.86. Ibid., p.86.

16

examination of samples of appropriate data. This, needless to say, is a principle of vital importance in statistical linguistics today, and a prerequisite for sound results, taking into account a period of eight long centuries that separate him from us. It should be pointed out that the total number of letters contained in those sheets was 3430, amounting to around 1100 letters per sheet and 550 letters per page. The following table (Table 1.1.) lists ibn Dunayn r's statistical findings as regards frequencies, in three sheets, of the letters of the Arabic alphabet, rendered in descending order of occurrence.

17

Letter ‫ا‬ ‫ي‬ َ ‫٘ـ‬ ٚ ٞ ْ ‫ه‬ ‫ع‬ ‫ف‬ ‫د‬ ‫ة‬ ‫ن‬ ‫ك‬ ً ‫ق‬ ‫ػ‬ ‫ط‬ ‫م‬ ‫ص‬ ُ ‫ؿ‬ ‫س‬ ‫ى‬ ‫ط‬ ‫ظ‬ ‫ؽ‬ ‫ض‬ Total/ %

Frequency of occurrence 575 360 265 260 250 230 225 195 170 145 115 105 95 80 75 62 50 43 32 28 17 13 11 9 8 7 5 0 3430

Percentage of occurrence 16.76 % 10.50 % 7.73 % 7.58 % 7.29 % 6.71 % 6.56 % 5.69 % 4.96 % 4.23 % 3.35 % 3.06 % 2.77 % 2.33 % 2.19 % 1.81 % 1.46 % 1.25 % 0.93 % 0.82 % 0.50 % 0.37 % 0.32 % 0.26 % 0.23 % 0.20 % 0.14 % 0.00 % 100 % 26

Table 1.1. ibn Dunayn r's work on the orders of letter frequency (statistical cryptanalysis)

One point that is highly relevant, and probably unknown to some, is that the computation of Arabic root-letters differs from the computation of word-letters as such; hence the disparity in the orders of letter occurrence in each case. The letter ‫( ه‬r), a moderatefrequency letter in words, takes precedence over high-frequency letters in Arabic roots. It goes without saying that, to cryptologists, 26

-Cf. al-Kind 's table in Volume One, p.58.-

18

letter orders relate to full words including affixes (rather than roots only). Chapter 9 Preamble to Letter Combination In this chapter ibn Dunayn r discusses the second principle of cryptanalysis; it is based on making use of linguistic knowledge associated with the combination and non-combination of letters in language. The effective utilization of this principle is related to the length of the message or the sufficiency of the number of its letters. A very short cryptogram implies a shortage of constituent words and letters ‫ـــ‬a factor that precludes the proper application of the statistical laws and calls for using the qualitative tool of cryptanalysis instead. This in itself is a skilful gesture on the part of ibn Dunayn r, reflecting his familiarity with the principle of the so-called law of large numbers. He says: "If the cryptogram is very short, there exists insufficiency in it of the frequency of letter occurrence. The expedient for cryptanalysis to be used here is to determine those letters [of the alphabet] which admit combination with each other, and those which do not…until 27 [the cryptologue] elicits the intended meaning of that scant cipher." ibn Dunayn r, however, is not the first to point out to this issue; al-Kind takes the lead on that score when he states in his treatise on cryptanalysis that "it could happen sometimes that short cryptograms are encountered, too short to contain all the symbols of the alphabet, and where the order of letter frequency cannot be applied. Indeed the order of letter frequency can normally be applied in long texts, where the scarcity of letters in one part of the text is compensated for by their abundance in another part. Consequently, if the cryptogram was too short, then the correlation between the order of letter frequency in it and in that of the language would no longer be reliable, and thereupon you should use another, qualitative expedient in cryptanalysing the 28 letters." A simple comparison immediately shows that al-Kind 's statement, though three centuries earlier than ibn Dunayn r's, is richer, more precise and transparent.

27 28

See ibn Dunayn r's book, p.88. See al-Kind 's treatise in Volume One, p.124 and p.126.

19

Some of ibn Dunayn r's successors also make reference to how critical the length of the cryptogram is. An example is ibn Adl n (d. 29 AH 666/ AD 1268) , who goes a step further to set a minimum length to the cipher sought for cryptanalysis. He writes: "The length of the text to be cryptanalysed should be at least in the neighborhood of ninety letters as a rule of thumb, because the letters thus would have had three rotations, Yet, the number of letters may be less than that in 30 certain cases." ibn Dunayn r concludes this chapter by maintaining that decryption by the qualitative means requires considerable professional expertise. He undertakes to establish, in the next chapter, what he terms "the rules of this art", by means of a "simplified" table of those Arabic letters which are combinable and those which are not. Chapter 10 Combination of Letters, or the Qualitative Method This chapter can be aptly described as a summary of al-Kind 's ideas regarding letter combination and non-combination, although ibn Dunayn r falls comparatively short of al-Kind 's finesse in expounding the combination phenomenon. He states towards the end of the chapter: "…and I abridged that considerably such that my version should suffice instead of al-Kind 's treatise and its long31 winded prolixity". In point of fact, however, al-Kind 's investigation of the laws regulating combination and non-combination of each Arabic letter, although sometimes characterized by repetition, proves otherwise very useful because these laws are, by nature, so prone to ambiguity, misspelling or distortion that their repetition by al-Kind guards against any possible misrepresentation. ibn Dunayn r's contribution in this respect has been to round up the scattered rules, bring them together, and eliminate repetition by means of presenting them in one table, which itself is not without repetition in more places than one. 29

-In fact ibn Adl n was a contemporary, rather than a successor, of ibn Dunayn r, although he outlived ibn Dunayn r by some 40 years.- (Translator) 30 See ibn Adl n's treatise (Volume Two of this series), p.52. 31 See ibn Dunayn r's book, p.94.

20

ibn Dunayn r divides Arabic letters into four groups: 1. Letters which combine with all other letters in both anterior and posterior positions, i.e. pre-positively and post-positively. These are: ‫ ا‬a, ‫ ة‬b, ‫ د‬t, ‫ ف‬f, ‫ ن‬k, ‫ ي‬l, َ m, ْ n, ‫ ٘ـ‬h, ٚ w/ , and ٞ y/ . 2. Letters that do not combine with some others neither in anterior nor in posterior position. This relates particularly to the letters that belong for their utterance to points quite close together in the human articulatory system, such as the apical letters ( ‫ ى‬z, ً s, ‫ ) ص‬in relation to each other, gingival letters (‫ س‬, ‫ م‬, ‫) ظ‬, and some of the guttural letters. 3. Letters that combine with some others in anterior position, but do not combine in posterior position, such as the letter (ُ ) with ‫ ى‬z, ً s, ‫ ظ‬, ‫ ص‬, ‫ س‬, ‫ م‬,… 4. Letters that combine with some others in posterior positions, but do not combine in anterior positions, such as the letter (‫ ) م‬with ُ and ‫ ; ؽ‬and (‫ ى‬z) with ُ and ‫… ض‬ ibn Dunayn r's table of letter combination covers the last three groups, excluding the first, since it is considered as being the 32 baseline. Immediately noticeable in his table is the needless repetition of letters in his treatment of the second group (i.e. letters non-combinable anteriorly nor posteriorly). This is due to his citing a certain letter against all those non-combinable with it, then citing it again upon handling each of those letters individually. For example, he starts his table with the letter ً s, citing all the letters noncombinable with it anteriorly nor posteriorly. He then reiterates the letter ً s when he treats each of those letters non-combinable with it. Consequently, we have opted to make a table of our own (Table 1.2.), incorporating the content of ibn Dunayn r's without repetition, along with another table (Table 1.3.) presenting the letters in alphabetical order, flanked on the right-hand side by the anterior non-combinables, and on the left-hand side by the posterior ones. Besides, a third table (Table 1.4.) is given representing non-combinable letters in Arabic roots (radicals); it is based on the outcome of a comperhensive statistical study we have conducted on five major Arabic dictionaries, foremost of which are Lis n al- Arab and al-Q m s al-Mu . al32

However, al-Kind mentions it "in the interest of making the statement most explicit". See al-Kind 's treatise, p.200.

21

Kind 's table (Table 1.5.) has also been found useful to quote here for comparative purposes. Together, these tables would serve to facilitate comparison and educe the results that follow. Sign

Letter(s) non-combinable with it

‫ى‬

‫ض‬ ‫ظ‬ ‫ض‬

‫ص‬ ‫ض‬ ‫ص‬

‫ظ‬ ‫ص‬ ‫ظ‬ ‫ض‬ ُ ‫ط‬

‫م‬ ‫ى‬ ‫ى‬ ‫ظ‬ ‫ظ‬ ‫ط‬ ‫ؽ‬ ‫ط‬ ‫ظ‬ ‫ع‬

‫ؽ‬

‫ؽ‬ ‫ض‬ ُ

‫ؽ‬

‫ؿ‬

‫ض‬

‫ى‬

ُ

‫ق‬ ‫س‬

‫س‬ ‫م‬ ‫ط‬ ‫ط‬ ‫ط‬ ‫ك‬ ‫ػ‬ ‫ق‬ ‫ص‬ ‫ػ‬ ‫ع‬ ُ ُ ‫ط‬ ‫ق‬ ‫ص‬ ‫ى‬ ‫ػ‬

ً ‫ؽ‬ ُ

Letter

ً ‫س‬ ‫م‬ ‫ص‬ ‫ض‬ ‫ظ‬ ‫ؿ‬ ‫ط‬ ‫ى‬ ‫ؽ‬ ‫ػ‬ ‫م‬ ‫ى‬ ‫ص‬ ‫ض‬ ‫ك‬ ‫ط‬ ‫ظ‬ ُ ‫ق‬ ‫س‬

Table 1.2. Noncombinable letters (in texts) as observed by ibn Dunayn r (without repetition). N.B.

non-combinable in anterior position (pre-positively) non-combinable in posterior position (post-positively) non-combinable in both anterior and posterior positions (pre- and post-positively)

22

‫‪Anterior non-combinables‬‬

‫‪Letter‬‬

‫‪Posterior non-combinables‬‬

‫مىًصضظ‬

‫س‬

‫مىًُصضظ‬

‫طظؽق‬

‫ط‬

‫طظؽق‬

‫ؿ ظعؽ‬

‫ػ‬

‫ؿعؽ‬

‫ػ ظؽ‬

‫ؿ‬

‫ػؽ‬

‫ظ‬

‫ك‬

‫ى ظصض‬

‫سىًصضطظ‬

‫م‬

‫سىًُصضطظؽ‬

‫سكمًصطظ‬

‫ى‬

‫سمًُصضظ‬

‫سمىصضظ‬

‫ً‬

‫سمىُصضظ‬

‫سمىًصضظ‬

‫ُ‬

‫ض‬

‫سكمىًضطظ‬

‫ص‬

‫سطمىًُضطظ‬

‫سكمىًُصطظ‬

‫ض‬

‫سمًُصطظق‬

‫مصضظ‬

‫ط‬

‫مىصضظ‬

‫سطكمىًصضط‬

‫ظ‬

‫سطػؿكمىًُصضطؽق‬

‫طػؿمظعق‬

‫ؽ‬

‫طػؿع‬

‫‪Table 1.3. Noncombinable letters (in texts) according to ibn Dunayn r,‬‬ ‫‪arranged alphabetically (with repetition).‬‬

‫‪23‬‬

Letter(s) non-combinable with it pre-positively

Letter

‫ع‬

‫ض‬

‫ص‬

ُ

‫ض‬ ‫ص‬ ‫ظ‬ ‫ؿ‬ ‫ػ‬ ‫ظ‬ ً

‫م‬

‫ظ‬ ‫ظ‬

‫ض‬ ‫ض‬

‫ص‬ ‫ص‬

ُ ُ

ً ‫ى‬

‫ق‬

‫ى‬ ُ

‫م‬ ‫س‬

‫ى‬

‫م‬

‫ك‬ ‫ن‬

‫ظ‬ ‫د‬ ‫ظ‬ ‫ؿ‬ ‫ق‬

‫ن‬

‫ع‬

‫ض‬ ‫ظ‬ ‫ض‬ ‫ػ‬ ‫ؽ‬ ‫ؽ‬ ‫ؿ‬

ُ ‫ص‬ ‫ص‬ ‫ط‬ ‫ط‬ ‫ؿ‬ ‫ط‬

ً ً ‫م‬ ‫س‬ ‫ض‬ ‫ػ‬ ‫ػ‬

‫ظ‬

‫ن‬ ‫ق‬ ‫ف‬ ‫ؿ‬

ُ

‫ظ‬

‫ط‬ ‫ض‬

‫ن‬ ‫ط‬

ُ

‫ك‬

ً

‫ظ‬

‫ص‬ ً ‫ق‬ ‫٘ـ‬ ‫٘ـ‬ ‫ض‬ ‫ى‬

‫م‬ ‫ى‬ ‫ؽ‬ ‫ؽ‬ ‫ؽ‬ ‫ط‬ ‫س‬

‫ء‬ ‫ف‬ ‫ظ‬ ‫م‬ ‫د‬ ‫ع‬ ‫ء‬ ‫د‬ ‫د‬ ‫ظ‬ ‫س‬ ‫س‬ ‫ض‬ ‫س‬ ‫م‬ ‫د‬ ‫د‬ ‫ص‬ ‫ء‬ ‫ء‬ ‫ة‬ ‫ط‬ ‫ط‬ ‫ة‬ ‫ػ‬

‫ء‬ ‫ة‬ ‫د‬ ‫س‬ ‫ط‬ ‫ػ‬ ‫ؿ‬ ‫ك‬ ‫م‬ ‫ه‬ ‫ى‬ ً ُ ‫ص‬ ‫ض‬ ‫ط‬ ‫ظ‬ ‫ع‬ ‫ؽ‬ ‫ف‬ ‫ق‬ ‫ن‬ َ ‫٘ـ‬

Table 1.4. Noncombinable letters as demonstrated in our statistical analysis of Arabic roots33.

33

Extracted from al-Mu am al- Arab : dir sa 'i 'iyya lidawar n al- ur f f alu r al- Arabiyya (The Arabic Dictionary: A Statistical Study of Letter Frequencies in Arabic Roots); Table no. 60, p.205.

24

Letter(s) noncombinable with it

Resultant noncombinable bigrams

Sign

Letter

Table 1.5. Table of noncombinable letters as observed by al-Kind Key:

pre-positively (anteriorly) post-positively (posteriorly) neither post- nor pre-positively.

25

Results of Comparison A. Between ibn Dunayn r's table and al-Kind 's table: Upon checking ibn Dunayn r's table against that of al-Kind , we see that ibn Dunayn r correctly adds one bigram of non-combinable letters to those of al-Kind , i.e. the bigram (‫)ظ ؽ‬, while he incorrectly misses one, i.e. the bigram (‫)ك ط‬. B. Between ibn Dunayn r's table and that of the Arabic-root statistical findings: An essential difference between the table of ibn Dunayn r (and that of al-Kind before) and our Arabic-root table is that while the former deals with Arabic words just as they occur in context, the latter treats of Arabic roots only (without affixation); hence its inclusion of noncombination cases not covered by ibn Dunayn r. This is quite natural a phenomenon because the area of non-combining letters grows wider the narrower the word inflection becomes, and the more the word is divested of its affixes, so much so that the non-combination scope culminates in root-words. Conversely, the non-combining letters grow less and progressively dwindle the broader the word inflection becomes, and the more the word is linked up with prefixes and suffixes. Thus the scope of non-combination keeps tightening until it becomes narrowest in words usually used in context and ordinary speech, regardless of their being bare, augmented, prefixed, suffixed, etc. As a matter of fact, al-Kind ‫ ـــ‬and indeed all later cryptologists, including ibn Dunayn r ‫ ـــ‬does not state explicitly the technique he adopts in constructing his rules of non-combination. However, contextual connections show his intention to be the ordinary speech as such. This is in evidence first from the fact that the examples he invokes of letters that combine pre-positively only or post-positively only do involve augmented as well as uaugmented words alike. Second, and this is no slight evidence, is his division of letters into basic ( ur f 'a liyya), which are always original and form an intrinsic part of words; and variable ( ur f muta ayyira), which may be now basic and now affixing ( ur f az-ziy da) and include the well-known affixing letters ‫ـــ‬those making up the Arabic word ( ‫ب‬ٙ١ّٔٛ‫)ٍؤٌز‬, plus the letters: ‫ة‬, ‫ ف‬and ‫ن‬. His addition of these last three to the affixing letters is an extra indication that he actually intends words ordinarily used in speech and writing, because the affixings alone do not cover all the letters that may be added to root words, so as to consummate a

26

word inflection in time, number, gender, genitive, comparison, causality, succession, and the like34. One more point that is crucially important to note is that these rules of non-combination are effectively utilized in cryptanalysis so long as the ciphertext is "spaced", that is provided with word spacers, but they practically prove useless in no-word-spacers. That is so on account of the possibility then of the occurrence of two consecutive non-combinable letters from two originally separate (but adjacent) letters, such as the occurrence of the letter (ً s) at the end of a word and the letter (‫ ) م‬at the beginning of the next word, e.g. … ٚ‫ِلهًِ م‬. In fact no-word-spacer encipherment is considered among the most intricate types of simple encipherment, since the cryptologue then fails to make use of a good few cryptanalysis algorithms, such as initial and final letters of words, word lengths (bigrams, trigrams, etc.), the frequency of the space symbol, and combination and noncombination of letters. Chapter 11 Simple Substitution This chapter handles encipherment by simple substitution35. It is done by substituting for each letter the form of another, such as using the form of the letter (a) to mean the letter (b), and the form of (b) to indicate (a); (d) for (c) and (c) for (d), and so forth. In today's terminology this method of encipherment is called monalphabetic simple substitution. ibn Dunayn r here makes reference to his other book a ih a i i a at-tar i (The shooting star in the science of making ciphers), where he elaborates the cryptanalysis algorithms of this method. However, he indicates that the process has been outlined earlier, meaning in Chapter 7, as part of treating the quantitative principles of cryptanalysis.

34 35

See al-Kind 's treatise in Volume One, p.174. This is the method no.13 in al-Kind 's tree diagram of the types of encipherment; see Volume One, p.144.

27

Chapter 12 Substitution Using Devised Forms This is a variety of monographic substitution [corresponding to the method no.14 in al-Kind 's tree diagram], in which encipherment is accomplished by changing letter forms into symbols not pertaining to letter forms (substitution by symbol). For example, given that a= =m ,‫ٱ‬ Ø , n= Ω, the word "man" is enciphered: Ø‫ٱ‬Ω. A possible variation of this method is to retain some of the plaintext letters beside their respective devised forms. The above example may look like this: a= ‫ٱ‬, m= Øm , n= Ωn, and the word "man" becomes: Øm‫ٱ‬Ωn. Cryptanalysis of this method would also entail the utilization of the quantitative expedient afore-stated. Chapter 13 Simple Transposition ibn Dunayn r addresses three types of encipherment by transposition. The first is the simple transposition based on changing the relative positions of letters without changing their forms. This method is easy to cryptanalyse, by restoring the letters to their original order through continuously re-arranging letter positions until a comprehensible message emerges. Most probably ibn Dunayn r's intention here is the simplest method of transposition, i.e. transposition within a single word. Accordingly, the message: "Fold the paper" is ciphered: "dlof eht repap". The second type, a composite one, is based on implementing both transposition and simple substitution. Undoubtedly this type is of paramount importance, since it incorporates the core of today's most sophisticated encipherment methods (for instance the current international Data Encryption Standard (DES), and the newer Advanced Encryption Standard (AES), both grounded on the principle of encipherment using substitution and transposition together, but carrying it to a higher degree of complication, using a binary number system). ibn Dunayn r expands on the decryption of this method, first by means of the quantitative resource, and then by transposition. As he puts it: "If the letters are devised forms [i.e. employing simple substitution] and interchanged as we have already stated [i.e. by transposition], the way for cryptanalysing them consists in the

28

utilization of the first instrument [i.e. the quantitative technique via letter computation]. Once the cryptologue works out the letter orders [of frequency], and places each letter of the alphabet against its devised counterpart in the cryptogram, he interchanges their relative positions reciprocally, shifting the letters backward and forward in relation to one another, until they slot into place and the intended meaning shows up."36 It is such a pity ibn Dunayn r does not state explicitly that this is composite encipherment, nor does he give it due deliberation, much proud as he is of understanding what others fail to understand for that matter! The third type is the encipherment by changing the position of the letter in relation to itself (i.e. its standard orientation), just by altering the angle of its setup (without changint its relative position within the word), assuming various angles of presentation such as writing it upside down or standing on its end. Example: A B C D E Plain Cipher Cipher

OR

Obviously, this type is so easy to unfold that "it would never miss the common sense of anyone with perceptive insight," ibn Dunayn r says. Chapter 14 Encipherment by Adding Nulls ibn Dunayn r's discussion of this method is something of an elaboration of al-Kind 's notions.37 Here two distinct cases can be identified: a) Addition of nulls within the single word, by splitting it and embedding one or more nulls in between its constituent letters. Note that nulls can be letters chosen from the alphabet, or devised forms irrelative to the alphabet. For Example: Clear: Cipher: 36 37

familiar fazmidlizard

See ibn Dunayn r's book, p.100. See al-Kind 's treatise, p.138.

29

The nulls used in this example are the letters "z" and "d" introduced alternately after every other letter. The algorithm for cryptanalysing this type of encipherment, when used in message cryptograms, is rendered through applying the quantitative tool, namely, counting the letters. If the occurrence frequency of the letters or forms in the cryptogram is found to be greater than the typical letter frequency in the alphabet of the language concerned, one ascertains that they are nulls, and are left out. ibn Dunayn r says: "The cryptanalysis of this encipherment is reasoned out by calculating the forms and sorting them out. If you find them in excess of the letter orders, try to work out some of them by the first expedients we have previously mentioned."38 b) Addition of one or more nulls at the end of words, indicating the space or the word spacer. ibn Dunayn r's frequent use of the word "null" in the plural indicates that he utilizes more than one null to represent a space. The cryptanalysis of this type of cipher involves manipulating those letters that are still covert amongst others already identified. The nulls-spacers are then dropped. As ibn Dunayn r says: "You now look into the letters none of which has yet shown, and seek their identical instances among those already puzzled out. If, by eliminating those letters sought for solution, the context makes sense and word composition straightens, you conclude the letters left out are all nullsspacers. When the encipherment is done using one null only, in that case you have already solved it ipso facto, since the single null is employed as a word-spacer."39 Chapter 15 Cryptanalysis of Composite Cipher ibn Dunayn r refers to his experience in cryptanalysing a composite cipher that is difficult to solve. Although not expressly stated, the fact that it is of the composite type manifests itself in the example he invokes, which is composed of the following three methods:

38 39

See his book, p.102. Ibid., p.102.

30

(a) Changing letter forms (simple substitution). (b) Changing letter positions (transposition). (c) Omitting some letters and using null forms instead. In this connection he says: "By changing the forms of letters, altering their positions, and at the same time omitting [certain] letters of the alphabet to replace them with null forms, the cipher would be very hard to solve indeed. Nevertheless, and by the good assistance of the Almighty, I managed to solve it straightway."40 Chapter 16 Encipherment by Omitting a Letter In this chapter ibn Dunayn r explains the algorithm for cryptanalysing the method of encipherment conducted by omitting one letter of the alphabet throughout the whole encrypted message. It seems that the employment of this method is always concomitant with the use of simple substitution. This is clear from ibn Dunayn r's exposition of the method: "The cryptanalysis here lies in computing the forms; if they are found less in number than the alphabet count, you detect them through the first expedients we have mentioned earlier in this book. Work out some letters of the cryptogram sought for cryptanalysis. If you notice, by seeking their identical counterparts elsewhere therein, the existence of one and the same letter omitted so that the context does not straighten, examine the context closely and weigh up what is [purposely] omitted, as the words and import would, in all likelihood, point to it."41 ibn Dunayn r illustrates this method by an example, maintaining that the purposely omitted letter is retrieved by sampling the vacancy (in several places) against all the letters of the alphabet, one by one, so as to exhaust all likely possibilities, until the dropped letter is determined once and for all.

40 41

See his book, p.104. Ibid., p.106.

31

Chapter 17 Encipherment by Changing the Forms of Letters with Conceptual Relationship and Diffusion This method is analogous to the current "key-dependent encryption". In his discussion, ibn Dunayn r obviously relies on alKind 's ideas as cited in his treatise.42 The fullness of the explanation there should suffice for its reiteration here. Further, ibn Adl n concludes his treatise with a rich practical example of cryptanalysing one variety of this method, where the relationship is bird species; each letter being replaced by the name of a bird.43

1.3.1.4. Composite Encipherment Having demonstrated in the previous eleven chapters (7 through 17) some of the simple encipherment methods and algorithms for their cryptanalysis, ibn Dunayn r shifts to discuss what he calls composite encipherment. In eighteen chapters (18 through 35) of his book he dilates on his own perception of composite encipherment, which differs from al-Kind 's and also the present-day established views on that respect. Examining the encipherment methods that ibn Dunayn r terms composite, as well as those he classifies under simple encipherment while considered composite in today's criteria, one can list the following conclusions regarding ibn Dunayn r's perception of composite encipherment: 1. The current view of composite encipherment is that it is a product of simple methods combined44. This is in conformity with alKind 's notion, so impressively demonstrated in his treatise. 2. In the context of addressing simple methods of encipherment, ibn Dunayn r goes (in Chapters 13, 15 and 16) to handle composite methods, mistakenly considering them, as simple. However, he specifically declares earlier that composite encipherment "falls into

42

See al-Kind 's treatise, p.93, and pp. 158-160. See ibn Adl n's treatise, pp.104-113. 44 -I choose to dub it "eclectic encipherment", using a wide range of cipher methods.- [Translator]. 43

32

two divisions: the one is a combination of simple methods, and the other is what ensues in consequence."45 3. It is evident from ibn Dunayn r's book that the concept of "composition" according to him is to manipulate the letters to be enciphered in such a way as to disguise the intended meaning through enveloping it in any device or medium that has nothing to do with the purport aimed at. This encipherment may take a host of forms such as building on a tale, a dream, a chessboard, beads, the motion of planets, or the arithmetic using decimally-weighted numerical alphabet ( is b al- ummal). In fact these methods bear no relation to composite ciphering, and would more correctly be associated with what is known as "concealment cipher", which is intended to pass without being suspected as the conveyor of a secret communication. To ibn Dunayn r's credit, it should be noted, he has developed a number of encipherment methods, which he might have taken over from his predecessors, and which are based on such accessory devices as the punctured wood sheet with a thread, folded paper, colour beads, etc. Chapter 18 An Overview of Composite Encipherment ibn Dunayn r seems fully conscious of the fact that the range of composite encipherment is so wide it is not confined to any limits; thus it is impossible to deal with all its multiplicity of forms. He states that what he is going to discuss is just an example for handling other composite instances. He argues that al-Kind has not considered these examples of composite encipherment ‫ـــ‬and indeed so, because they are worlds apart in their views about it. To ibn Dunayn r it is more of a concealment cipher than proper composite encipherment, as we shall see in subsequent chapters. Chapter 19 A Preamble to Solving Composite Cipher Of all types of encipherment the composite type is regarded by ibn Dunayn r as the most complicated. Its decryption requires a lot of 45

See his book, p.82.

33

expertise and thorough training. The algorithm for cryptanalysis is attained by: 1) Experimenting with each and every type of simple encipherment. If, after all, the cipher remains inscrutable, it is concluded to be composite. 2) Experimenting with the types of composite encipherment, some of which ibn Dunayn r will mention in the following chapters. Chapter 20 Encipherment by Replacing Letters with Generic Names ibn Dunayn r considers this method as composite encipherment, although it, in fact, belongs under simple substitution using the principle of conceptual relationship and diffusion. It is based on the idea of enciphering letters in terms of genera, thereby a letter can be represented by more than one symbol. This type is analogous to polyalphabetic encipherment, but with a symbol-letter relationship, i.e. relationship of the different symbols to each letter. For instance, the letter (‫ ا‬a) may be enciphered using the "people" genus through employing any proper name to symbolize it. Keen to help his reader in cryptanalysing this type of cipher, ibn Dunayn r proposes a table of generic names (relationships) representing each letter of the Arabic alphabet, followed by a practical illustrative example. The cryptanalysis assumes taking up the generic names and combining the letters that they stand for. ibn Dunayn r suggests that this cipher defies cryptanalysis. That is probably so, because each letter is replaced by more than one symbol ‫ـــ‬a process which turns void the quantitative as well as the qualitative techniques of cryptanalysis. Furthermore, a message enciphered this way, if put in a well-chosen context, is likely to mislead the cryptanalyst and distract his/her thought from suspecting the message to be a cryptogram. It is patently evident that ibn Dunayn r's demonstration of this type of encipherment puts him one up over his fellow scholars for that matter. His predecessor al-Kind gives only a brief account of it46; his contemporary ibn Adl n restricts himself to a

46

See al-Kind 's treatise, p.132, and pp.158-160.

34

simple example towards the end of his treatise47; whereas his successor ibn ad-Durayhim makes use of his description, as can be readily observed from the uniformity of generic denominations of ibn ad-Durayhim in his treatise48 and ibn Dunayn r in this chapter. Chapter 21 Encipherment Using the Arithmetic of Decimally-Weighted Numerical Alphabet (ADWNA) Or " is b al- ummal" Important as it is, this method of encipherment has been overlooked by al-Kind in his treatise on cryptanalysis, despite his awareness of is b al- ummal, and his reference to it elsewhere49. The Author of the Two Essays, however, does refer to it in his First Essay, and ibn Dunayn r seems to have quoted from him particularly the use of the "quarter" and "half" fractions. " is b al- ummal" is an old method of encipherment, well-known to the Arabs at an early stage of their civilization, and was practised later in other languages such as Hebrew. ibn Dunayn r addresses this method in its two divisions, the major and the minor, expanding on its significant applications by developing highly relevant ways of ciphering that have subsequently been adopted by ibn ad-Durayhim. The following table (Table 1.6.) shows the letters of the numerical alphabet, with corresponding decimal numerical values in ADWNA.

47

See ibn Adl n's treatise, p.104 ff. See ibn ad-Durayhim's treatise, pp.76-80. 49 As reported by ibn an-Nad m in his al-Fihrist, p.21 quoting al-Kind . 48

35

‫ا‬

‫ة‬

‫ط‬

‫ك‬

‫٘ـ‬

ٚ

‫ى‬

‫ػ‬

1

2

3

4

5

6

7

8

‫ط‬ 9

ٞ

‫ن‬

‫ي‬

َ

ْ

ً

‫ع‬

‫ف‬

‫ص‬

10

20

30

40

50

60

70

80

90

‫ق‬

‫ه‬

ُ

‫د‬

‫س‬

‫ؿ‬

‫م‬

‫ض‬

‫ظ‬

100

200

300

400

500

600

700

800

900

x

1

2

3

4

5

6

7

8

9

1 10 100 1000

‫ا‬ ٞ ‫ق‬ ‫ؽ‬

‫ة‬ ‫ن‬ ‫ه‬

‫ط‬ ‫ي‬ ُ

‫ك‬ َ ‫د‬

‫٘ـ‬ ْ ‫س‬

ٚ ً ‫ؿ‬

‫ى‬ ‫ع‬ ‫م‬

‫ػ‬ ‫ف‬ ‫ض‬

‫ط‬ ‫ص‬ ‫ظ‬

‫ؽ‬ 1000

Table 1.6. Numerical values of letters. Thus, the numerical cipher of the proper name ‫ل‬٠‫ى‬, for example, can be expressed: 7, 10, 4; or (in words): seven, ten, four. Equally important is that this type of encipherment is simple substitution, with each letter substituted by a single symbol throughout the cryptogram. Cryptanalysis is accomplished by utilizing the quantitative technique stated earlier. According to ibn Dunayn r, the concept of composition in the areadependant decimal numerical alphabet as a "composite" method of encipherment is predicated on making the cryptogram look like a peasant-farming financial register. The measurement is done through adopting length units in common use at the time, such as al- ar b, alqaf z, and al- a r. The cryptogram is composed by representing the letters as land dimensions, simulating an outward semblance of buying, selling, or otherwise similar bargains. This, ibn Dunayn r suggests, tends to boost the concealment of the cipher and renders it even more difficult to cryptanalyse. He says: "If you fail to do like we have told you as regards giving the cryptogram the semblance of a financial register of expenditure, an episode about somebody, taking, buying or giving, you would incur a raw and unhappy [state of affairs], over and above an unmistakable clue to exposing the intended

36

encipherment. Otherwise, this course of action would be quaint and pretty efficient."50 Chapter 22 Encipherment by Communication through Finger-Spelling, Using the Manual Alphabet and ADWNA In this type of encipherment ADWNA is instrumental in letter substitution; letters are replaced with numbers communicated by bending the fingers in specific shapes so as to convey to a recipient the numerical values corresponding to the respective letters. This kind of esoteric communication is particularly used by those specially initiated, in the presence of another who is not meant to understand the discourse. Such a "manual alphabet" is an already well-known Arab signaling method of communication. It can assume many different shapes. ibn Dunayn r's method is based on representing the intended number by relative finger configurations. Thus he represents the units and number ten, referring to other numbers by analogy. The following table (Table 1.7.) demonstrates the Arabic numerical alphabet, with the corresponding values in ADWNA of the individual letters, and the finger configuration for each; the units being quoted from ibn Dunayn r, the rest from other sources.

50

See his book, p.116.

37

Hand Letter Value

Finger Configuration

1

Right

‫( ا‬a) ‫( ة‬b)

Right

‫) (ط‬

3

Right

‫( ك‬d)

4

Right

‫( ٘ـ‬h)

5

Right

ٚ (w/ )

6

Ring finger folded and pinkie rested on it from behind. Little and ring fingers folded to their base in palm. Little, ring, and middle fingers folded to their base in palm. Pinkie spread up; ring and middle fingers folded. Middle finger folded in palm, with little and ring fingers spread out. Ring finger folded in palm, with middle finger spread up. Little finger bent inside, with all the rest spread. Little and ring fingers folded. Little, ring, and middle fingers folded. Thumb and index fingers made into a loop. Thumb tip placed between index and middle fingers. Index inner tip placed on thumb inner tip. Inner tip of thumb placed on outer tip of index finger. Tip of thumb placed on back of index finger while stretched out. Index tip placed on thumb tip. Tip of thumb nail placed between inner joints of index finger that is twisted. Thumb tip placed in the index joint towards its tip. Index-finger tip placed on thumb tip. Index-finger tip placed in joint of thumb while spread out. Thumb tip placed between index and middle fingers towards their base. Inner tip of index finger joined to inner tip of thumb. Inner tip of thumb placed on outer tip of index finger. Tip of thumb placed on back of index finger while stretched out. Index tip mounted on thumb tip. Tip of thumb nail placed after inner joints of index finger that is twisted. Thumb tip placed in the index joint towards its tip. Index-finger tip placed on thumb tip. Pinkie folded to its base in left palm, with ring finger mounted on it.

Right

Right

‫( ى‬z) ‫) (ػ‬ ‫)(ط‬

Right

ٞ (y/ )

Right Right

2

7 8 9 10

Right

‫( ن‬k) ‫( ي‬l) َ (m)

Right

ْ (n)

50

Right

ً (s)

60

Right

‫)(ع‬

70

Right

‫( ف‬f)

80

Right

‫) (ص‬

90

Left

‫( ق‬q)

100

Left

‫( ه‬r)

200

Left

300

Left

ُ( ) ‫( د‬t)

Left

‫)(س‬

500

Left

‫) (ؿ‬

600

Left

‫) (م‬

700

Left

‫) (ض‬

800

Left

‫) (ظ‬

900

Left

‫) (ؽ‬

1000

Right Right

20 30 40

400

Table 1.7. Finger-spelling (dactylology) using ADWNA

38

Chapters 23 & 24 Encipherment by "Composing" Letters on the Chessboard This method is based on simple substitution. It is originally intended to address someone who is present, but can also be employed to communicate with absent people ‫ـــ‬a method which ibn Dunayn r credits to himself, maintaining that he establishes the precedent for it. His explanation is lucid enough to spare any elucidation. One noteworthy remark here is that ibn ad-Durayhim, in his Mift alkun z f ' al-marm z, seems to have taken over this method from his predecessor ibn Dunayn r.51 Chapter 25 Cryptanalysis of Cipher "Composed" on the Arithmetic of Decimally-Weighted Numerical Alphabet (ADWNA) ibn Dunayn r asserts, right from the outset, that this type of cipher is "very easy to cryptanalyse,"52 and rightly so, because that kind of arithmetic was then widespread and in common use. The cryptanalysis is effected by reconstructing letters against their corresponding numbers in ADWNA. It is interesting to remark here that ibn Dunayn r discusses encipherment using ADWNA twice in his book, but he has not been consistent in the symbols he uses to denote the orders of tens, hundreds, and thousands. While in the first instance (that composed on area) he uses numbers with super-dots to indicate the tens order, and numbers with under-dots to indicate the hundreds order, he in this chapter opts to use numbers preceded by one circle to indicate the tens, two circles to indicate the hundreds, and three circles to denote the thousand. Nevertheless, it is understood that the circles here are equivalent to the dots there. Moreover, ibn Dunayn r observes the nicety that is b al- ummal is basically one of three varieties of the Hindi calligraph (cipher alphabet). In his words: "The algorithm is to place each letter of the alphabet against its Indian decimal numerical equivalent in the system… Consequently, if you wanted to encipher the statement

51 52

See ibn ad-Durayhim's treatise, p.66. See his book, p.124.

39

‫ك‬١‫ف‬ٛ‫ اٌز‬ٌٟٚ ‫ اهلل‬by this method, you would have to replace the letters with their corresponding Indian characters…"53. ibn Dunayn r's description of this method as easy to solve may be meant to serve as a preamble to what he is about to develop in the next chapter. Through the introduction of sophisticated improvements this encipherment turns out to be complicated and difficult to decrypt. This fact is attested by his repetition in the following chapter of the same illustrative example " ‫ك‬١‫ف‬ٛ‫ّ اٌز‬ٌٟٚ ‫"اهلل‬, probably to enable the reader to appreciate how far the method has been developed. Chapter 26 Encipherment by ADWNA Using Further Numerical Processing Though simple substitution in substance, this method of ciphering, which is credited to ibn Dunayn r as its originator, is extremely important in terms of its content and effect. Its importance stems especially from the fact that it lends itself to a special numerical processing, through arithmetical operations governed by a set rule, that makes it assume more complicated forms. This may be represented by the following model (Figure 1.2.). The Cleartext (LETTERS)

Substitution of Numbers for Letters

Numerical Processing

Resubstitution of Numbers for Letters

The Cipher-text (CRYPTOGRAM)

Figure 1.2. Encipherment by numerical processing using ADWNA. Numerical processing involves making the representative numbers two, three, four, etc. times as great in value, thus increasing the difficulty of cryptanalysis. For example, we encipher the phrase ‫ك‬١‫ف‬ٛ‫ّ اٌز‬ٌٟٚ ‫ اهلل‬as follows:

53

See his book, p.124.

40

Cleartext Numerical value in ADWNA Encipherment by doubling the number (twofold) Reconversion to letters Encipherment by quadrupling the number (fourfold) Reconversion to letters

‫ق‬

ٞ ‫ف‬

‫ي‬

‫ا‬

ٞ

‫ي‬

ٚ

ٖ

‫ي‬

‫ي‬

‫ا‬

400 30

1

10

30

6

5

30

30

1

200 20 160 12 800 60

2

20

60

12 10

60

60

2

‫ة‬

‫ن‬

ً

‫ت‬٠

ً

ً

‫ة‬

100 10

‫ه‬

‫ن‬

80

ٌ‫ل‬

ٚ 6

‫ت‬٠

‫د‬

‫ض‬

ً

400 40 320 24 1600 120 4

‫د‬

َ

‫شه‬

‫ول‬

‫غـ‬

‫له‬

‫ك‬

ٞ

40 120 24 20 120 120 4

َ

‫له‬

‫ول‬

‫ن‬

‫له‬

‫له‬

‫ك‬

Fully awake to the significance of this method, ibn ad-Durayhim later takes up this method from where ibn Dunayn r left off, developing it and further expanding on it. He makes the numerical processing take other forms by breaking up the number into a sum of two or more numbers of various choices, each corresponding to its respective letter in ADWNA. For instance, enciphering the proper name ‫ ِؾّل‬this way gives: Plaintext Numerical value in ADWNA Numerical processing of one choice Corresponding letters

‫ك‬

َ

‫ػ‬

َ

4

40

8

40

(3+1) (10+30) (6+2) (10+30)

‫اط‬

ٌٟ

ٛ‫ث‬

ٌٟ

Numerical processing of another choice (2+2) (20+20) (7+1) (20+20) ‫ثت‬ ‫وه‬ ‫اى‬ ‫وه‬ Corresponding letters

54

It is well worth emphasizing that although far more sophisticated numerical processing is used in cipher algorithms nowadays, this

54

See ibn ad-Durayhim's treatise, pp.24-25 and p.68.

41

method forms, in principle, the basis of many algorithms in present-day cryptography. Chapter 27 Encipherment by Substituting For Letters the Days of the Week and Hours In this type of encipherment the cryptogram is "composed" on the seven days of the week, by coining seven words that cover all the letters of the Arabic alphabet in such a way as to avoid the repetition of any of them. The words are then associated with the days of the week one apiece, assigning to each letter of the cryptogram a specific hour of the day. ibn Dunayn r elucidates this method by enciphering the phrase: ‫ اٌؾّل هلل‬as follows (with a slight change, as most of the seven words in the original Arabic manuscript are illegible): Days of the week: Coined words: Number of letters

Friday Saturday Sunday Monday Tuesday Wednesday Thursday

5

+

4

+

5

+

4

+

3

+

4

+

3

= 28

‫ ٘ـ‬+ ‫ ي‬+ ‫ ي‬+ ‫ ك‬+ َ + ‫ ػ‬+ ‫ ي‬+ ‫اٌؾّل هلل = ا‬ ‫ = ا‬the second hour of Friday ‫ = ي‬the last hour of Sunday ‫ = ػ‬the second hour of Wednesday َ = the second hour of Thursday ‫ = ك‬the first hour of Tuesday ‫ = ي‬the last hour of Sunday ‫ = ي‬the last hour of Sunday ‫ = ٘ـ‬the last hour of Wednesday ibn Dunayn r concludes by establishing that "the algorithm of cryptanalysing such ciphers is pursued through the application of the quantitative expedients, namely by computing the order of letter occurrence frequencies. This type of encipherment is most conveniently performed by way of a tale."55

55

See his book, p.128.

42

Chapter 28 Encipherment by Folded Paper This method of encipherment is not based on letter substitution, but has more the appearance of a concealment than real cipher. One should think, in all probability, that ibn ad-Durayhim has picked it up from ibn Dunayn r.56 It is more or less similar to a cryptographic device that dates back to the Spartans of ancient Greece, as early as the fifth century B.C., called the "skytale", which is "the earliest apparatus used in cryptology and one of the few ever devised in the whole history of the science for transposition ciphers."57 The idea is to write the secret message down a narrow strip of papyrus or parchment wrapped round a staff of wood close-packed, with edges meeting uniformly at all points. The parchment is then unwound and sent on its way. The disconnected letters and fragments make no sense unless the parchment is rewrapped (by the recipient) round a baton of the same thickness as the first, thus forming the message. The decryptor of today, however, would make short work of such a system. Another related encipherment method is achieved by writing the secret message on a sheet of paper folded in pleats, and concealed by unfolding it, filling up the spaces by adding extra letters that, together with the original letters of the cryptogram, make new innocentlooking context of different import from the one intended. Chapter 29 Encipherment by a Punched Board Much as this method employs a device, it belongs under simple substitution cipher. Encipherment is achieved by puncturing holes, in a sheet of wood, equal in number to the language letters (28 for Arabic), not necessarily arranged alphabetwise but according to an agreed succession. The cryptogram is represented by a thread driven through the intended holes, marking a route which defines the letters of the message. The recipient reads the letters represented by the holes through which goes the thread. Obviously, decrypting this kind of 56 57

See ibn ad-Durayhim's treatise, p.82. Kahn, D. The Codebreakers, New York: Macmillan, 8th printing, 1976, p.82; and Gaines, Helen Fouché Cryptanalysis: A Study of Ciphers and their Solutions, New York: Dover Publications, 1956, p.14.

43

cipher depends on the quantitative technique, explained by ibn Dunayn r so fully as to make any addition here redundant. Chapter 30 Encipherment by Coloured Beads This method uses beads distributed, according to their colours, among the letters of the alphabet. Encipherment is done by threading or "composing" letters represented by beads on a string as a rosary, in which the succession of colours tallies with the succession of letters of the text to be enciphered. Note that colour-bead encipherment can take numerous methods, as ibn ad-Durayhim later states in his Mift alKun z: "This type gives rise to scores of ramifications."58 The algorithm for cryptanalysing this cipher is also through the employment of the quantitative technique of counting the frequency of coloured beads against each letter. ibn Dunayn r's method of coding, however, is by no means economical; alternative methods can be utilized, pursuing an agreed rule, to produce the same result with a fewer number of beads. Morse code (alphabet) is a case in point much in evidence; with just a couple of colours the Code permits the representation of the whole gamut of letters. Chapter 31 Encipherment by Concealment within Context In this method the true message is "concealed" within another context by spreading the intended words at the beginning, middle, and end of lines, according to some rule known only to the sender and the recipient. To exemplify this let us agree that the message is to be read clockwise starting end first. The concealed message would read: "Don't just stand there, do something": There's a lot to say and do before I leave, darling. Say something; stand before me. Let's just not forget our love; please don't.

58

pp. 80-82.

44

Chapter 32 Encipherment by Letters Embedded in Words The message is "composed" on the words of a written epistle, conformably with a fixed rule. This can be accomplished by taking the first, second, last, etc. letter of each word. The following example demonstrates enciphering the name ٍٟ‫ ِؾّل ػ‬in this way twice: the one by taking the last letter, the other by taking the first. ٞ ٍٟ‫ػ‬ ٖ‫وا‬٠

‫ي‬ ً‫ِض‬ ٟ‫ٌى‬

‫ع‬ ‫هافغ‬ ‫ػبِو‬

‫ك‬ َ‫فوك‬ ‫كاه‬

َ ُ‫ى‬١ٍ‫ػ‬ ً‫ب‬٠‫ِؾبم‬

‫ػ‬ ‫صبٌؼ‬ ‫ؽبِل‬

َ ٍٍَُ ٝ‫ِش‬

ibn ad-Durayhim later handles this method down to the smallest detail, citing several varieties and giving many examples.59 Chapter 33 Encipherment by Reversing Letter Order of a Word This type comes under encipherment by transposition, and is performed by writing each word of the cryptogram in reverse order.60 The name ‫اؽّل‬, for example, is enciphered: ‫ كِؾب‬and ْ‫ا‬ٛ‫( هض‬plain)= ‫ضو‬ٚ‫( ٔب‬cipher). It would have been more accurate if ibn Dunayn r were to classify this method under simple rather than composite encipherment. We do not know for certain the reason for his choice, but it is probably motivated by a personal confused definition of composite encipherment. Chapter 34 Encipherment by Numerical Calculations This method is closely akin to the method of encipherment "composed" on area (Chapter 21), with the slight difference of employing whole dinars for the units order, fractions of quarters of the dinar for the tens, fractions of halves for the hundreds, and fractions of both halves and quarters for the thousands. It seems likely that ibn Dunayn r has taken this method from the Author of the Two 59 60

See his treatise, pp.26-27 and p.70 ff. This type of encipherment has been later handled by ibn ad-Durayhim in more detail and diversification. See his treatise under the "transposition" type of encipherment, p.56 ff.

45

Essays (in his First Essay). In both manuscripts, however, the transcription suffers much from corruption and misrepresentation, owing to omission on the part of the scribes. It might be for this reason that ibn ad-Durayhim does not make any reference to this method in his treatise. Indeed we have managed, by studying the examples in both manuscripts, to make out the following correct form of ibn Dunayn r's example illustrating this method: ‫ة ا‬ 1 2

‫ط‬ 3

‫ك‬ 4

‫٘ـ‬ 5

‫ى‬ 7

‫ػ‬ 8

‫ط‬ 9

dinar

ٞ ‫ن‬ 1 2

‫ي‬ 3

َ 4

ْ ً ‫ع‬ 5 6 7

‫ف‬ 8

‫ص‬ 9

quarters of the dinar, indicating the number times 10

‫ق‬ 1

ُ ‫س د‬ 3 4 5

‫ض م‬ 7 8

‫ظ‬ 9

halves of the dinar, indicating the number times 100

‫ه‬ 2

‫ؽ‬ 1

ٚ 6

‫ؿ‬ 6

Three-quarters of the dinar, indicating the number times 1000

Thus, the proper name ٍٟ‫أؽّل ثٓ ػ‬, for instance, can be enciphered: ٞ 1

‫ي‬ 3

‫ع‬ 7

ْ 5

quarter Quarters quarters quarters

‫ة‬ 2

‫ك‬ 4

َ 4

‫ػ‬ 8

‫أ‬ 1

dinars

dinars

quarters

dinars

dinar

Chapter 35 Encipherment by Conditions of planets and Other Celestial Bodies With this chapter ibn Dunayn r concludes his discussion of prose encipherment. Here the cryptogram is "composed" on an astronomical text addressing planets and other heavenly bodies: their motions, distances, durations, mansions, revolutions, rotations, etc. He brings forth an example of enciphering the name ‫ ِؾّل‬by this method: "Having completed forty revolutions, the Moon eclipsed at such and such degrees of such and such constellation. Eight revolutions thence remained. Its motion straightened after it had waned in appearance and faded in colour. Thereafter it moved to Sagittarius and completed forty revolutions thus far. At the end of Sagittarius the planet Venus approached it. Four turns elapsed before its motion evened out in

46

orbit, and its light became as bright as to emulate planets".61 It is clear that the algorithm for cryptanalysis lies in the realization of the letters corresponding to the numbers [set in boldface] in ADWNA. ibn Dunayn r attributes this type of encipherment to Hermes Trismegistus of wisdom and learning, the legendary author of mystical, astrological and alchemical works, and one of seven wise men known to have possessed calligraphs of their own, barred off to all but the "sons of wisdom", hence the epithet "hermetic" (in English) or "hermetique" (in French), meaning completely sealed or impervious to external influences. Many ciphers were ascribed to Hermes; ibn Wa iyya an-Naba , in his awq al-mustah m f ma rifat rum z al'aql m (The seeker's joy in identifying the written symbols of languages) gives a detailed account of the Hermetic calligraphs. ibn Dunayn r concludes this chapter by pointing out the following two notions: 1. that "the cryptanalyst of this cipher should be knowledgeable about arithmetic and astronomy"62, and rightly so, in order that he/she can identify the text as a cryptogram, and that the astronomical content is not what is intended. 2. that the cryptanalyst "should make use of the first statistical principles of calculating the frequencies of letter occurrence"63, namely the quantitative technique. Here ibn Dunayn r is wide of the mark. It may be an unfortunate oversight on his part, because cryptanalysing such a cipher requires nothing else but an acquaintance with the arithmetic using decimally-weighted numerical alphabet, or is b al- ummal.

1.3.2. Cryptanalysis of Poetry Ciphers ibn Dunayn r's work, much important as it is, is not without precedent of its kind; it is simply one link of an integral chain in which every scholar make good use of, and adds to, the contributions of his predecessors. It has already been noted (1.2.1.) that ibn Dunayn r tends to draw upon quite a few of his earlier peers, quoting 61

See ibn Dunayn r's book, p.140. Ibid., p.140. 63 Ibid., p.140. 62

47

their ideas, recapitulating their concepts, or building on their findings. This tendency, in fact, is even more pronounced in this part, where he seems to lean notably on al-Kind , ibn ab ab and the Author of 'Adab a - u ar ' (The Art of Poets).

1.3.2.1. Tools for Cryptanalysing Poetry Ciphers Chapters 36 and 37 of ibn Dunayn r's book serve as an introduction to cryptanalysing poetry ciphers. In Chapter 36 he reiterates the tools of cryptanalysis that are common to both prose and poetry; these are: 1. Determining the orders of letter frequency of occurrence; 2. Familiarity with the variable and basic letters; and 3. Knowledge of letter combination and non-combination. In Chapter 37 he mentions those principles of cryptanalysis exclusive to poetical ciphers, considering them as indispensable conditions to any cryptanalyst of poetical cryptograms: "Thereafter, the keynote element of this science is that the cryptologue should be: 1. widely conversant with prosody and metrical structures; 2. thoroughly acquainted with rhymes; 3. deeply familiar with the science of poetry [the art of appreciating poetical delicacy]; 4. a person of insight into the knack of writing; 5. a person with capacious memory for committing to heart poetry galore; and 6. skilful and resourceful in cryptography."64 To be noted is the fact that poetical ciphers do not typically exceed a few verses.65 It follows that the letter order of frequency is scarcely sufficient to render the quantitative techniques reliably applicable in cryptanalysis. Nevertheless, adopting the afore-stated principles is apt to make the process less difficult.

64 65

See ibn Dunayn r's book, p.142. See the practical examples of ibn ad-Durayhim and ibn Adl n in their respective treatises, p.102 ff and p.104 ff.

48

1.3.2.2. On Prosody (Metrics)  Metrical Circles (Chapter 38) ibn Dunayn r dedicates this chapter to the five circles of Arabic prosody, from which all poetical meters (measures of versification) originate. This is so because the meters themselves are so engaged or overlapped that one meter disengages itself from the other. Each group of meters that are capable of undergoing such disengagement share in a circle designated according to the nature of its parts. These metrical circles are: circle 1 of the different, circle 2 of the consistent, circle 3 of the similar, circle 4 of the extraneous, and circle 5 of the harmonious.  Poetical Meters (Chapters 39 & 40) Chapter 39 deals with the sixteen meters of Arabic poetry and the feet [the basic units] that are peculiar to each meter. In Chapter 40 the meters are distributed to their respective circles. Then ibn Dunayn r points out to three prosodic terms, all belong under metrical variations in Arabic poetry, namely, az-zi f, (an optional variation that befalls the second of a couple of letters, called sabab, in a line of verse), al- arm (a measured omission of the first vocalized letter of a threeletter foot segment, called watid, occurring at the beginning of a line of verse), and al- azm (a measured addition of up to four letters made at the beginning of a verse, not considered in scansion). ibn Dunayn r's specific reference to these variations is apparently due to their direct effect on poetic meters ‫ـــ‬an effect that could turn them away from what is familiar in Arabic poetry. Other variations, however, do not have such an effect.

1.3.2.3. On Rhymes ibn Dunayn r devotes Chapter 41 to rhymes in poetry [correspondence of terminal sounds in lines of verse, involving identity of sound rather than spelling. "Fix" and "sticks", like "buffer" and "rougher" are perfect rhymes]. He refers to their names, letter structures ( aw ri ) and defects, inasmuch as is necessary for the cryptanalyst.

49

1.3.2.4. Insight into Writing Knack This term, also used by the Author of Adab a - u ar ', means the penetrating discernment in the art of writing, its rules an principles. ibn Dunayn r discusses this topic at length, covering more than ten chapters (42-52) of his book. Arranged along the same lines as the Author of Adab a - u ar ', these rules and principles include the following:  The letters ‫ ) ( ا‬and ‫( ي‬l) (Chapter 42) This bigram is of highest frequency and combinability, since it occurs, more often than not, as the definite article. Definition is a prevalent feature in most Arabic nouns.  Two-letter words (Chapter 42) These words are bigrams either inherently (words like ِٓ, ٓ‫ )ػ‬or by inflection (e.g. imperative verbs like ‫كع‬, ًٍ, and letters governed by prepositions such as ٗ‫ث‬, ‫ٌه‬, etc.). Pure bigrams, in fact, are limited in number (there are 115 of them according to our statistics on Arabic root-words). Seeking words of this kind (called "word-spotting" in today's terminology) in a cryptogram contributes favourably towards solution; indeed it is an algorithm of cryptanalysis, as ibn Dunayn r states.  The relation between the number of letters of a verse and its meter (Chapter 43) The number of letters contained in a line of verse is likely to indicate its meter. ibn Dunayn r sets boundaries to the approximate number of letters in a verse for each meter. Example: the number of a - aw l (the long) and al-bas (the simple) meters ranges between 40 and 50 letters. The shortest meter in Arabic poetry, however, consists of seven letters and is called manh k ar-ra az. He proceeds to consider algorithms of cryptanalysis, which include the following in order: 1. Cryptanalysing the letter (‫ـــ ) ا‬mainly through the well-known quantitative fact that the letter (‫ )ا‬has the highest frequency of occurrence of all the letters of the alphabet. 2. Cryptanalysing the letter (‫ ي‬l) ‫ـــ‬depending either on its combinability with the letter (‫)ا‬, or on its combinability with itself, i.e. its occurrence repeated in words such as: ‫اهلل‬, ‫ش‬١ٌٍ‫ا‬, ‫ت‬١‫اٌٍج‬.

50

3. Cryptanalysing the letter preceding or following (‫ـــ )ا‬taking into account that decrypting (‫ )ا‬often makes for working out two-letter words starting or ending with it, particularly those frequently occurring bigrams such as: ٚ‫أ‬, ‫إم‬, ْ‫إ‬, ٞ‫( أ‬starting with ‫ ;)ا‬and ‫ِب‬, ‫ب‬٠, ‫( ما‬ending with ‫)ا‬. 4. Cryptanalysing the letter preceding (‫ اي‬al) ‫ـــ‬depending on the fact that, in one word, (‫ )اي‬is preceded mostly by one of the letters: (ٚ w), (‫ ف‬f) or (‫ ن‬k). 5. Spotting five- and seven-letter words ‫ـــ‬concentrating especially on the six labials in them, i.e. the letters: ‫ي‬, ‫ة‬, ْ, ٚ, ‫ ف‬and َ. Linguists, however, include the letter (‫ )ه‬in place of (ٚ), dubbing these letters as the "liquid letters" or al- ur f a - ulq. No pentagram or heptagram, ibn Dunayn r maintains, is practically devoid of at least one of these letters, with very rare exceptions.  Silent letters: letters written but not pronounced (Chapter 44) ibn Dunayn r draws attention to a set of properties inherent in the Arabic language, which are beneficial to cryptologues. He begins with those letters that are orthographically written, but not vocalized, and therefore they are not considered in metrical scansion since, in prosody, it is only the enunciated letters that count. Of these letters ibn Dunayn r mentions: 1. the letter (‫ )ا‬that is added to the letter (ٚ) in verbs denoting plurality, e.g. ‫ا‬ٚ‫صبه‬, ‫ا‬ٍٛ‫( كه‬the functional (‫ )ا‬of differentiation, called alif at-tafr q or al-f riqa), as distinguished from the intrinsic (ٚ) terminating verbs like ٚ‫غي‬٠, ٚ‫جل‬٠, etc. 2. the terminal "hamza" in some words such as ‫شبء‬, ‫ثٕبء‬, which used to be written as ‫شب‬, ‫ ثٕب‬and nonetheless pronounced. This is common practice in ancient manuscripts. In fact this item would have been more aptly subsumed by ibn Dunayn r under the following heading, i.e. letters pronounced but not written. 3. the terminal (ٚ) of the proper name ٚ‫ ( ػّو‬Amr), written to differentiate it from another proper name ‫ ( ػّو‬Umar). ibn Dunayn r favours not writing this (ٚ) in enciphered poetry lest it should cause ambiguity. However, since poetry is metrically measured, there would be no possibility of any mix-up in these two proper names.  Voiced letters: letters pronounced but not written (Chapter 45) These are mainly ‫'ا‬s (alifs) within proper names, often dropped by scribes since times of old, probably in the interest of damping the

51

vocalization. Examples: ُ١٘‫( إثو‬for ُ١٘‫) إثوا‬, ً١‫( إٍّؼ‬for ً١‫)إٍّبػ‬. ibn Dunayn r favours spelling out such (‫ )ا‬in poetry, as the meter necessitates its retention.  The letters ( ٚ : w, ) and ( ٞ : y, ) (Chapter 46) Being of high frequency, these two letters are of service towards cryptanalysis; hence the need, on the part of the cryptanalyst, to spot them "in mid- and end-positions",66 and consider their different modes of usage with vowel points. They occur as "geminated (mu addad), neutral (s kin) and vocalized (muta arrik)",67 says ibn Dunayn r.  On glottal stops (hamzas) (Chapter 47) ibn Dunayn r refers briefly to examples of hamzas that might prove problematic, such as the mid-glottal catch (or medial hamza).  Prefixes and suffixes (Chapters 48 & 49) Also helpful in cryptanalysis is a fair knowledge of Arabic prefixes and suffixes ‫ـــ‬letters that, when joined to other letters make up integral entities of significance. Of the prefixes ibn Dunayn r states the letters: ٚ (w), ‫( ف‬f), ‫( ة‬b), ‫( ن‬k), and ‫( ي‬l); and of the suffixes he makes reference to the letter ‫( د‬t) in three modes.  Doubled letters (Chapter 50) Consecutive repetition of the same letter contributes towards cryptanalysis. ibn Dunayn r gives examples of words containing a letter repeated: ًٍَ‫( ف‬in which the letter ‫ ي‬repeated) ‫( َِلَك‬in which the letter ‫ ك‬repeated) ُّ‫ل‬ (in which the letter َ repeated).  Word patterns defined with (‫( )اي‬Chapters 51 & 52) If the letter (‫ )ي‬is repeated, after (‫ )اي‬at the beginning of a word, this word is all but certain to be the name of God (‫)اهلل‬. However, ibn Dunayn r suggests alternatives. By that he is alluding to the possibility of cryptanalysing certain letters by an assumption based on their positions in a word, and on the structure and measure of the word. This principle of cryptanalysis is further expounded by the Author of Adab a - u ar '.

66 67

See ibn Dunayn r's book, p.162. See ibn Dunayn r's book, p.162.

52

1.3.2.5. Other Useful Observations In chapters 53 through 59 ibn Dunayn r draws attention to a number of special problems that may crop up and hinder the cryptologue's endeavour towards solution: 1) long words which are devoid of the definite article (‫)اي‬, such as: ُٙ‫( فََٕزلهع‬10 letters); ُٙ‫ى‬١‫ىف‬١َ‫( ف‬9 letters); ْٕٛ٠‫( ٍزَزل‬9 letters). 2) nonsensical verses, though with sound meter ‫ـــ‬which requires the cryptanalyst to be conversant with such tools as rhyme, language, prosody, and competent to cope with any possible metrical variations and defects. This kind of meaningless poetry is described by ibn Dunayn r (in Chapter 59) as "sheer raving".68 3) absence of letter-dotting, either through the deliberate use of undotted letters alone, or by choosing not to dot letters whose shape causes ambiguity. For example, the first letter of the undotted word ( ) might just as well be one of these letters: ‫ ة‬, ‫ س‬, ٞ or ْ . 4) employing separate letters (letters that cannot be linked with following letters); e.g. ‫ػ‬ٚ‫ك كاه ه‬ٚ‫ ىاه كا‬. 5) using each letter just once without repetition, as in the verses that round up all the letters of the alphabet ‫ـــ‬the so-called "keys", such as the following line attributed to al- al l ibn 'A mad al-Far h d : 6) the verse sought for cryptanalysis being of a new form and unheard-of before. 7) the intended verse being too short to allow sufficient letter frequency; the longer the verse the better for the cryptologue. 8) unsound meter and language scales, owing to the poet being of inferior class or shallow knowledge. 9) problematic peculiarities in rhyme and meter, such as curtailing the seven-unit metric foot ( ٍٓ١‫ )ِفبػ‬by at once omitting the fifth and seventh neutral units of the foot, which is unacceptable in poetry.

68

ibn Dunayn r's book, p.174.

53

ibn Dunayn r, moreover, cautions (in Chapter 58) against the possibility of erroneous conclusions in cryptanalysis resulting from some default on the part of the encipherer. This might well impede cryptanalysis, too. - COMMENT ON AN IMPORTANT CIPHER METHOD (Chapter 60) ibn Dunayn r puts forward this method in the context of his discussion of cryptanalysis barriers. It is actually quoted from the Author of the Two Essays: "Towards the end of his Second Essay, the Author of the Two Essays on cryptanalysis states that we are destined to follow an intricate path."69 ibn Dunayn r settles for propounding the basis of the method, which involves assuming for the same letter [of the plaintext] three different symbols [in the cryptogram], to be used, one at a time, to represent that letter. On the other hand, a single symbol is assumed to represent three letters [often of the same orthographic pattern such as ‫ ة‬, ‫ د‬, ‫] س‬. He criticizes the method and its proponent on the basis of its susceptibility of equivocality, and concludes by saying that the Author of the Two Essays was "not wellinformed in ciphers".70 It turns out, however, that ibn Dunayn r's statement is not without prejudice for that matter. Complicated as it may seem, this method is deemed one of the important substitution methods that answer to the latest theories and principles of encipherment, in which two or more letters are substituted for one letter (homophonic substitution).

1.3.2.6. Practical Examples (Chapters 61 & 62) In keeping with the common practice of most writers in this science, ibn Dunayn r works out practical examples to illustrate his 71 ideas. He therefore chooses two lines of verse, the first (Chapter 61) is of his own composition: in which the letters ‫ ا‬, ‫ ي‬, ٚ are found to be especially frequent. He restricts himself to disposing the letters of the verse, attaching to each 69

See ibn Dunayn r's book, p.176. Ibid., p.176. 71 See also ibn Adl n's treatise, p.104 ff., and ibn ad-Durayhim's treatise, p.102 ff. 70

54

letter its symbol. The following table (Table 1.8.) shows these letters arranged in descending order according to their frequency of occurrence. Note that all symbols are chosen to be three-letter words ending with the letter (‫)ه‬, with the middle letter diacritically marked with the neutral "suk n". Letter ‫ا‬ ‫ي‬ ٚ ‫ع‬ ‫ة‬ ‫ك‬ ‫د‬ َ ْ ‫ى‬ ‫ف‬ ‫ق‬ ‫م‬ ً ‫ن‬ SPACE

Symbol ‫ظفو‬ ‫ٍفو‬ ‫شؼو‬ ‫فغو‬ ‫غّو‬ ‫ٍؼو‬ ‫ثؾو‬ ‫ؽغو‬ ‫ثله‬ ‫و‬ٙ‫ش‬ ‫شمو‬ ‫ٔنه‬ ‫شّو‬ ‫صفو‬ ‫و‬ٙ‫ف‬ ْ

Frequency 9 8 8 3 2 2 2 1 1 1 1 1 1 1 1 7

Table 1.8. The first of ibn Dunayn r's two practical examples. In the other verse (Chapter 62) ibn Dunayn r expands on the algorithm of cryptanalysis, which is conducted according to the following steps: 1. Calculating the number of letters that constitute the verse (34 in this example), to deduce its meter (al-bas in our case). 2. Based on step 1, inferring that the rhyme is of the overlapping type. 3. Preceiving that the final letter of the verse is the same as that at the end of its first hemistich ‫ـــ‬a phenomenon in Arabic poetry called at-ta r . 4. Sorting out the letters according to their order of frequency, and thereupon eliciting the name of God ‫ اهلل‬, utilizing the repetition of the letter (‫)ي‬. Three letters are thus determined, i.e. ‫ا‬, ‫ ي‬and ‫٘ـ‬.

55

5. Checking the next high-frequency letters (after ‫ ا‬and ‫) ي‬, holding that they would probably be َ and then ٞ . 6. Experimenting with probable words, based on letters so far uncovered. 7. Composing a word-group that carries meaning and meter: ... ٟٔ‫ؼٍُ أ‬٠ ‫اهلل‬ 8. Carrying on after this pattern, always building on what has already come out, and guessing yet unknown letters in three- or four-letter words, until the following verse develops: Right from the outset, ibn Dunayn r lists the letters of the verse, together with their respective symbols. In the following table (Table 1.9.) these letters are re-arranged according to their descending order of frequency. Letter َ ‫ي‬ ‫ا‬ ٞ ‫ن‬ ‫٘ـ‬ ْ ‫ه‬ ‫ة‬ ‫ػ‬ ‫ع‬ ‫ؽ‬ ٚ ‫ط‬ ‫د‬

Symbol ‫ٍِل‬ ‫ل‬ٙ‫ف‬ ‫ٍؼل‬ ‫ٌجل‬ ‫عٍل‬ ‫هك‬ٚ ‫ل‬ٍٙ ‫ىٔل‬ ‫ثؼل‬ ‫ِوك‬ ‫ػجل‬ ‫ػمل‬ ‫ٔغل‬ ‫ٕ٘ل‬ ‫غوك‬

Frequency 6 4 3 3 3 2 2 2 2 2 1 1 1 1 1

Table 1.9. The second of ibn Dunayn r's two practical examples.

1.3.2.7. Conclusion (Chapters 63-66) ibn Dunayn r brings his book to a close by priding himself on having broken fresh ground, suggesting that he manages to run the

56

gamut of encipherment from simple to composite on the one hand, and from prose to poetry on the other. He insinuates that al-Kind 's and ibn ab aba's treatises on cryptanalysis "both failed to develop the topic exhaustively in either case".72 He then cites lines of verse [cipher alphabets or cryptographic keys], each embracing the Arabic alphabet in such a way as to avoid the repetition of any letter. These are quoted almost entirely from the treatise extracted from Adab a - u ar ', to be followed by verses sometimes used in encipherment, and intended for sustained mental exertion in pursuit of solution. The difficulty underlying these verses stems from one or more of the following practices: 1) using undotted letters of identical spelling patterns. 2) repeating such letters in a manner so unfamiliar as to upset the principle of letter frequency. 3) purposely using letters that do not admit linking with one another all through the verse; e.g. 4) repeating in the second hemistich the same words of the first hemistich, but in different order. Example: 5) writing the verse adroitly such that the first hemistich is read forward as the second hemistich is read backward. Example: 6) using odd or out-of-the-way poetic meters, or yet neo-meters that never belong to the well-known meters of al- al l. Also, failure to observe a uniform rhyme or rhyme letter. ibn Dunayn r subjoins a statement restricting the limits of the cryptanalyst by analogy: "The cryptanalyst is not obliged to puzzle out ciphers intended for mental exertion, just as the grammarian is not bound to enter into intricate issues."73

72 73

See ibn Dunayn r's book, p.184. Ibid., p.186.

57

1.4.

Originality of ibn Dunaynir

Regardless of his drawing upon the works of his predecessors, ibn Dunayn r stands great amidst cryptological figures. The features of his originality are manifested first and foremost in the following contributions: 1. The utilization of numbers in substitution encipherment. 2. The employment of several numbers in ciphering each letter by substitution. This method as developed by ibn Dunayn r (though tackled before him by the Author of the Two Essays, substituting several symbols for a single letter) underscores his profound cryptographical knowledge, and is known today as the principle of "frequency reversals". To be noted is that the earliest instances of using this method in Europe date from the reign of King Henry IV of France, in his correspondence with 74 the Landgrave of Hesse between 1602-1606, that is four hundred years after ibn Dunayn r. 3. The demonstration of composite methods of encipherment such as the one implementing transposition and substitution together, which has proved important in today’s block cipher algorithms such as the Data Encryption Standard (DES) and the more recent Advanced Encryption Standard (AES), both are based on the principle of encipherment using both methods simultaneously, but carrying it to a higher degree of sophistication by means of a binary number system. 4. The abundant use of encipherment by concealment, which he describes as composition on a background or medium that disguises the actual intent, such as composing on a tale, dream, chessboard, financial register, planets, etc. 5. The utilization of encipherment devices such as coloured beads, punched board and thread, folded paper, etc. 6. The use of encipherment by signaling, applying the arithmetic of decimally-weighted numerical alphabet (ADWNA) and the finger-spelling method of communication between two individuals (manual alphabet). 74

See Treatise on Cryptography, A. Lange and E. A. Soudart; Laguna Hills, CA: Aegean Park Press, 1981, p.10.

58

It would finally be just as well to remark that most of ibn Dunayn r's contributions listed above relate to prose encipherment. Not that his contribution in poetry is any less worthy, but contributions there are common ground among fellow authors of similar treatises; hence the difficulty defining clear-cut aspects of ibn Dunayn r's originality. Suffice it to say that it is to his credit that he could exhaust the subject of encipherment and cryptanalysis of both prose and poetry at such length that is unique to him among all those who have written on this art.

59

Section 2

ibn Dunayn r's Edited Book: Expositive Chapters on Cryptanalysis

60

61

2.1. Editing Methodology The main purpose of editing is the reproduction of a text as close to the author's original as possible. In line with this objective we have opted for preserving the statement of the original whenever possible.  The very nature of the original manuscripts required the addition -where appropriate- of explicatory titles in the interest of marking out divisions or classifications. This would prove useful for easy understanding and clarity of ideas.  No effort has been spared in the interpretation of citations (Koranic verses, Prophetic traditions, lines of poetry, sayings, etc.) contained in the treatises. We have given brief biographical identification of personalities (in footnotes to Arabic text only), relegating interested readers (in Arabic) to such authorities as al-A l m by ayr al-D n al-Zirkily or Mu am al-mu'allif n by Omar Ri Ka la, for further and more detailed biographical reference. Those citations and personalities that our efforts fell short of their interpretation or identification have also been properly recorded.  In explaining the linguistic terms included in the treatise we have made use of various dictionaries, old and modern, foremost of which are: Lis n al- Arab and Matn al-lu a. Unless otherwise helpful, no reference has been made to any dictionary.  We have adopted the same symbols and signs commonly employed by editors of Arabic manuscripts, and conformed to the modern spelling norms. We have enclosed requisite contextual additions -i.e. explanatory insertions and comments other than the writer's own words- within square brackets [ ]; examples illustrating rules of encipherment have been set off by round brackets (parentheses) ( ); book titles in italics; quoted material and Prophetic traditions have appeared within quotation marks ― ‖ , while floral brackets  have been used to enclose Koranic verses.75 75

Translator's explanatory additions are placed between pairs of hyphens: -…-.

62

2.2. Description of the manuscript ibn Dunayn r’s book is one of several treatises making up the assemblage of cryptology, which is part of the stock of the F ti Library, preserved in as-Sulaym niyya Ottoman Archives in Istanbul under number 5359. The largest in that aggregate, ibn Dunayn r’s book spans the sheets 54/A to 80/A. The first sheet contains the title: Zubad fu l ibn Dunayn r f all at-tar im (The gist of ibn Dunayn r’s chapters on cryptanalysis), followed immediately by six lines of poetry on rhymes and related topics.76 The second sheet bears the title: Maq id al-Fu l al-Mutar ima an all at-Tar ama. Following are photocopies of these two sheets, as well as the last sheet of the book.

76

It has been found appropriate to shift the contents of this sheet to the end of the book, where it fits more snugly in the context of cryptanalysing poetry.

63

Figure 2.1. A photocopy of the first sheet of ibn Dunayn r's book (Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)

64

Figure 2.2. A photocopy of the second sheet of ibn Dunayn r's book (Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)

65

Figure 2.3. A photocopy of the last sheet of ibn Dunayn r's book (Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)

66

2.3. ibn Dunaynir’s Book Expositive Chapters on Cryptanalysis (Original Arabic Text and English Translation)

67

In the name of God the Compassionate, the Merciful.

Maq id al-Fu l al-Mutar ima an all at-Tar ama

68

He said, following the honorific opening statement in praise of God and the introduction: This book is divided into two parts: the first tackles the cryptanalysis of prose ciphers; the other deals with cryptanalysing poetry ciphers. I have further divided each part up into well-organized chapters, covering all types of encipherment and their respective algorithms for cryptanalysis. In so doing I always turn to God for right guidance and support; most sufficient unto me is He, the Holy One, in whom I trust.

[PART ONE] [Cryptanalysis of Prose Ciphers] 77 I say: It is true that cryptanalysis is achieved first and foremost through conjecturing about the cipher sought for solution. The cryptanalyst keeps trying alternatives and assuming possibilities until all the forms of the ciphertext reveal all their corresponding letters of the alphabet. However, there are measured principles and rules governing this art, so that what is assumed by the cryptanalyst is an outcome of reasoning and argument by analogy, and not an issue of haphazard, hit-or-miss endeavour. Successful cryptanalysis involves two aspects: First, familiarity with the order of letter frequency of occurrence; namely knowledge of the letters of high occurrence [abundant letters], those of medium occurrence [common letters], and those of least occurrence [scarce letters].

77

Square brackets contain useful explanatory additions to the original text.

70

The second aspect is a thorough knowledge of letter combination and non-combination; namely having cognizance of the combinable and non-combinable letters, letters combinable in both pre- and postpositions [anteriorly and posteriorly], those non-combinable both in pre- and post-positions, those combinable pre-positively only, and those combinable post-positively in relation to each other. I am herein stating them in a way that serves the purpose well without much toil. Moreover, every pursuit needs some kind of instrument expressive of, and responsive to, one’s intention. The requisite instrument of this art is the familiarity with the methods of encipherment I am going to mention in the course of the book. Any person involved in this science should be endowed with intelligence, observation, insightful delicacy, keen intuition, equanimity of mind, proper flair and apt speculation. Otherwise he would never stand to benefit by any of the methods conducive to cryptanalysis. Nay, some may have the plaintext already right under their very nose, yet they are not well-guided to read the cipher message contained therein, let alone to put to use or even grasp my say! Chapter [1] 78 Cryptanalysing enciphered letters can be done through the utilization of either quantitative or qualitative expedients. By ―quantitative‖ is meant the frequency of occurrence of a letter sought for cryptanalysis in a ciphertext. By ―qualitative‖ is meant the mode of the letter occurrence [as regards combinability] in the ciphertext.

78

Chapter numbering is an addition for easier cross-referencing.

72

Chapter [2] As for cryptanalysis by the quantitative occurrence of a letter in a ciphertext, I say: Of all the letters of the alphabet, long and soft letters, or what is called ―vowel letters‖, have the highest frequency in the Arabic tongue. These are ‫) ( ا‬, ٚ (w/ ) and ٞ (y/ ). Some give preference to the letter ‫( ي‬l) over ٚ on account of the fact that the letter ‫ ي‬is of high occurrence with the letter ‫ا‬, specifically to form the Arabic definite article (‫)اي‬, although it often occurs with other letters or doubled. Because of its high frequency in use, which exceeds the frequency of the letter ٚ, the letter ‫ ي‬takes precedence [over ٚ], and so is the case with the letter َ (m), which has priority over ٚ and ٞ 79. The letters ‫ ا‬, ٚ and ٞ are called the vowel letters because they represent the voiced speech sounds created with air passing out free without causing undue friction. That is why they have the highest frequency among all letters in all tongues. Other letters vary in their frequency from one language to another. The letter ً (s), for example, is more abundant in Latin than all other letters except for the vowels. Turkish and Mongol are abundant in the letter ْ (n), and so forth. If we set out to describe the algorithms of cryptanalysis in each tongue, the book would grow larger. Let us now start to address the methods of encipherment in the Arabic language, and their algorithms for cryptanalysis.

79

Thus the frequency count of abundant letters according to ibn Dunayn r, in order of precedence, is: ‫ا‬, ‫ي‬, َ, ٚ and ٞ.

74

Chapter [3] Encipherment of letters falls naturally into two major types: i.e. simple encipherment and composite (or super-) encipherment. SIMPLE encipherment is divided into two parts: in the first part letters change their forms; in the other, letters retain their forms. Simple encipherment where letters change their forms can either be with conceptual relationship and diffusion, or without conceptual relationship and diffusion. That with relationship and diffusion can be either relation by species, or relation by genus. In each case the symbol indicative of a letter may be either one symbol or numerous symbols. By one we mean representing the letter ‫) ( ط‬, for instance, by a symbol suggesting a single bird such as a pigeon. By numerous is meant the representation of the letter ‫ ط‬by a symbol suggesting any bird, since the bird genus includes all species of birds.

76

Chapter [4] The other division [of simple encipherment where letters change their forms] is that without relationship and diffusion. This splits up into two subdivisions: EITHER by changing the forms of letters -substitution-, OR by keeping the forms of letters -transposition-. Changing the forms of letters is accomplished by adopting a cipher alphabet of devised shapes [or symbols] not having the usual forms of letters. This may be done EITHER by replacing each letter by one symbol, OR by assuming symbols for those letters that often go together. Simple encipherment by keeping the forms of letters branches into two types: the one involves changing the original positions of letters; the other is without changing the original positions. Changing the original positions of letters is divided into two methods: the one is transposition by changing the position of a letter in relation to surrounding letters, viz in anterior and posterior positions; the other is transposition by changing the position of a letter in relation to itself, viz in terms of only changing its angle of presentation. As for enciphering without changing the original positions of letters, there are two methods: EITHER by the addition of extra symbols -nulls-; OR without adding such symbols [rather by omitting one or more symbols]. If nulls are used, they may be either one or numerous.

78

Chapter [5] The other part of simple encipherment [where letters retain their forms] is achieved via two principles: the one is quantitative; the other is qualitative. The quantitative principle divides into two subdivisions: the one is to double, triple, quadruple, etc. the letter. Duplication may be applied to all or some of the letters. The other subdivision of the quantitative principle is to merge all the letters that can be merged, by assuming one common symbol for those which have the same contour. This may be exercised over all the letters, or only over some. The qualitative principle, on the other hand, can be accomplished either by linking all or some of the letters that are inherently separated, or by separating all or some of the letters that are inherently linked.

80

Chapter [6] The other major type of encipherment of letters, i.e. COMPOSITE (or super-) encipherment, falls into two divisions: the one is a combination of simple methods, and the other is what ensues in consequence80. Now then, I have gone through with all the types of simple as well as composite encipherment, numerous and diverse as they are81. This is all that is necessary for the encipherer to know, as these divisions cover the long and the short of encipherment. If we set out to dilate on them all, it would take long, and time would press. Now let us start with simple ciphers that are prerequisites for the encipherer in practice. Then we state the relevant algorithms of cryptanalysis, before we embark on composite ciphers. What applies to cryptanalysing simple ciphers also applies to

cryptanalysing

corresponding composites; and thus developing a thorough knowledge of simple methods of encipherment will render superfluous the exposition of all composite methods, since these would then never miss the cryptologue’s perspicacity and insight a priori. Nevertheless, I am to mention the various divisions of composite encipherment, and algorithms for their decryption [in due course].

80

There is no mention to the latter division in al-Kind ’s treatise (q.v., p.142). ibn Dunayn r is probably referring to composing through a medium, as we shall see.

81

In fact ibn Dunayn r’s handling of the types of encipherment here tends to be more of an honest rendition of his predecessor al-Kind than an original investigation. Compare with al-Kind , Volume One, p. 132 ff.

82

Chapter [7] I say: The type of encipherment characterized by changing the forms of letters is achieved by devising shapes or symbols not attributed to letters at all. In this method every letter is represented by a symbol that is unique to it. The cryptanalysis is accomplished by counting the symbols of the cipher message, and establishing the frequency of occurrence for each symbol, by affixing the frequency number to the respective symbols of the cipher. Having done that, you dispose the symbols in order of frequency precedence, designating the most frequently-occurring symbol in its locations throughout the cryptogram. Do the same with the next frequently-occurring symbol, and so forth until you exhaust all the symbols of enciphered letters. Now place the highest-frequency symbol against the highestfrequency letter of the Arabic alphabet, doing the same with the rest, conformably with their order of frequency. Keep going in the same vein until you use up all the letters and symbols. Make sure to place the symbol of highest frequency against the Arabic letter (‫)ا‬, for it has the highest frequency of all letters in all languages, as we have already stated in the context of discussing the vowel letters. Remember also that the letter (‫ )ي‬is the next highly frequent letter after (‫ )ا‬in all tongues, followed by the letter (ٚ), then (َ), ( ‫)٘ـ‬, (ٞ) and (ْ) respectively. You keep on matching letters until they begin to show intelligible relationship. Symbols defying solution should be tracked down time and again, using fair conjecture until their purport comes right for you.

84

Chapter [8] I have considered the orders of letter frequencies according to the reckoning of Ya q b al-Kind , peace be on his soul. He said he had turned to seven parchments and counted all the orders of letter frequency of occurrence in them, to find that the frequency of the letter ‫ ) ( ا‬was 600. the frequency of the letter ‫( ي‬l) was 437, that of the letter َ (m) was 320, and so on till the end of his citation82. It so occurred to me to take up [other] written sheets myself and count the letter frequency orders in them. Thus I took three sheets of prose epistolary texts and calculated the frequency of the letter ‫ ;) ( ا‬it turned out to be 575. the frequencies of other letters were found to be as follows [in descending rank]: the letter ‫( ي‬l) occurred as often as 360 times; the letter َ (m) 265 times; ‫( ٘ـ‬h) 260; ٚ (w/ ) 250; ٞ (y/ ) 230; ْ (n) 225; ‫( ه‬r) 195; ‫ ) ( ع‬170; ‫( ف‬f) 145; ‫( د‬t) 115; ‫( ة‬b) 105; ‫( ن‬k) 95; ‫( ك‬d) 80; ً (s) 75; ‫( ق‬q) 62; ‫ ) ( ػ‬50; ‫ ) ( ط‬43; ‫ ) ( م‬32; ‫ ) ( ص‬28; ُ ( ) 17; ‫ ) ( ؿ‬13; ‫ ) ( س‬11; ‫( ى‬z) 9; ‫ ) ( ط‬8; ‫ ) ( ظ‬7; ‫ ) ( ؽ‬5.83 So it came home to me the validity of the statement of Ya q b ibn 'Is q [al-Kind ], peace be on his soul.

82 83

See other letter frequencies according to al-Kind and ibn Adl n in Volume One, p.168 and Volume Two, p.48 respectively. The letter ‫ ) ( ض‬does not appear in this count, neither does it in al-Kind ’s count; see al-Kind ’s treatise, p.168. Its frequency according to ibn Adl n is 23; see his treatise, p.48.

86

Chapter [9] If the cryptogram is very short, there exists insufficiency in it of the frequency of letter occurrence. The expedient for cryptanalysis to be used here is to determine those letters [of the alphabet] which admit combination with each other, and those which do not. The cryptologue should be ambly experienced to cope, until he elicits the intended meaning of that scant cipher. Let us then start to address combinable and non- combinable letters, so as to guide the seekers of cryptanalysis to this honourable science, and acquaint them with the rules of this art. In the following table, we shall demonstrate the various divisions of letters and their relative non-combinability, numerous and diverse as they are, with the good assistance of God.

88

ً (s)

‫س‬

‫م‬

‫ى‬

‫ص‬

‫ض‬

‫ظ‬

‫) (م‬

‫س‬

‫ى‬

‫ط‬

‫ظ‬

‫ص‬

‫ض‬

ً

‫( ى‬z)

‫س‬

‫م‬

‫ص‬

‫ظ‬

ً

‫س‬

‫م‬

‫ى‬

‫ط‬

‫ظ‬

ً

‫ض‬

‫س‬

‫م‬

‫ص‬

‫ط‬

‫ظ‬

ً

ُ

anteriorly

‫س‬

‫كم‬

‫ى‬

‫ط‬

‫ص‬

‫ضط‬

ً

nor

‫) (ػ‬

‫ؿ‬

‫ع‬

‫ؽ‬

‫) (ؿ‬

‫ػ‬

‫ؽ‬

‫) (ط‬

‫ق‬

‫ط‬

‫ظ‬

‫ؽ‬

‫) (ؽ‬

‫ط‬

‫ػ‬

‫ؿ‬

‫ع‬

‫)(س‬

‫م‬

‫ى‬

‫ص‬

‫ض‬

‫) (ص‬ ‫) (ض‬ ‫) (ظ‬

does not combine with

posteriorly

‫ظ‬

ً

[Relative non-combinability of letters]

90

Chapter [10] I say: Letters are divided into four groups: the first group represents letters that combine with each other in both anterior and posterior positions; the second group covers those letters that do not combine with other letters neither in anterior nor in posterior position; the third designates those letters combinable with other letters anteriorly, but non-combinable posteriorly; and the fourth group embraces letters that combine with some others posteriorly rather than anteriorly. These are the possible divisions of all letters with respect to their combinability, disparate as they are in their characteristics and peculiarities. Letters combinable anteriorly as well as posteriorly are all the [variable] letters, with the exception of those that I am to exclude for you. These are: ‫ ٘ـ ْ َ ي ن ف ً د ة ا‬ٚ ٞ , of which the letter (ً) combine with some letters rather than some others. It does not combine in anterior nor posterior position with these letters: ‫ ; ى ض ص ظ م س‬but it does combine [in both positions] with: ‫ ٘ـ ْ َ ي ن ق ف ؽ ع ط ُ ه م ك ؿ ػ ط‬ٚ ٞ ‫د ة ا‬. The

basic

letters,

sixteen

in

number,

are

these:

‫ ق ؽ ع ظ ط ض ص ُ ى ه م ك ؿ ػ ط س‬, which are intrinsic and never change. Variable letters are not sheer basics, but they occur now as basic now as affixing letters.

92

Basic letters are so designated because some of them are not combinable with one another prepositively nor postpositively; some are combinable prepositively only; while some others are combinable postpositively only. Variables are so denominated owing to the fact that they vary, i.e. can combine with all letters anteriorly and posteriorly, save the letter ً as already stated. Let us now draw up a comprehensive table of non-combinable letters,

letters

combinable

anteriorly,

and

those

combinable

posteriorly; also those letters that are used and that are not used. This is particularly helpful to elucidate the matter at issue, and expose it smoothly without striking snags to its pursuer, who should be keen to attend to it, ponder on it, and seek the advice of those who know better. This table, together with the previous one, portrays all letter potentials of combinables, non-combinables, variables, basics, letters used and not used. And I abridged that considerably such that my version should suffice instead of al-Kind ’s treatise and its longwinded prolixity.84

84

Contrary to ibn Dunayn r’s belief, al-Kind 's treatise is far from prolix; it is a typical example of brevity and depth of investigation.

94

Letters not used are these

Letters used are these

96

(2)

(1)

These letters do combine anteriorly with all letters in column 1

These letters do not combine anteriorly with any letter in column 2

Chapter [11] Encipherment by changing the forms of letters [monoalphabetic simple substitution] is accomplished by substituting for each letter the form of another, such as using the form of the letter (‫ )ق‬to denote the letter (‫)ؽ‬, and (‫ )ن‬to indicate (‫)ك‬, and the like. I have already elaborated this method fully in my book [a - ih b an-n im f ilm] wa

at-tar im, which serves well instead of restatement here. The

algorithm of cryptanalysis thereof has been outlined earlier.

Chapter [12] Encipherment by changing the forms of letters can also be attained by devising a symbolic cipher alphabet, not in the least pertaining to the plaintext letters [substitution by symbol]. These devised forms may be substituted one for each letter and aligned beside one another. However, substitution can be applied to all or only some of the letters. The algorithm of cryptanalysing this method entails the utilization of the [quantitative] expedients mentioned earlier.

98

Chapter [13] I say: If encipherment is done by maintaining the forms of letters but changing their relative positions in relation to the surrounding letters, it is very easy to cryptanalyse. Observing the incoherence of the connection, you realize that letters have been interchanged. You try to restore their original arrangement time and again, and you are in line for hitting the mark. If the letters are devised forms [i.e. employing simple substitution] and interchanged as we have already stated [i.e. by transposition], the way for cryptanalysing them consists in the utilization of the first instrument [i.e. the quantitative expedient]. Once the cryptologue works out the letter orders [of frequency], and places each letter of the alphabet against its devised counterpart in the cryptogram, he interchanges their relative positions reciprocally, shifting the letters backward and forward in relation to one another, until they slot into place and the intended meaning shows up85. Encipherment by changing the position of a letter in relation to itself is done simply by altering the angle of its setup, assuming various angles of presentation, such as writing it upside down or standing on its end. Cryptanalysing this type is so easy that it would never miss the common sense of anyone with perceptive insight. It is to set straight the forms by turning the angles of their setup. Once any of the letters is adjusted, you take that form as a clue to that letter in all places. 85

This is the first indication to a composite cipher achieved by substitution and transposition together.

100

Chapter [14] Encipherment without changing the positions and forms of letters is rendered by embedding [within or between words] additional insignificant letters [nulls], that must not be vowels. The cryptanalysis of this encipherment is reasoned out by calculating the forms and sorting them out. If you find them in excess of the letter orders, try to work out some of them by the first expedients we have previously mentioned. You now look into the letters non of which has yet shown, and seek their identical instances among those already puzzled out. If, by eliminating those letters sought for solution, the context makes sense and word composition straightens, you conclude the letters left out are all nulls-spacers. When the encipherment is done using one null only, in that case you have already solved it ipso facto, since the single null is employed as a word-spacer.

102

Chapter [15] I was asked to cryptanalyse a ciphered message, but found it incompatible with any of the [simple encipherment] divisions. I pondered on it, sorted out its characters against the letters of the alphabet, but it was still impenetrable through utilizing those algorithms. When I dropped certain characters and re-composed the letters they fell into place and turned out well. I did the same elsewhere in the cipher, and words also tied in. So I kept dropping those letters wherever they occurred in the cryptogram, and the thread came right for me. I grasped its content to the end, and realized that the characters dropped were all nulls, and that some letters of the alphabet might be omitted, to be replaced by nulls. That is perhaps the most intricate and problematic encipherment possible. By changing the forms of letters, altering their positions, and at the same time omitting [certain] letters of the alphabet to replace them with null forms, the cipher would be very hard to solve indeed. Nevertheless, and by the good assistance of the Almighty, I managed to solve it straightway.

104

Chapter [16] There is another method of encipherment [without relationship and diffusion] and without changing the forms of letters, their positions or setup, and implemented not by adding nulls, but by omitting letters from the cipher message86. The cryptanalysis here lies in computing the forms; if they are found less in number than the alphabet count, you detect them through the first expedients we have mentioned earlier in this book. Work out some letters of the cryptogram sought for cryptanalysis. If you notice, by seeking their identical counterparts elsewhere therein, the existence of one and the same letter omitted so that the context does not straighten, examine the context closely and weigh up what is [purposely] omitted, as the words and import would, in all likelihood, point to it. For example, instead of writing ‫ ثَُ اهلل‬you write ‫ثٌ اهلل‬, dropping the letter َ. You will soon realize that the context tends to bespeak its existence. To establish the identity of the missing letter, you sample the vacancies against all the letters of the alphabet [one by one]. If, in two or three places of the cipher, the cryptanalyst finds that the same letter is missing, he concludes, in positive assertion, that it has been [deliberately] dropped. Chapter [17] The next type of [simple] encipherment to consider is that where letter forms are changed with relationship and diffusion; namely the letters here are conceptually related by species or by genus. Their relationship by species involves representing the ciphered letter ‫) ( ط‬, for instance, with the symbol of a single bird, say a dove. Their relationship by genus entails designating the same letter ‫ ط‬using the symbol of every bird, as flight is a feature that all birds have in common. This is the most demanding aspect of this type of encipherment. Once it is observed, the rest would be manipulated by the first afore-stated technique.

86

This is the method ibn Dunayn r drops in his discussion of the types of encipherment; see p.13.

106

Chapter [18] In the preceding chapters we have tackled simple ciphers accomplished via the qualitative principle, given that there are just a few simple methods which remain unmentioned. Now let us enter upon composite ciphers here as they also pertain under the qualitative principle. So I say: Ciphers that are intended to be composite could really be a combination of practically all the afore-mentioned simple methods. Composition of [simple] methods tends to give rise to quite a large multitude of ciphers, too many to be addressed all herein. But I mentioned a good few of them to serve as a guideline in deciding on unmentioned cases, if any. al-Kind never attended to composite encipherment except incidentally87 [without dwelling on details]. Whoever attempted to deal with it, other than al-Kind , certainly raved and went astray on that score. I am going to present it to you on the spot, along with the algorithm for its cryptanalysis, by the good assistance of God Almighty.

87

In fact al-Kind ’s treatment of composite encipherment and the algorithms for its cryptanalysis is precise and in conformity with the system of brevity and compactness that he adopts and observes throughout. See his treatise p.142 and p. 164.

108

Chapter [19] To identify a cipher as composite, check it against all types of simple encipherment individually. If, after all, the cipher remains abstruse, it is concluded to be composite; thereupon it should be matched up against the type by which a part of the cryptogram has been worked out, until it makes sense. Bear in mind that the composite type of encipherment is definitely the most complicated; its cryptanalysis for those with insufficient expertise is virtually impossible. Let us proceed to mention some of the types [of composite encipherment], as they are the ultimate in cryptanalysis.

Chapter [20] One type of composite encipherment is to represent each letter of the alphabet by instruments, foods, clothing, jewellery, animals, and such other items listed in the following extensive table of generic names. It is rewarding to always be at pains to study this table over and over again until you exhaust it and comprehend its content perfectly well. We pray to God, the Ever-Nigh, the All-Hearing for that He has guided us to, and from Him we invoke support.

110

of people: someone, whom you know or whom you do not.

b t

of herbs: endive, cress, etc. of dates: varieties of dates, e.g. makt m, barn , etc. of clothing: shirt, turban, etc. of leather: hide (raw or dressed),skin, etc. of iron: swords (varieties of swords, e.g. Damascene, Indian, etc.), steel of wood: sandal, fir, etc.

d

of animals: horse, bull, etc. of gold: varieties of gold, e.g. Egyptian, etc.

r z s

of aromatic plants: lily, lotus, violet, etc. of glass: bottle, cup, etc. of fishes: carp, mackerel, etc. of chess: pawns, individual chess pieces. of brass: brassware, e.g. (drinking) glass, tazza, etc. of regions: specific regions. of birds: hawk, falcon, etc. of deer: gazelle, stag, roe, etc. of perfumes: specific makes and types of scents. of sheep: goats, ewes, rams, lambs, etc.

f q k l m n h w/ Y/

of fruits: apples, quinces, etc. of villages: so-and-so’s village, etc. of books: names of books, e.g. al-'A , al-mu mal f allu a, etc. of milk: types of milk (e.g. colostrum), milk products, etc. of towns: Mosul, Cairo, etc. of stars [and planets]: Sirius, Canopus; Saturn, Jupiter, etc. of vermin, pests, etc.: scorpion, snake, etc. of paper: varieties of paper, e.g. papyrus, stock paper, etc. of jewellery: emerald, diamond, etc.

112

To take up one of these letters, you turn to each genus and to the species thereof relevant to that letter. From that species you name one of its types. For example, to encipher the statement "

" you

may write: "Mr. so-and-so bought colostrum and yoghurt in which he found a scorpion. He bought stockpaper and used it to wrap wet cheese in which he found a sapphire stone. He went with such-andsuch a person somewhere on the outskirts of the town, to buy wet cheese and dates. He put them in a paper, along with some apples. He saw a crystal kohl jar. Together they walked to the judge's village." Our saying "so-and-so"signifies the letter ‫ ;) ( ا‬the words "colostrum" and "yoghurt" indicate the letter ‫( ي‬l) twice; the word "scorpion" stands for the letter ‫( ٘ـ‬h), and so on you proceed to the end by analogy. This is one type of composite encipherment that defies cryptanalysis. The words in between are inane redundancy; the intended purport is sought via the nouns placed against the letters indicative of cryptanalysis. Note that such a cipher can be [and is better] presented in the framework of a dream, a tale, an episode or the like.

114

Chapter [21] Another type of encipherment is the one that is "composed" on numbers. Each letter is designated by its numerical value in the system of is b al- ummal (the arithmetic using decimally-weighted numerical alphabet) the minor and the major. That numerical value having been written indicates the letter it represents. I am about to elucidate the manipulation of letters according to is b al- ummal in both its minor and major divisions, God being willing. 88 The highest degree of concealment using this type is attained in an area-dependent cipher, where letters are rendered in terms of numbers suggestive of what used to be called ar bs, qaf zes and a rs [oldfashioned length units]. Qaf zes and a rs are expressed by upper dots and lower dots respectively. The technique is based on making the cryptogram look like a peasant-farming financial record or something of the kind, simulating an outward aspect of buying, selling, or other similar bargains. Meanwhile you state the number of ar bs placed against the letters, one by one. Letters with upper dots89 serve to represent qaf zes; letters with lower dots90 serve to represent a rs. These should go after ar bs. If you fail to do like we have told you as regards giving the cryptogram the semblance of a financial register of expenditure, an episode about someone, taking, buying or giving, you would incur a raw and unhappy [state of affairs], over and above an unmistakable clue to exposing the intended encipherment. Otherwise, this course of action would be quaint and pretty efficient.

88

See Chapter 25.

89

i.e. the letters (ٞ, ‫ن‬, ‫ي‬, َ, ْ, ً, ‫ع‬, ‫ف‬, ‫ )ص‬according to the numerical-alphabet order, representing the tens places.

90

The rest of letters, i.e. (‫ق‬, ‫ه‬, ُ, ‫د‬, ‫س‬, ‫ؿ‬, ‫م‬, ‫ض‬, ‫ )ظ‬designating the hundreds places, followed by the letter (‫ )ؽ‬in the thousands position.

116

Chapter [22] This type is used to address a person who is in attendance, through finger signaling the numbers [numerical values] corresponding to the respective letters. It is a straightforward method of composition. To express a letter you give its numerical equivalent [in ADWNA] by means of relative finger configurations using the right-hand fingers for the numbers one to hundred, 91 and the left-hand fingers for the numbers hundred to thousand. I shall demonstrate the method for the numbers one to ten to serve as a clear example for representing other numbers. The communicator signals the number one [designating the letter ] by folding his ring finger and mounting his pinkie onto it from behind. He folds the little and ring fingers inwards to represent the number two [for the letter ]. Then he joins the middle finger to both of them to represent the number three [corresponding to ]. He now spreads the little finger whilst keeping the ring and middle fingers folded, thus expressing the number four [i.e. the letter ]. Next he spreads out the ring finger leaving the middle finger folded to represent the number five [i.e. the letter ]. Now he spreads the middle finger whilst keeping the ring finger folded, and so representing the number six [ ]. Thereafter he spreads out all fingers but the pinkie, and that is the number seven [ ]. If he folds the ring finger and the pinkie together, then he is representing the number eight [ ]. With the middle finger also folded, the number nine [ ] is thereby demonstrated. The number ten [ ] is indicated by spreading out all fingers, with the thumb and index made into a loop. After this pattern he proceeds to the number [ninety]; and, now using the left hand, to hundred and to thousand until what he intends to communicate is figured out exactly right.

91

-Rather "ninety"-.

118

Chapter [23] A cipher that is rendered by composing its letters on a chessboard is also addressed to someone who is present. It may be employed to address an absent person in a way I shall tell you without precedent. For instance, to convey to your fellow a private message intended solely for him, you resort to a chessboard and two chessmen: black and white. Putting on an air of play, you leave the piece in the square assigned for the first letter of your message, then you move it to the square assigned for the next letter, then to that meant for the letter that follows, until you exhaust all you have got to say. Your fellow, in turn, does the same until the message is driven home to both of you. It can be outlined as follows:

Example: To convey the word "

" you place the chessman in the

first, sixth, twenty-fourth and eighth squares representing the letter , , and respectively.

120

Chapter [24] Thus to set down a cryptogram opening with the word " ", you write: Two men were on hand and started a game of chess. They took two playing pieces. One of the two guys left his chessman in the first square, then moved it to the twenty-third square twice, thereupon he moved it to the twenty-sixth square. What does that mean? The first square signifies the letter , the twenty-third square denotes the letter square indicates the letter

twice, and the twenty-sixth

. It is after this pattern that you should

reason and identify cases of the kind.

122

Chapter [25] Ciphers rendered by is b al- ummal (the arithmetic utilizing decimally-weighted numerical alphabet) are very easy to cryptanalyse. The algorithm is to place each letter of the alphabet against its Indian decimal numerical equivalent in the system. The following are the shapes of the Indian numerical character units:

When the number one is preceded by a small circle it becomes ten. If the circle is placed before the number two it becomes twenty; and that is how you get the tens orders. If the number one is preceded by two circles it becomes a hundred. If these two circles go prior to the number two, it is then two hundred; and these are the hundreds orders. Likewise, the use of three circles in front of the number one makes it a thousand, and in front of the number two makes it two thousand, etc. Consequently, if you wanted to encipher the statement ( ) by this method, you would have to replace the letters with their corresponding Indian characters, as follows: 10 (ten) ٞ

30 (thirty) ‫ي‬

6 (six) ٚ

5 (five) ‫٘ـ‬

30 (thirty) ‫ي‬

30 (thirty) ‫ي‬

1 (one) ‫ا‬

100

10

80

6

400

30

1

(one hundred)

(ten)

(eighty)

(six)

(four hundred)

(thirty)

(one)

‫ق‬

ٞ

‫ف‬

ٚ

‫د‬

‫ي‬

‫ا‬

This is an example of encipherment using the decimal numerical alphabet. Examine it carefully, and always keep this book within your reach.

124

Chapter [26] One method of composite ciphering is to multiply the numerical value of a letter twofold, threefold, or more— a process which makes the cryptogram even more complicated to solve. For instance, you may write the statement ( ‫ك‬١‫ف‬ٛ‫ّ اٌز‬ٌٟٚ ‫ ) اهلل‬in cipher like this: "‫ه‬

‫ن‬

ٌ‫ل‬

‫ت‬٠

‫ض‬

ً ‫ة‬

‫ن‬

ً

‫ت‬٠

ٞ

ً

ً

‫"ة‬,

increasing the numerical values twofold; the letter ‫ ة‬whose value in ADWNA is 2 represents the letter ‫ ا‬whose value is 1. Similarly, the letter ً (= 60 in ADWNA) is twice the value of the intended ‫ي‬, and so on for the rest of letters and other multiplications. Note how interesting this nicety is.

126

Chapter [27] Encipherment may be accomplished by having the letters of the alphabet rounded up in seven words, specially coined to represent the days of the week, a word apiece. Each letter of the word is further assigned a specific hour of that day, so that you may say: the first hour, the second hour, the third hour, etc., thereby building your cipher as follows: Thursday ٌّ‫ش‬

Wednesday ‫ٌؾظخ‬

Tuesday ‫ه‬ٚ‫ك‬

Monday ‫عجوق‬

Sunday ‫ي‬

Saturday ٓ١‫صٕز‬

Friday ‫ا‬

92

For example, to encipher the phrase ( ‫ )اٌؾّل هلل‬you write: the second hour of the day of Friday, the last hour of the day of Sunday, the second hour of Wednesday, the second hour of Thursday, the first hour of Tuesday, the last hour of Sunday (twice), and the last hour of Wednesday. Our statement "the second hour of Friday" denotes the letter (‫)ا‬, "the last hour of Sunday" indicates the letter (‫)ي‬, and all the other hours signify the rest of the letters. The algorithm of cryptanalysing such ciphers is pursued through the application of the quantitative expedients, namely by computing the order of letter occurrence frequencies. This type of encipherment is most conveniently performed by way of a tale.

92

Most the words in the Arabic original are practically illegible; see p.42.

128

Chapter [28] Ciphers can also be effected by folding a scroll [writing sheet], on which pleats the sender writes whatever they want to convey. Upon unfolding it, writing would look something like dots and strokes on those pleats. The concealment is done by unfurling the scroll and making the dots and strokes into [extra] complete letters until all pleats are covered. Employing the same technique you can also write the message on the back of a sheet which has already been used to write irrelevant material. The dots and letter fragments give the impression that the sheet was folded while still wet, and that the back therefore soiled. The exposure of the intended text is very easy. All you have to do is to re-fold the sheet and read the message.

130

Chapter [29] Encipherment can be implemented by puncturing twenty-eight holes in a sheet of wood, one hole for each letter of the alphabet. The cryptogram is rendered by a thread driven through the intended holes. For example, to write the word ( ‫ )أؽّل‬using this method the thread is driven into the first, sixth, twenty-fourth and eighth holes in succession. Uncovering the message requires correct identification of the letters in relation to their respective threaded holes. You remove the thread from the holes one after another, marking the representative letters in their due positions. Having done that, you read the letters in reverse, starting with the hole from which the thread has been removed last, and ending up with the one from which the thread has been removed first. The same process is also applicable with long cryptograms. This method is illustrated as follows:

132

Chapter [30] Another method of encipherment [using cipher devices] is that which uses beads of different colours substituted for the letters of the alphabet. One way of so enciphering is to designate specific colour beads to represent a letter. The beads are threaded on a string as a rosary, with identical colours separated by a distinctive mark. For example, to represent the proper names ( ‫ )ِؾّل‬and ( ٍٟ‫ )ػ‬using this method, you thread one of the beads designated to the letter (َ), then you thread one of those designated to the letter (‫)ػ‬, followed by one assigned to (َ) again, and another of those designated for (‫)ك‬. Now you carry on with individual beads corresponding to the letters (‫)ع‬, (‫ )ي‬and (ٞ) respectively. Do the same for whatever message you want to convey. The algorithm of solution comes down to perceiving the colour bead of highest recurrence and judging it to be against the letter (‫)ا‬. The next highest would be determined to stand for the letter (‫ ;)ي‬the following one for (َ), and so on, utilizing the [quantitative] expedients stated earlier.

134

Chapter [31] Encipherment may be accomplished by concealing the intended message within another context. The procedure is to take a white sheet of paper, on which to write any form of account. The cipher message is embedded within the context by dispersing it abroad at the beginning, end, or middle of the account, or yet diagonally, splitting the sheet into two triangular parts [according to an agreed rule]. The algorithm of cryptanalysis is very easy by carefully considering the contextual connection, or otherwise setting apart the beginnings, the ends, the middle sections, and the diagonal. On such basis the message bids fairly to come out. Chapter [32] And we have straightforward methods out of composites. One such method is implemented by simulating words [consistently with a set rule], of which the intended letters are made to be the first, the second, the third, etc. For instance, the name ( ٍٟ‫ )ِؾّل ػ‬may be enciphered: ٍٟ‫ىُ فوكَ هافغ ِضً ػ‬١ٍ‫[ ٍٍُ صبٌؼ ػ‬taking the last letter of each word]. This method is within easy reach of the enlightened people of this profession, who consider it carefully. Chapter [33] Another of these methods is to encipher by writing each word of the cryptogram in reverse order. That is easy indeed; to render the word ( ‫)أؽّل‬, for example, in cipher you write ( ‫)كِؾب‬. Cryptanalysis is also very easy, by experimenting with various algorithms, or otherwise trying to read it inversely, if the cryptogram is made up of letters.

136

Chapter [34] This type of encipherment is fulfilled using special numerical calculations based on whole numbers and fractions of quarters and halves. Whole [dinars] are employed to express the units order [i.e. numbers from 1 to 9]; quarters are utilized to indicate the tens order [10-90]; halves for the hundreds [100-900]. Thus, the name ‫أؽّل‬, for example, can be written in cipher: 93

Four [dinars]

Four quarters [of the dinar]

Eight [dinars]

One [dinar]

Cryptanalysing such ciphers requires the cryptologue to be knowledgeable about arithmetic and keen on investigation. To him one dinar means the letter (‫ )ا‬and eight dinars are equivalent to the letter (‫)ػ‬, and like this he proceeds till he exhausts all.

93

ibn Dunayn r's example in the Arabic original does not consist with his above and subsequent explanation; it takes the same lines as simple ADWNA rather than the fraction concept of quarters and halves. It is herein set right, however .

138

Chapter [35] Encipherment can be rendered on an astronomical text demonstrating the conditions of planets [and other celestial bodies]: their motions, distances, periods, durations, mansions, revolutions, and their mutual relationship. The technique is to impart numbers to some planets in terms of distance covered in orbit or in the constellation, or suchlike. For instance, to encipher the name ( ‫ )ِؾّل‬you may write: Having completed forty revolutions, the Moon eclipsed at such and such degrees of such and such constellation. Eight revolutions thence remained. Its motion straightened after it had waned in appearance and faded in colour. Thereafter it moved to Sagittarius and completed forty revolutions thus far. At the end of Sagittarius the planet Venus approached it. Four turns elapsed before its motion evened out in orbit, and its light became as bright as to emulate planets. Our statement "forty revolutions" designates the letter (َ); the "eight revolutions" suggests the letter (‫ ;)ػ‬and so on for the rest. This method of encipherment is complicated, and is ascribed to [the learned] Hermes in his treatise entitled: The war of planets, denoting the generous nature. The cryptanalyst of this cipher should be knowledgeable about arithmetic and astronomy, and should make use of the first statistical principles of calculating the frequencies of letter occurrence. 94 Thus far I have addressed the bulk of simple and composite encipherment types encompassed by the first part of this book, viz. prose ciphers, numerous and diverse as they are, with the good assistance of Almighty God.

94

-As a matter of fact the cryptanalysis of this method has more to do with ADWNA than with the quantitative technique.- (Translator)

140

PART TWO Cryptanalysis of Poetry Ciphers Chapter [36] I am going to provide you with rules that serve for a basis in this highly sought-after art, and also to guide you to the right way therein. I say: Among the tools that are utilized in cryptanalysing cipher rendered in poetry [as well as prose] is a thorough knowledge of the orders of letter frequency of occurrence stated earlier. Frequency of certain forms is, more often than not, an indication of expected letters. The pursuer of this art also need to be familiar with the variable and basic letters, and well-informed in the letter combination and noncombination phenomenon—letters that combine pre-positively (anteriorly), those that combine post-positively (posteriorly), others that combine both pre- and post-positively, and those that do not combine pre-positively nor post-positively. He should also be acquainted with letters that are used and those that are not used, as discussed in PART ONE. 95

Chapter [37] Thereafter, the keynote element of this science is that the cryptologue should be widely conversant with prosody, rhymes, and metrical structures; deeply familiar with the science of poetry; a person of insight into the knack of writing, with capacious memory for committing to heart poetry galore, and skilful and resourceful in cryptography [consequent on long experience and exercise]. Meeting such requisites, the cryptologue is apt to be able to handle the more difficult aspects of poetical ciphers.

95

Chapters 8, 9 & 10.

142

Chapter [38] Prosody has five metrical circles: (1) the circle of the different (al-mu talif), the pentameters and heptameters of which tend to vary; (2) the circle of the consistent (al-mu'talif), the heptameters of which are regular and steadily in tune; (3) the circle of the extraneous (almu talab), whose measures are drawn from the first circle; and (4) the circle of the similar (al-mu tabih), whose constituent meters are marked by correspondence or resemblance; (5) the circle of the harmonious (al-muttafiq), whose pentameters are in agreement. Further expansion on these circles would take long, and is outside our terms of reference. Chapter [39] Poetical meters, according to al- al l [ibn 'A mad al-Far h d ],96 are fifteen in number, supplemented or "redressed" later by 'Ab alasan al-'A fa [Sa d ibn Mas ada al-'Awsa ] 97 with one more meter, the so-called al-mutadarak [=the redresser], thus scaling up the number of meters to sixteen. The poetical meters are: a - aw l, based on the feet of fa lun maf lun; al-mad d, based on the metrons of f il tun f ilun; al-bas , its basic units being mustaf ilun f ilun; al-w fir, which is based on muf alatun; al-k mil, based on mutaf ilun; al-haza , with its feet maf lun [six times]; ar-ra az, mustaf ilun; ar-ramal, f il tun; as-sar , mustaf ilun mustaf ilun maf l tun; al-munsari , mustaf ilun maf l tu mustaf ilun; al- af f, f il tun mustaf ilun f il tun; al-mu ra , maf lun f il tun maf lun; al-muqta ab, maf latu mustaf ilun mustaf ilun; al-mu ta , mustaf ilun f il tun f il tun; al-mutaq rib, based on fa lun. Ab al- asan said: and al-mutad rak, which is based on f ilun. Each of these meters has its own particularities, ramifications, and views on it, which are not of interest for our purpose.

96 97

d. AD 786. d. AD 830.

144

Chapter [40] As for the first [metrical] circle, it has three meters, i.e. a - aw l, al-mad d and al-bas ; the second circle has two meters, i.e. al-w fir and al-k mil; the third has three, i.e. al-haza , ar-ra az and ar-ramal; the fourth has six, i.e. as-sar , al-munsari , al- af f, al-mu ra , al-muqta ab and al-mu ta ; the fifth circle contains one meter, i.e. al-mutaq rib (according to al- al l), or al-mutad rak (according to al-'A fa ). He [The cryptanalyst] must also be familiar with such metrical variations as az-zi f, al- arm, and al- azm. As for az-zi f, it may occur in all meters, and varies with them. Its occurrence is peculiar to the so-called sabab. In a - aw l meter, for example, the ْ of the foot ٌٓٛ‫ فؼ‬can be omitted and ‫ي‬ٛ‫ فؼ‬remains. This phenomenon is called qab . As to al- arm, it is the omission of the first vocalized letter of a [three-letter] foot segment called watid, that occurs at the beginning of a stich. al- azm, on the other hand, concerns the addition [of letters] made at the beginning of a stich, that is taken into consideration in terms of meaning and counted insignificant in terms of poetic scanning.

146

Chapter [41] Rhymes are five, namely al-mutak wis, al-mutar kib, almutad rik, al-mutaw tir, and al-mutar dif. al-Mutak wis is that rhyme in which are found four vocalized letters located between two neutral letters (suk ns). al-Mutar kib is that rhyme in which are found three vocalized letters between two neutral letters. al-Mutad rik is a rhyme in which are found two vocalized letters between two neutrals. al-Mutaw tir of rhymes is the one in which is found one vocalized letter between two neutrals. The last of rhymes is al-mutar dif, in which are found two [consecutive] neutral letters. These rhymes has six letter structures or aw ri , namely the exit, the relief, the basal (‫)ا‬, the linkage, the extraneous, and the rhyme letter. The rhyme letter (or raw ) is that on which the entire poem is built. For example, in the following verse, 98

the letter ‫ ق‬of the word ‫ طوّاق‬is the rhyme letter, and the rhyme of the whole poem is also ‫ق‬. Note that all letters may occur as rhyme letters except for the three vowel letters, i.e. ‫) ( ا‬, ٚ (w/ ), and ٞ (y/ ) which often form the so-called release letters (i l q). Supposing the final word of a stich be ‫ػب‬ٌٛٚ, you see that the rhyme is ‫ع‬ٌٛٚ, the letter ‫ ع‬is the rhyme letter, and the letter ‫ ا‬is for release. The same is true with ِٛ‫ب‬١‫ اٌق‬or ِٛ‫ اٌَال‬in which the rhyme, according to some, is َ‫اٌَال‬, the َ is the rhyme letter, and the ٚ the release letter. Similarly, the rhyme in ٟ‫ اٌوثؼ‬and ٟ‫ اٌغوػ‬is ‫ اٌوثغ‬and ‫اٌغوع‬.

98

See also ibn Adl n's treatment of drawing on prosody and rhyme towards cryptanalysis in his treatise (Volume Two of this series), rules 16 & 17, pp.88-98.

148

The relief letter (or ridf) is a vowel letter ( ‫ا‬, ٚ or ٞ) that occurs immediately before the rhyme letter. It is a common practice [in Arabic poetry] to alternate ٚ with ٞ as relief letters in one poem.99 The basal (or ta's s) is the letter (‫ )ا‬occurring prior to the rhyme letter but one. It is not counted basal if it occurs in a word while the rhyme letter is in another word. Moreover, if the rhyme letter is an implicit noun or part of such a noun, it is possible that the (‫ )ا‬emerging from it be now basal now not. [To be noted is that the basal (‫ )ا‬is a requisite element; once used in a poem, it should be observed throughout.] The linkage letter (or wa l) is a vowel ( ‫ا‬, ٚ or ٞ) resultant [among other things] from fully lengthening the sound value of the rhymeletter diacritic; or the letter ‫٘ـ‬, neutral or vocalized, that follows the rhyme letter. The exit (or ur ) is any one of the vowel letters (‫ا‬, ٚ or ٞ) occasioned by the linkage ‫ ٘ـ‬when fully lengthened in articulation. [Like the basal (‫)ا‬, the exit is a requisite element that, when adopted, should be adhered to throughout the poem without fail.] The extraneous (or da l) is the letter that lies between the basal (‫)ا‬ and the rhyme letter.100

99

-Example:

(Translator) 100

-It is interesting to note that in one rhyme it is possible to have a combination of the basal (‫)ا‬, the extraneous, the rhyme letter, the linkage, and the exit simultaneously. In the following verse: the letter (‫ )ا‬of the word ٗ‫ ِضبعؼ‬is basal, The letter (‫ )ط‬is extraneous, the (‫)ع‬ rhyme letter, the ( ‫ )٘ـ‬linkage, and the (ٚ) that results from lengthening the sound value of the (‫ )٘ـ‬diacritic is the exit. Also possible is a combination of the relief letter, the rhyme letter, the linkage, and the exit. In the following verse: the letter (‫ )ا‬of the word ِٗ‫ ٌضب‬is relief, the (َ) rhyme letter, the ( ‫ )٘ـ‬linkage, and the (ٚ) resultant from lengthening the final (‫ )٘ـ‬exit.(Translator)

150

Rhyme, however, may undergo some flaws or defects; these are: al-'ikf '—the use [in one poem] of two rhyme letters that belong to slightly different points of articulation.101 al-'iqw '—the use in one poem of different rhyme-letter diacritic.102 al-' '—the repetition of rhyme by using two rhyming words that agree in form and meaning (identical rhyme).103 at-ta m n—the state in which the rhyme of one stich, though metrically complete, is dependent upon the following stich so that both lines incorporate an integral whole as far as meaning is concerned.104 as-sin d—the occurrence, in one poem, of a line with a basal (‫)ا‬, and another without one.105 This has many ramifications that are not within our scope here.

101

102

103

104

105

Example:

and

Example:

and

Example:

and

Example:

Example:

and

and

in this verse:

in the following:

in the following lines:

in:

in:

152

Chapter [42] It is those with expertise and discernment in orthography who are the aptest to break ciphers, since they are likely to recognize the mainstream principles underlying proper writing. The letters (‫ )ا‬and (‫)ي‬, forming the [Arabic] definite article ‫=[ اي‬the] as in ً‫=[ اٌوع‬the man], ‫=[ اٌؾغوح‬the room], and the like, are of highest frequency among all letters. The cryptologue should be able to spot two-letter words [bigrams], three-letter words [trigrams] and four-letter words [tetragrams], as these are favourably promotive to cryptanalysis. Pure bigrams are words such as the following: ِِْٓ, َِْٓ, ََ ‫س‬ ‫ ـَـ‬, ََ ‫س‬ ‫ ـُـ‬, َ‫ ُهة‬, ِ‫ َهة‬, ٓ‫ػ‬, َ‫ػي‬, ًََ‫ع‬, ْ‫ُِن‬, َ‫َِل‬, َ‫َِو‬, ّ‫ُِو‬, َ‫ػَل‬, ْ‫ ػُل‬, َُ‫ه‬, ّ‫ثو‬, ّ‫هك‬, ٌّ‫ؽ‬, َ‫ك‬, ‫ل‬٠, ‫أؿ‬, ‫أة‬, ُ‫ػ‬, َ‫أ‬, ُّ‫غ‬, ّ‫عَل‬, ّ‫فل‬. Bigrams, however, may be single letters governed by prepositions such as: ‫ثه‬, ٗ‫ث‬, ‫ٌه‬, ٌٗ, etc. They could also be verbal nouns like َْٗ‫ ص‬and َِْٗ, or even verbs expressing command as ْ‫كَع‬, ْ‫ ٍِو‬and َْ‫لـُ ـ‬. Trigrams are words such as ‫ل‬٠‫ى‬, ٚ‫ػّو‬106, ‫ثىو‬, ‫ػجل‬, ً‫هع‬, ‫كاه‬, ‫ة‬ٛ‫ص‬, ‫ػ‬ٛٔ, ‫ط‬ٌٛ, ‫ؽوف‬, et cetera. Spotting some words of the kind is likely to conduce towards spotting the rest, seeing that they lend significant indications indeed. Thus we have established rules wherewith algorithms of cryptanalysis are fulfilled.

106

Numbered by ibn Dunayn r among 3-letter words in respect of its utterance. The extra final in it he will discuss soon (in Chapter 44).

154

Chapter [43] Upon trying to work out a line of poetry ciphered for you by someone else, you start by counting the number of constituent letters. Should they be found between forty and fifty, the verse would probably belong to the aw l or bas meter in view of the fact that these are of the longest meters. If the number is found to be forty more or less, the meter would probably be one of the whole meters such as: a - aw l, al-mad d, al-bas , al-w fir, al-k mil, perfect ra az, perfect ramal, as-sar , al-munsari , al- af f, or perfect mutaq rib. Thirty letters or thereabouts suggest brachycatalectic mad d, brachycatalectic bas , square k mil, al-w fir, al-haza , ar-ra az, ar-ramal, as-sar , alaf f, al-mu ra , al-muqta ab, al-mu ta or al-mutaq rib. In case the number is found some ten odd, it indicates certain varieties of such short meters as curtailed munsari and ra az. A ten-letter line expresses a variety of ra az. A line of verse might sometimes consist of as few as seven letters like:

[How splendid the moon is. Rain poured down in torrents.]

Such one unit verse is the shortest possible in Arabic poetry; it rhymes with ( ٍٓ‫)َِزفؼ‬. In fact I have here estimated the number to be in the neighborhood of forty because a line of verse, when enciphered, is transcribed according to the standards that are familiar to people. Thus a geminated letter is metrically represented as two letters, while considered one letter in ordinary writing. A line of poetry may undergo some foot variations, in which case the letters so affected take the place of those geminated. Having decided on the number of letters, and pondered deeply over relevant poetic meters, you look closely at the names juxtaposed with each letter of the poetic cipher. The most highly frequent name is held to represent the letter (‫)ا‬, although, in some rare occasions, other letters may take precedence. Of course, by no means do rarities stand for established rules.

156

The letter (‫ )ي‬can be sought by observing in the cipher verse long words beginning with the letter (‫)ا‬. The letter that follows immediately is likely to recur once or twice, and it is positively thought to be the letter (‫)ي‬, since it is far more combinable with (‫ )ا‬than any other letter. Further, a line of verse may contain a signal clue to the definite (‫)اي‬, by observing the occurrence of the letter (‫ )ي‬repeated in words such as: ‫اهلل‬, ً١ٌٍ‫ا‬, ‫ش‬١ٌٍ‫ا‬, ‫ت‬١‫اٌٍج‬, and the like. If you encounter, in a cipher verse, a bigram the first of whose letters has already been identified as (‫)ا‬, you have a good reason to hold that, with the other letter, the bigram may be one of the following (descending from the odds-on probability): ٚ‫أ‬, ‫إم‬, ْ‫إ‬, َ‫ أ‬or ٞ‫أ‬. Conversely, where the first letter is still covert and the other being (‫)ا‬, you can then assume the bigram to be one of these: ‫ِب‬, ‫ب‬٠, ‫ما‬, ‫ شب‬or ‫ؽب‬.107 Other bigrams are yet possible. On the other hand, the letter preceding (‫ )اي‬in one word should, in all probability, be (‫)٘ـ‬108 or ‫ن‬. Having made out most of the highly frequent letters in the cipher, you now turn to those of less frequent occurrence. Thus you guess on heptagrams [seven-letter words] and pentagrams [five-letter words]. Such words should incorporate one or more of the labial letters: ‫ي‬, ‫ة‬, ْ, ٚ, ‫ف‬, [and َ], which are all but inherent in pentagrams and heptagrams. Exceptions are too rare to merit consideration.

107 108

The last two bigrams are actually not all that frequent in usage; they can possibly and more rightly be: ‫٘ب & ال‬. So in the original Arabic manuscript; perhaps (ٚ) or (‫ )ف‬is the correct letter.

158

Chapter [44] Special attention should be paid to the [terminal] letter (‫[ )ا‬added to te letter (ٚ) of plurality] in verbs like: ‫ا‬ٛٔ‫وب‬, ‫ا‬ٚ‫صبه‬, ‫ا‬ٌٛ‫لب‬, ‫ا‬ٛ‫ثبػ‬. Such an (‫)ا‬ is not metrically considered, yet it might pose ambiguity for the cryptanalyst. Also problematic are verbs [with an intrinsic terminal ٚ] such as: ٚ‫غي‬٠, ٚ‫غل‬٠, ٛ‫ؾج‬٠, which might wrongly be written by some with a terminal (‫ )ا‬in the same way as they mistakenly write verbs like ‫ا‬ِٛ‫لب‬ and ‫ا‬ٛٔ‫ وب‬without one. A cryptologue should also keep an eye on terminal hamza's in words like ‫ شبء‬and ‫ثٕبء‬, and be equally heedful of the extra (ٚ) subjoined to the proper name ( ٚ‫ )ػّو‬to differentiate it from another name, i.e. ( ‫)ػّو‬. It might just as well be avoided altogether in ciphered poetry because it can be problematic. However, since poetry is strictly qualified by metrical measures, it would be realized on the spot which of the two names is intended.

Chapter [45] A cryptologue ought to be aware of the letter (‫ )ا‬that is often dropped in writing in the interest of damping the vocalization. In poetry I favour fixing it in names such as: ُ١٘‫[ إثو‬for ُ١٘‫]إثوا‬, ً١‫[ إٍّؼ‬for ً١‫ ]إٍّبػ‬and ‫[ إٍؾك‬for ‫ ]إٍؾبق‬since poetry calls for its retention to put up the meter. Likewise, variants in writing the word ( ‫ )٘الي‬are ( ًٍ٘) and (ً١ٍ٘), which are equally baffling and should therefore be avoided.

160

Chapter [46] He has to be alert to the letters (ٚ) and (ٞ). All-often they occur in mid- and end-positions as diacritically geminated, neutral and vocalized. They also occur following the rhyme in the form of release letters, as has previously been stated. Their occurrence as neutral is profuse; e.g. ٓ٠‫ل‬٠, ٓ١ٕ١‫ػ‬, ٗ١ٌ‫إ‬, ٗ١ٍ‫ػ‬, ‫ف‬ٛ‫ف‬, ‫ف‬ٛ‫ع‬, ‫ف‬ٛ‫ط‬, ‫ى‬ٌٛ and ‫ي‬ٛ‫م‬٠. They may occur at end-positions; e.g. ٟ‫ف‬, ٌٝ‫إ‬, ٍٝ‫ػ‬109, ٛ٘, ٛ‫ف‬, ٌٛ. They may occur geminated; e.g. ‫ّل‬١ٍ, ّٞ ‫ط ك‬, ‫ّك‬ٛ‫ع‬, ‫ّك‬ٛ‫ػ‬, ‫ّك‬ٛ‫ل‬. They may occur following the rhyme letter; e.g. ‫ٍالِب‬, ‫ٍمبِب‬, in which the (‫ )ا‬is for release; and ِٟ‫ ٍال‬, ِٟ‫غال‬, ِٝ‫ٍمب‬, ِٛ‫ٍمب‬, ِٛ‫غال‬, ِٛ‫ٍال‬, where the (َ) is the rhyme letter, and the next for release. When they occur as rhyme letters they may be diacritically neutral (e.g. ُٝٙٔ, ٜ‫ُ٘ل‬, ٞٚ‫م‬, ٚٚ‫م‬, ََٚٛ٘ ); or geminated (e.g. ‫ّب‬٠‫صو‬, ‫ّب‬١َُّ‫ؽ‬, ‫ّب‬١‫اٌٍز‬, ‫ّب‬٠‫اٌٍن‬, ّٚ‫ػل‬, ّٛ‫ ;)ُُٔج‬or vocalized (e.g. ٍٟ‫هػ‬, ٍٟ‫ٍم‬, ْٚ ٍ ‫ػَل‬, ٍٚ‫)غي‬.

Chapter [47] He ought to be particularly familiar with the modes of [medial] hamza; for instance: ‫أفئلح‬, ‫كح‬ُٚ‫ء‬ِٛ, ‫كح‬ٚ‫ِفؤ‬.

109

It is the graphic representation rather than the way of reading that matters by cryptanalytical standards; hence, undotted (ٜ) is considered (ٞ), not a special variant of (‫)ا‬.

162

Chapter [48] He should also be fully acquainted with: 1) The five types of the letter (ٚ), viz. the conjunctive, the circumstantial, the comitative, the potential, and that of oath. Some add to these the so-called "(ٚ) of the number eight". 2) The eight categories of the letter (‫)ف‬, i.e. that of comment and succession; also the (‫ )ف‬that occurs in response to command, prohibition, negation, interrogation, wish, statement, and invocation. 3) The three categories of the letter (‫ ;)ة‬i.e. as a preposition, as a letter for oath-taking, and as a "narrative" letter underlying an implicit noun, such as: 4) The two categories of the letter (‫)ن‬, viz. the superfluous (‫)ن‬, and that governed by a pronoun. 5) The three categories of the letter (‫ ;)ي‬namely as a preposition, as an initial letter, and as an emphatic letter. An additional occurrence of (‫ )ي‬is its use as emphatic in the predicate of (َْ‫)إ‬. 6) The high recurrence of the definite (‫ = اي‬the), as in: ‫٘نا‬ ُ‫إٌَبء‬ٚ ً ُ ‫ =( اٌوع‬This man and the women), ًَ‫ذُ اٌوع‬٠‫هأ‬ َ‫إٌَبء‬ٚ (= I saw the man and the women), and ُ‫ِوهد‬ ِ‫إٌَبء‬ٚ ‫ي‬ ِ ‫ =( ثبٌوعب‬I walked past the men and the women). In fact (‫ )اي‬is a vigorous leading light toward cryptanalysis. However, it can be problematical if preceded by such letters as ٚ, ‫ف‬, ‫ة‬, and superfluous ‫ن‬.

164

Chapter [49] The letter (‫ )د‬occurs in such words as: ‫لبِذ‬, ‫لؼلد‬, ‫ٍبهرب‬, ‫لؼلَرب‬, ‫ضوثَزب‬, َ

‫َذ ٘ب‬ ‫ضَهَث ـْـ‬ ‫ ـ‬, ‫ب‬ٙ‫ِذـ‬ ْ‫ًـــ ـ‬, and ‫د ٘ب‬ ‫أؿ ـم ـْـ‬. When repeated it serves as a robust lead-in to its solution, especially if used immediately next to (‫)اي‬. Chapter [50] You should also see to letters repeated consecutively [doubled letters] such as (‫ي‬/l) in words like: ًٍ‫ ُـقـ‬, ًٍِِ, ًٍِ‫ػ‬, ًٍِ‫ؽ‬, ًٍَ‫ك( ;ف‬/d) in words like: ‫لوكك‬, ‫ِوكك‬, ‫ِشلّك‬, ‫ ;َِلّك‬and (َ/m) in: ُّ٘, ُّ‫ل‬, ُِ‫أ‬, and َُِ‫ ـيَـ‬. Moreover, the occurrence of the letter ( ‫٘ـ‬/h) next to a double (‫ي‬/l) creates an impression that the word sought is likely to be the name of God (‫)اهلل‬. It can also be one of these words: ّ‫اٌٍت‬, ّ‫اٌٍظ‬, ‫ت‬١‫اٌٍج‬, ‫ف‬١‫اٌٍف‬, ً١ٌٍ‫ا‬, ٓ‫اٌٍج‬, ْ‫ب‬٠‫اٌٍـَـ‬, and ‫اًٌـن‬ ّ‫– ـ‬a typical Arab dialect for ٞ‫اٌن‬. Chapter [51] One of the reliable conjectures in cryptanalysis is that the letter between the definite (‫ )اي‬and an (‫ )ا‬is fairly guessed to be َ, ‫ك‬, or ُ, making these words: ‫اٌّآ‬, ‫ اٌلآ‬or ‫اٌشآ‬. In case the (‫ )ا‬is followed by another letter, then you may guess at words like: ً‫إٌب‬, ‫اٌلاه‬, ‫إٌبه‬, ‫اٌؼبه‬, ‫إٌبق‬, ‫اٌَبق‬, and so forth. If the letter next to (‫ )اي‬and the final letter were identical, the word produced would possibly be: ُ‫اٌجبة‬, ٚ‫ا‬ٌٛ‫ا‬, َ‫إٌّب‬, ‫إٌؾبػ‬, ٌ‫( أٌجبة‬plural of ّ‫)ٌُت‬, or suchlike.

166

Chapter [52] Two identical letters after the definite (‫)اي‬, followed by [‫ ا‬plus] another letter, are together guessed to be a word such as ‫اٌّّبى‬, ْ‫( اٌججب‬a Turkish noun), etc. If the two letters were found unidentical, take a guess at: َ‫إٌّب‬, َ‫اٌّمب‬, َ‫اٌغّب‬, ‫اة‬ٛ‫اٌص‬, ‫اٌضواة‬. If the (‫ )ا‬is followed by two other letters, these words are possible options: ‫إٌّبلت‬, ‫اٌّمبٔت‬, َ‫اه‬ٛ‫اٌص‬, ُ‫اٌضواغ‬, and the like. If one letter is there immediately after (‫)اي‬, and two letters next to the other (‫)ا‬, then the possibilities are words such as: ‫اٌغبئت‬, ‫اٌشب٘ل‬, ‫إٌبصت‬, ِٟ‫اٌوا‬, and ٟ‫اٌىبف‬. Chapter [53] Remember that there exist long words which are devoid of the definite (‫)اي‬, such as: ُٙ‫فََٕزلهع‬, ُٙ‫ى‬١‫ىف‬١َ‫ف‬, ٍُّٙ‫ٍَٕزؼ‬, and ْٕٛ٠‫ٍزَزل‬. The cipher verse may also be nonsensical though sound in its meter. Knowledge of metrics often leads to hit the entire verse. The cryptanalyst ought to be conversant with all the possible cases of the verse in hand, such as its metrics, rhyme, language, as well as the predominant trends and variations thereof. Proper familiarity with these requisites, together with the utilization of the afore-mentioned directive indicators to letters and words, and also reasoning in the light of the orders of letter frequency of occurrence, would make favourably for cryptanalysis. You should also be fully aware to the [deliberate] use of undotted or non-combinable letters, the stinted employment of repeated letters, or choosing new or unheard-of verse as the cipher sought for cryptanalysis. Notice that the longer the verse the better for the cryptologue, since in that case it allows for sufficient frequency of letters to be achieved.

168

Chapter [54] Encipherment may be rendered by the poet himself, who can be ignorant of, or otherwise deficiently acquainted with, poetic meters, parsing and the language in general. Subsequently he comes up with a syntactically erroneous and metrically unsound poetry. This kind of cipher is very problematic indeed. The following sample has nothing to do with prosody. To be noted is that much of the poetry of Ab al- At hiya, among others, does not pertain under prosody, too. For example, one says:

Chapter [55] An enciphered line of verse may contain some disincentives in meter and rhyme that prove to the cryptanalyst extremely problematical. The meter peculiarities include the occurrence of the so-called phenomena of al-qab and al-kaff at the end of a verse. This involves curtailing the seven-unit metric foot ٍٓ١‫ ِفبػ‬by at once dropping its fifth unit so that ٍٓ‫ ِفبػ‬remains (qab ), and the seventh unit of the foot so that ً‫ ِفبػ‬remains (kaff). The occurrence of either of them alone is not much of a problem, but their occurrence simultaneously poses a knotty problem to the cryptologue. What augments the difficulty is the occurrence of alm, arm, arm or azm at the beginning of a verse. We have already addressed the arm and azm.110 As for alm, it is like ٌٓٛ‫فؼ‬, if subjected to arm, ٌٓٛ‫ػ‬ remains, which is shifted to ْ‫فعـْـ ـيُـ‬ ‫ ـَـ‬.

110

See Chapter 40.

170

Chapter [56] Besides, the first hemistich of a verse that belongs to the aw l meter may undergo the arm phenomenon, making it into the k mil meter, while the other hemistich remains of the aw l. Example:

(Zuha r ibn Ab Sulm )111 Note that the first hemistich is k mil and the other is aw l. Had the poet said ْ‫ػوِط‬ٚ or ْ‫ رؼوَط‬or ْ‫ فؼوِط‬instead of ْ‫ػوِط‬, the measure would have straightened. But it seems that he has been more attentive to meaning than to measure.

Chapter [57] Bear in mind that you ought to practise on prosody, rhymes and verse composition in order that you keep your hand in, and get the feel of this art that I have given you. As for the cryptanalysis of prose ciphers, use the algorithms propounded towards the end of PART ONE of this book of mine: they should suffice for the one who experiences them, and sure enough they should.

111

This verse is rather attributed to Ku ayyir Azza in praise of the Caliph Umar ibn Abd al- Az z. The exact wording as stated in his poetical corpus (divan) is as follows:

172

Chapter [58] And beware of cryptograms that might have been wrongly enciphered through slipping up on a letter or so. That would prejudice your chances of success in cryptanalysis. Chapter [59] You may encounter cryptograms made up of opaque lines of meaningless verse, whose component words are sheer raving, intended only to establish the meter. The following is a case in point:

It goes without saying the meaninglessness of these lines in the Arabic language. A similar example reads:

Like the preceding lines, this verse is a senseless inanity with sound metrics.

174

Chapter [60] Towards the end of his Second Essay, the Author of the Two Essays on cryptanalysis states that we are destined to follow an intricate path. Nevertheless we shall be able to cope with it to achieve cryptanalysis. This method involves assuming for the letter (‫ ) ا‬a light name such as ( ‫)ظفو‬, whose component letters [‫ظ‬, ‫ ]ه & ف‬are systematically used to represent the letter (‫ )ا‬wherever it occurs in the cryptogram. Then he says that a single symbol is also assumed to at once represent three letters having the same orthographic pattern such as (‫ة‬, ‫د‬, ‫ )س‬or ( ‫ط‬, ‫ػ‬, ‫)ؿ‬, thereby suggesting the method of encipherment but not the algorithm for cryptanalysis. Obviously that is something of an idle talk.112 If the encipherer intends to write a word containing the letter (‫)ة‬, for example, then how would he come to know his own intention so long as this shape ( )suggests (‫ )ة‬and two more letters? A cipher rendered by this method is likely to be equivocal in case it is left over for days and the cipher itself forgotten, let alone the mix-up expected on the part of the cryptanalyst with regard to the orders of letter frequency, considering that the letter (‫) س‬ is of low frequency, the (‫ ة‬b) of medium frequency, and the (‫ د‬t) of higher frequency than (‫)ة‬. On the other hand, assigning three symbols to represent one letter, whilst assigning just one symbol to represent three letters would make the count of letters versus symbols in the cryptogram proportionate. This shows the Author of the Two Essays not well-informed in ciphers.113

112 113

See p.54. On the contrary, the Author of the Two Essays has proved himself to be a seasoned old hand at cryptography and cryptanalysis. This method, which conforms to the latest principles of encipherment, is intended to augment the number of cipher symbols.

176

Chapter [61] Now I am to give you an illustrative example by enciphering the following verse of my own composition, in which the letters ‫ا‬, ‫ ي‬and ٚ are highly frequent, and a few more also circulate:

114

114

From the previous letters one can string together the following verse: - What made the heart grow fonder is the tattler who said: be obedient!-

178

Chapter [62] A line of verse has once been given to me in cipher, of which I contrived to break only the initial words in the first instance. I, however, managed to go through with it later, and came off well. It took me several hours of exertion before it ran full and for good as follows:

115

115

From the letters above one can piece together the following verse: - God knows how much I am besotted with you heart and soul.-

180

For cryptanalysis I started on telling the occurrence frequency of letters right through. Having found thirty-four letters, I concluded that the verse belongs to al-bas al-ma b n meter. It also came home to me that the last word involved the rhyme, which was of the overlapping type as it consisted of three vocalized letters lying between two neutral suk ns. I further perceived that the final letter of the second hemistich is identical with the final letter of the first hemistich. Sorting out the letters according to their order of frequency, I elicited first and foremost the name of God (‫)اهلل‬, utilizing the repetition of the letter (‫ )ي‬in it and the fact that His name all-often goes in front position. I thus labeled the letters ( ‫ا‬, ‫ ي‬and ‫)٘ـ‬. Then I checked the form of the letter (َ) and found it repeated six times, i.e. exceeding in frequency the form of the letters (‫ )ا‬and (‫)ي‬. Therefore I held it would probably be (َ). Switching over to the next frequent form of the letter (ٞ), I found it recurring three times, and I made it (ٞ). Thereupon I took up the tetragram (four-letter word) following the name of God, with the letters (‫)ي‬, (ٞ) and (َ) already known, and sampled such words as: ٍَُ٠, ٍُ‫ؼ‬٠, ٍُ‫ظ‬٠, ٍُ‫ض‬٠, etc. to reserve judgement on it for a while. I now sought the next word—a trigram (three-letter word) the middle letter of which was still covert, the initial and terminal letters being (‫ )ا‬and (ٞ) respectively. By sampling words such as ِٟ‫أ‬, ٟ‫أث‬, ٟٔ‫ أ‬the following got out as possibilities: ( ٚ‫ أ‬ٟ‫ أث‬ٚ‫ أ‬ِٟ‫ظٍُ أ‬٠ ‫اهلل‬ ٟٔ‫)أ‬, which I immediately dismissed as out of the question. Of these words I had my heart set on ٟٔ‫أ‬, promptly turning my assumption to the word ( ٍُ‫ؼ‬٠) instead of ( ٍُ‫ظ‬٠) by extension, and thus sounding meaningful and poetical. The next word was another tetragram beginning and ending with the letter (َ). I guessed at words such as َ‫ِغو‬, َ‫ ِؼي‬and the like, but the context soon lent credence to َ‫ ِغو‬as the apposite choice, and so the word-group read: ( َ‫ ِغو‬ٟٔ‫ؼٍُ أ‬٠ ‫)اهلل‬. Now I looked into the next word which was a trigram ending with the letter (َ). Experimenting with letters in the light of contextual connection, the word ( ُ‫ )ثى‬developed. It was along these lines that cryptanalysis was carried out.

182

Chapter [63] I have [herein] adduced something novel that none else had ever broached before, because al-Kind 's book [treatise] tackles prose simple encipherment only; and Ab

al- asan's book treats poetry

encipherment. Both failed to develop the topic exhaustively in either case.

Chapter [64] And I supplement this [discourse] with lines of verse that embrace the letters of the alphabet [without repetition]. Examples: 1)

116

2) 3) The second hemistich of this last line has another variant:

4)

116

Termed by ibn ad-Durayhim al-Fahlaw cipher alphabet, and by ibn- Adl n one of the regulators or cryptographic keys. See Volume Three, p. 62 and Volume Two, p. 42.

184

Chapter [65] Many verses have been indited to be used in encipherment, and are intended for sustained mental exertion in pursuit of solution. The following are some: 1) 117 2) 3) 4) Of the poetry that is particularly tough to crack is that composed on al-mad d meter in its original, rather than catalectic, version. Another such type is a special reversed form of al-mutaq rib meter (called bad ), not reported to have been ever used in the refined traditional poetry. Chapter [66] Cryptanalysis can be extremely demanding if poetical ciphers are rendered using meters that are not based on the established rules of prosody and uniformity of rhyme. I say: The cryptanalyst is not obliged to puzzle out ciphers intended for mental exertion, just as the grammarian is not bound to enter into intricate issues. Glory be to God, the Lord of grace and favour, the granter of natural gifts and talents. Sufficient unto me is God! Most Excellent is He in Whom I place my trust. No t e: The following verse also encompasses the alphabet: 118

117

118

This verse appears in the treatise on cryptanalysis of poetry by the author of 'Adab a - u ar ', as an illustrative example of the deliberate use in encipherment of letters that never link with each other, but are used as separate disconnected letters. This verse is appended malapropos to the book, probably by the scribe. No reference to it has been made in any of the treatises incorporating the assemblage of cryptology.

186

The Gist Of ibn Dunayn r's Chapters On Cryptanalysis The rhyme structures are six; take them as concisely as can be: LETTERS: raw , wa l, ur , ridf, ta's s, and da l. DIACRITICS: naf , 'i b , mu r , a w, rass, and taw h. The rhyme defects are five; take them as tractably wrought as possible: sin d, ' ', ta m n, 'ikf ', and 'iqw '.  raw : the letter on which the poem is based.  ridf: the pre-raw vowel letter; e.g. , and respectively in , and .  ta's s: the letter ( ) prior to the raw but one; e.g.  da l: the letter between ta's s and raw ; e.g. in

. .

 wa l: one of the vowel letters ( , , ) or the letter , next to the raw .  ur : a post- raw vowel letter; e.g. the final ( ) in ( ).  naf : the vowel point of the letter of wa l.  taw h: the vowel point of the restricted pre-raw letter.  mu r : the vowel point of the raw .  'i b : the vowel point of the unrestricted pre-raw letter.  rass (or ras s): the vowel point of the pre-ta's s.

*

*

188

*

69

1

2

3 4

5

(1) (2) (3) (4) (5)

71

1

)2(

] 1[ 3

5

4

(1) (2) (3)

215 1

(4) (5)

73

2

1 2

3 4

6

5

(1)

237 236 216 215 1 124 3

19 1 126 84 (2) (3) (4) (5)

(6)

216 215 1

75

3

1

(1)

77

4

1

3

2

4

(1)

14 13 11

221 1 114 1 (2) (3) (4)

62

79

5

1 2

3

5

4

(1)

(2)

223 1 (3) (4)

224 1 24

(5)

23

81

225 1

6 3

2

1

4

5 6

(1)

224 1 (2) (3)

224 1

(4)

224 220 1 (5) (6)

224 1

83

‫فصل [‪]7‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬

‫)‪(1‬‬

‫‪55‬‬

‫)‪(2‬‬ ‫)‪(3‬‬ ‫)‪(4‬‬

‫‪58‬‬

‫‪85‬‬

‫‪58‬‬

‫فصل [‪]8‬‬

‫‪1‬‬

‫‪3‬‬

‫‪2‬‬ ‫‪4‬‬

‫‪5‬‬

‫‪6‬‬

‫‪7‬‬ ‫‪8‬‬

‫)‪(1‬‬

‫‪236 2‬‬ ‫‪274 1‬‬

‫‪600‬‬

‫‪600‬‬

‫‪575‬‬ ‫)‪(2‬‬ ‫)‪(3‬‬

‫‪236 1‬‬

‫‪4307‬‬

‫‪437‬‬ ‫)‪(4‬‬

‫‪274 1‬‬ ‫‪360‬‬ ‫‪274 1‬‬

‫‪236 1‬‬

‫)‪(5‬‬ ‫)‪(6‬‬ ‫)‪(7‬‬ ‫)‪(8‬‬

‫‪236 1‬‬ ‫‪275 1‬‬

‫‪87‬‬

‫‪23‬‬

‫فصل [‪]9‬‬

‫‪1‬‬

‫)‪(1‬‬

‫‪89‬‬

91

‫فصل [‪]10‬‬

‫‪1‬‬ ‫‪2‬‬

‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫‪7‬‬

‫‪6‬‬

‫‪8‬‬

‫)‪(1‬‬

‫‪240 1‬‬ ‫)‪(2‬‬

‫)‪(3‬‬

‫)‪(4‬‬

‫)‪(5‬‬

‫‪239 1‬‬

‫)‪(6‬‬

‫)‪(7‬‬ ‫)‪(8‬‬

‫‪239 1‬‬ ‫‪240 1‬‬

‫‪93‬‬

1

2 3 4 5

6

(1) (2) (3)

241 240 238 1

(4) (5) (6)

95

97

‫فصل [‪]11‬‬

‫‪1‬‬

‫فصل [‪]12‬‬

‫‪2‬‬

‫‪3‬‬

‫)‪(1‬‬

‫‪62 1‬‬

‫‪81 1‬‬

‫)‪(2‬‬ ‫)‪(3‬‬

‫ڤ ‪x‬‬ ‫ڤ‬

‫‪99‬‬

‫‪‬‬

]13[ ‫فصل‬ 1 2

3

4 5 6

7

(1) (2) (3) (4)

Substitution Transposition

(5) (6) (7)

101

‫فصل [‪]14‬‬ ‫‪1‬‬

‫‪2‬‬ ‫‪4‬‬

‫‪3‬‬ ‫‪5‬‬

‫‪6‬‬ ‫‪8‬‬

‫‪7‬‬

‫)‪(1‬‬ ‫)‪(2‬‬

‫‪223 222 1‬‬ ‫‪256 230 225‬‬ ‫)‪(3‬‬ ‫)‪(4‬‬ ‫)‪(5‬‬

‫)‪(6‬‬

‫)‪(7‬‬

‫‪57‬‬

‫)‪(8‬‬

‫‪103‬‬

‫فصل [‪]15‬‬ ‫‪1‬‬

‫‪2‬‬

‫)‪(1‬‬ ‫)‪(2‬‬

‫‪105‬‬

16

1

2

3 5

4

17

57

(1) (2)

(3) (4) (5)

107

‫فصل [‪]18‬‬

‫‪1‬‬

‫‪2‬‬

‫‪3‬‬

‫)‪(1‬‬

‫‪234 1‬‬ ‫)‪(2‬‬

‫‪234،224 1‬‬ ‫)‪(3‬‬

‫‪109‬‬

‫فصل [‪]19‬‬ ‫‪2‬‬

‫‪1‬‬

‫فصل [‪]20‬‬

‫)‪(1‬‬ ‫)‪(2‬‬

‫‪111‬‬

113

115

‫فصل [‪]21‬‬

‫‪1‬‬ ‫‪2‬‬

‫‪3‬‬

‫‪5‬‬

‫‪4‬‬

‫‪7‬‬

‫‪6‬‬

‫)‪(1‬‬ ‫)‪(2‬‬

‫‪25‬‬

‫‪67‬‬

‫)‪(3‬‬

‫‪2304‬‬

‫‪50 11‬‬

‫‪92‬‬

‫)‪(4‬‬

‫‪92‬‬

‫‪147.456‬‬ ‫)‪(5‬‬

‫‪92‬‬

‫‪0.7456‬‬ ‫)‪(6‬‬ ‫)‪(7‬‬

‫‪117‬‬

‫فصل [‪]22‬‬

‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬

‫‪4‬‬

‫)‪(1‬‬

‫‪4‬‬

‫)‪(2‬‬ ‫)‪(3‬‬

‫~‬ ‫‪5‬‬

‫)‪(4‬‬

‫‪44 31‬‬

‫‪119‬‬

‫‪5‬‬

‫فصل [‪]23‬‬ ‫‪1‬‬

‫‪2‬‬

‫)‪(1‬‬

‫‪762‬‬

‫)‪(2‬‬

‫‪121‬‬

‫‪331 330 1‬‬

‫فصل [‪]24‬‬

‫‪123‬‬

‫فصل [‪]25‬‬ ‫‪2‬‬

‫‪1‬‬

‫‪3‬‬

‫‪4‬‬

‫)‪(1‬‬ ‫)‪(2‬‬

‫‪332 331 1‬‬

‫)‪(3‬‬

‫‪6 5 4‬‬ ‫‪74 1‬‬

‫)‪(4‬‬

‫‪10 30 6 5 30 30 1‬‬

‫‪400 30 1‬‬

‫‪100 10 80 6‬‬

‫‪74 1‬‬

‫‪125‬‬

‫فصل [‪]26‬‬

‫‪1‬‬

‫)‪(1‬‬

‫‪75 1‬‬

‫‪127‬‬

‫فصل [‪]27‬‬

‫‪1‬‬

‫)‪(1‬‬

‫‪129‬‬

‫فصل [‪]28‬‬ ‫‪1‬‬

‫‪2‬‬

‫‪3‬‬

‫)‪(1‬‬

‫)‪(2‬‬ ‫)‪(3‬‬

‫‪339 1‬‬

‫‪131‬‬

29

1 2

3

(1) (2) (3)

133

‫فصل [‪]30‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪5‬‬

‫‪3‬‬

‫‪4‬‬

‫‪6‬‬

‫‪7‬‬ ‫‪8‬‬

‫‪9‬‬ ‫‪10‬‬

‫)‪(1‬‬ ‫)‪(2‬‬ ‫)‪(3‬‬ ‫)‪(4‬‬ ‫)‪(5‬‬ ‫)‪(6‬‬ ‫)‪(7‬‬ ‫)‪(8‬‬ ‫)‪(9‬‬ ‫)‪(10‬‬

‫‪135‬‬

‫فصل [‪]31‬‬

‫‪1‬‬

‫فصل [‪]32‬‬

‫فصل [‪]33‬‬ ‫‪2‬‬

‫)‪(1‬‬ ‫)‪(2‬‬

‫‪325 1‬‬

‫‪137‬‬

‫فصل [‪]34‬‬

‫‪2‬‬

‫‪1‬‬

‫‪3‬‬

‫‪4‬‬

‫)‪(1‬‬

‫‪1000‬‬

‫)‪(2‬‬

‫)‪(3‬‬ ‫)‪(4‬‬

‫‪139‬‬

‫فصل [‪]35‬‬ ‫‪1‬‬

‫‪2‬‬ ‫‪4‬‬

‫‪3‬‬ ‫‪5‬‬

‫)‪(1‬‬ ‫)‪(2‬‬

‫‪17 15‬‬

‫)‪(3‬‬ ‫)‪(4‬‬

‫‪13‬‬

‫)‪(5‬‬

‫‪141‬‬

‫‪1‬‬

‫فصل [‪]36‬‬ ‫‪2‬‬

‫‪3‬‬

‫فصل [‪]37‬‬ ‫‪4‬‬

‫)‪(1‬‬

‫‪54‬‬

‫)‪(2‬‬ ‫)‪(3‬‬ ‫)‪(4‬‬

‫‪10 9 8‬‬ ‫‪204 1‬‬

‫‪143‬‬

‫فصل [‪]38‬‬

‫‪1‬‬

‫فصل [‪]39‬‬ ‫‪2‬‬

‫‪3‬‬

‫‪4‬‬ ‫‪5‬‬ ‫(‪)3‬‬

‫(‪)5‬‬ ‫(‪)5‬‬

‫‪6‬‬

‫)‪(1‬‬

‫‪178 135 18‬‬ ‫‪52‬‬

‫)‪(2‬‬

‫‪215‬‬ ‫‪1394‬‬

‫‪101 3‬‬

‫‪1974‬‬

‫)‪(3‬‬ ‫)‪(4‬‬ ‫)‪(5‬‬ ‫)‪(6‬‬

‫‪194‬‬

‫‪145‬‬

‫فصل [‪]40‬‬ ‫‪1‬‬

‫‪2‬‬ ‫(‪)2‬‬

‫‪3‬‬

‫‪4‬‬

‫)‪(1‬‬ ‫)‪(2‬‬ ‫)‪(3‬‬ ‫)‪(4‬‬

‫‪187‬‬

‫‪147‬‬

‫‪61‬‬

‫فصل [‪]41‬‬ ‫‪2‬‬

‫‪1‬‬

‫‪3‬‬ ‫‪4‬‬ ‫‪5‬‬

‫‪6‬‬

‫)‪(1‬‬

‫‪7‬‬

‫‪299 297 1‬‬

‫)‪(2‬‬ ‫)‪(3‬‬

‫‪208‬‬ ‫)‪(4‬‬ ‫)‪(5‬‬ ‫)‪(6‬‬

‫‪231 224‬‬

‫‪119‬‬

‫)‪(7‬‬

‫‪149‬‬

2

1 3

4

5

(1) (2) (3) (4)

28 228 228

151

31 29

(5)

1

2

(1)

137 134

227 215

153

74 46

(2)

‫فصل [‪]42‬‬

‫‪1‬‬ ‫‪2‬‬

‫‪3‬‬

‫‪4‬‬

‫‪5‬‬

‫)‪(1‬‬ ‫)‪(2‬‬ ‫)‪(3‬‬ ‫)‪(4‬‬

‫‪44‬‬ ‫)‪(5‬‬

‫‪155‬‬

‫فصل [‪]43‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪3‬‬ ‫‪4‬‬

‫‪5‬‬

‫)‪(1‬‬ ‫)‪(2‬‬

‫)‪(3‬‬

‫‪297 1‬‬ ‫‪185‬‬

‫)‪(4‬‬

‫‪73‬‬

‫‪74‬‬

‫‪1989‬‬ ‫)‪(5‬‬

‫‪157‬‬

1

3

2

4 5

6

(1) (2) (3) (4) (5) (6)

159

‫فصل [‪]44‬‬

‫‪1‬‬

‫فصل [‪]45‬‬ ‫‪2‬‬

‫)‪(1‬‬

‫)‪(2‬‬

‫‪122‬‬

‫‪161‬‬

‫‪46‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪3‬‬

‫‪4‬‬

‫(‪)3‬‬

‫‪5‬‬

‫‪6‬‬

‫فصل [‪]47‬‬

‫)‪(1‬‬ ‫)‪(2‬‬ ‫)‪(3‬‬

‫‪363 1‬‬

‫)‪(4‬‬ ‫)‪(5‬‬ ‫)‪(6‬‬

‫‪123‬‬

‫‪163‬‬

‫فصً [‪]48‬‬ ‫‪2‬‬

‫‪1‬‬

‫‪3‬‬

‫‪4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪7‬‬

‫‪9‬‬

‫‪8‬‬

‫‪10‬‬

‫‪11‬‬

‫)‪(1‬‬

‫‪482 463‬‬

‫)‪(2‬‬ ‫)‪(3‬‬

‫‪223 213‬‬

‫)‪(4‬‬

‫‪151 137‬‬

‫)‪(5‬‬ ‫)‪(6‬‬

‫‪366 2‬‬ ‫‪148 2‬‬

‫‪64 112 1‬‬ ‫‪8 29‬‬

‫‪153 2 3 1‬‬

‫‪330 1‬‬ ‫‪120 2 6 1‬‬

‫‪62 3‬‬

‫‪279‬‬ ‫‪762 388 9‬‬

‫)‪(7‬‬ ‫)‪(8‬‬

‫‪241 233‬‬

‫)‪(9‬‬ ‫)‪(10‬‬

‫‪312 274‬‬

‫)‪(11‬‬

‫‪123‬‬

‫‪165‬‬

‫فصل [‪]49‬‬ ‫‪1‬‬

‫فصل [‪]50‬‬

‫‪2‬‬

‫فصل [‪]51‬‬ ‫‪3‬‬ ‫‪4‬‬

‫)‪(1‬‬

‫‪158 157‬‬

‫)‪(2‬‬

‫‪124‬‬

‫)‪(3‬‬

‫‪124‬‬ ‫)‪(4‬‬

‫‪124‬‬

‫‪167‬‬

‫فصل [‪]52‬‬ ‫‪1‬‬

‫‪2‬‬

‫فصل [‪]53‬‬

‫‪3‬‬ ‫‪4‬‬

‫)‪(1‬‬ ‫)‪(2‬‬ ‫)‪(3‬‬ ‫)‪(4‬‬

‫‪60‬‬

‫‪169‬‬

‫فصل [‪]54‬‬

‫‪1‬‬

‫‪2‬‬

‫فصل [‪]55‬‬

‫‪3‬‬

‫‪4‬‬ ‫‪5‬‬

‫‪6‬‬

‫)‪(1‬‬

‫‪211‬‬

‫‪826‬‬

‫‪321 1‬‬

‫)‪(2‬‬

‫‪128‬‬

‫)‪(3‬‬

‫‪43‬‬

‫)‪(4‬‬ ‫)‪(5‬‬

‫‪71‬‬

‫)‪(6‬‬

‫‪178 43‬‬

‫‪171‬‬

‫‪32 31‬‬

‫فصل [‪]56‬‬ ‫‪2‬‬

‫‪1‬‬

‫‪4‬‬

‫‪3‬‬

‫فصل [‪]57‬‬ ‫‪5‬‬ ‫‪6‬‬

‫)‪(1‬‬

‫‪128‬‬ ‫)‪(2‬‬

‫‪333‬‬ ‫‪128‬‬

‫)‪(3‬‬

‫‪128‬‬

‫)‪(4‬‬

‫‪38‬‬

‫)‪(5‬‬ ‫)‪(6‬‬

‫‪173‬‬

‫فصل [‪]58‬‬ ‫‪1‬‬

‫فصل [‪]59‬‬

‫شـرّافتا ُه وفاض في الخَرْ َبعْطلِ‬

‫لما رمى بالخمطجوب تجرضفت‬ ‫‪2‬‬

‫‪3‬‬

‫‪4‬‬

‫)‪(1‬‬ ‫)‪(2‬‬ ‫)‪(3‬‬

‫)‪(4‬‬

‫‪129‬‬

‫‪175‬‬

]60[ ‫فصل‬ 2

1 3

4

5

6

(1)

115 118

(2)

108 115

(3)

Homophones

(4)

36 1

(5) (6)

82 81

177

‫فصل [‪]61‬‬ ‫‪1‬‬

‫‪2‬‬

‫)‪(1‬‬

‫)‪(2‬‬

‫‪179‬‬

‫فصل [‪]62‬‬

‫‪1‬‬

‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬

‫)‪(1‬‬

‫‪2‬‬ ‫‪3‬‬ ‫‪4‬‬

‫‪181‬‬

1

2

3 4

54

(1) (2) (3) (4)

183

‫فصل [‪]63‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪3‬‬

‫فصل [‪]64‬‬ ‫‪4‬‬

‫‪5‬‬

‫‪6‬‬ ‫‪7‬‬

‫‪8‬‬

‫)‪(1‬‬ ‫)‪(2‬‬

‫‪322‬‬ ‫‪53 48‬‬ ‫‪80‬‬

‫‪81‬‬

‫)‪(3‬‬ ‫)‪(4‬‬

‫‪272،327 1‬‬ ‫‪352‬‬

‫)‪(5‬‬

‫‪169 168 144 1‬‬

‫‪559 1‬‬ ‫‪101‬‬

‫)‪(6‬‬

‫‪353‬‬

‫)‪(7‬‬ ‫)‪(8‬‬

‫‪353‬‬

‫‪185‬‬

‫فصل [‪]65‬‬ ‫‪1‬‬ ‫‪2‬‬

‫‪3‬‬ ‫‪4‬‬

‫‪5‬‬

‫فصل [‪]66‬‬

‫‪6‬‬

‫)‪(1‬‬

‫‪352‬‬

‫)‪(2‬‬

‫‪44 41 173 169‬‬ ‫‪225‬‬ ‫)‪(3‬‬

‫‪353‬‬

‫)‪(4‬‬

‫‪353‬‬

‫)‪(5‬‬

‫‪47‬‬

‫‪74‬‬

‫)‪(6‬‬

‫‪187‬‬

1

2

3

(1)

54 70

54 (2)

205 39 15

72

71

(3)

41 233 221

189

190