Arabic Origins Of Cryptology Vol. 6

Series on Arabic Origins of Cryptology Volume Six

Two Treatises on Cryptanalysis The Two Essays The Treatise of ibn Wahab al-K tib

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

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

Published by KFCRIS & KACST

ii

Acknowledgments The editors of this series greatly appreciate the encouragement they received 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 into English. Many thanks go to Dr. Daham Ismail Alani, the Secretary General of the Scientific Council of KACST, for his efforts to make this publication possible. Special thanks are also due to Dr. M. I. alSuwaiyel and to His Royal Highness Dr. Turki ibn Muhammad ' l Suoud, the former and present vice-Presidents of KACST, for their unceasing encouragement of the project. The typesetting of this bilingual series was realized with skill and dedication by Mr. Ousama Rajab, to whom we express our deepest appreciation. 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-Fahham, the late Prof. Rateb an-Naffakh and, last but not least, to Dr. Fouad Sezgin.

iii

Series on Arabic Origins of Cryptology Volume 6

Translated by Said M. al-Asaad

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

iv

Contents Transliterating Arabic words .......................................................vii Preface ............................................................................................ ix

The First Treatise The Two Essays Chapter 1: Analytical Study of the Two Essays on Cryptanalysis ....................................................... 3 1.1. Preliminary ............................................................................ 5 1.2. The First Essay on the Cryptanalysis of Straightforward Ciphers (Simple Encipherment) ............................................ 6 1.2.1. Requisite Tools for the Cryptanalyst ............................. 7 1.2.2. Algorithms Not Based on Statistical Analysis ............... 8 1.2.3. Algorithms Based on Statistical Analysis ...................... 14 1.2.4. A Practical Example ....................................................... 16 1.2.5. Conclusions ..................................................................... 16 1.3. The Second Essay on the Cryptanalysis of Elaborate and Demanding Ciphers (Advanced Cryptanalysis) .................... 17 • Introduction ............................................................................ 17 1.3.1. Algorithms for Cryptanalysis ......................................... 17 1.3.2. Cryptanalysis of Simple-Substitution Ciphers Using Two Cipherforms for the Letter (‫ )ا‬....................................... 18 1.3.3. Cryptanalysis of Ciphers Rendered Using Forms of Close Frequency ....................................................................... 19 1.3.4. Unanswering Ciphers ...................................................... 21 1.3.5. Annex .............................................................................. 24 1.4. Originality of the Author of the Two Essays ........................ 24

Chapter 2: The Edited Two Essays on Cryptanalysis ..............27 2.1. Editing Methodology ............................................................ 28 2.2. Description of the Manuscript .............................................. 29 v

2.3. The Texts (Arabic Original and English Translation) ........... 33 2.3.1. The First Essay ................................................................ 34 2.3.2. The Second Essay. ........................................................... 56

The Second Treatise The Treatise of ibn Wahab al-K tib Chapter 1: Analytical Study of ibn Wahab’s Treatise .............71 1.1. Preliminary ........................................................................... 73 1.2. Structure of the Treatise ....................................................... 73 • Introduction: Motives for Using Secret Writing .................... 74 1.2.1. Letter Forms and Representations ................................... 74 1.2.2. Methods of Encipherment .............................................. 76 A) By Substitution (at-Tar ama) ................................... 76 B) By Concealment and Transposition (at-Ta miya) ..... 76 1.2.3. Algorithms of Cryptanalysis ...........................................80 - Form Count ....................................................................80 - Statistical Analysis (Frequency of Letters) ................... 80 - Combination of Letters ..................................................81 - Bigrams ..........................................................................81 - The Probable-Word Principle ........................................82 - Outlets of Letters ........................................................... 82 - Word Length ..................................................................85 1.2.4. An Overview of Poetry Cryptanalysis ............................86 1.2.5. An Encipherment Method ................................................87 1.3. Originality of ibn Wahab al-K tib ..........................................87

Chapter 2: ibn Wahab’s Edited Treatise ................................. 89 2.1. Description of the Manuscript .............................................. 90 2.2. ibn Wahab‟s Treatise (Original Arabic Text and English Translation) .................. 93

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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).

‫ب‬ ‫خ‬ ‫ز‬ ‫ض‬ ‫غ‬ ‫ؾ‬ ‫د‬ ‫ر‬ ‫س‬

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.

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‫ص‬ ‫ط‬ ‫ش‬ ‫ظ‬ ‫ض‬ ‫غ‬ ‫ظ‬ ‫ع‬ ‫غ‬ ‫ؾ‬ ‫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.

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Preface This is the sixth 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. The first four books are each dedicated to one treatise. Volume One was devoted to the oldest treatise ever found on cryptanalysis, written by al-Kind , the well-known Arab philosopher, about 1200 years ago. That volume is introduced by a chapter studying the historical background of cryptology as part of the Arab civilization. It studies the factors that led to the early advances of Arab cryptology, highlighting important aspects of the science in relation to other sciences. Volume Two tackles ibn Adl n's treatise al-mu'allaf lil-malik al-'A raf (A manual on cryptanalysis written for King al-A raf). Volume Three deals with ibn ad-Durayhim's treatise Mift al-Kun z f al-Marm z (Key to treasures on clarifying ciphers). Volume Four covers ibn Dunayn r's book Maq id al-Fu l al-Mutar ima an all at-Tar ama (Expositive Chapters on Cryptanalysis). Volume Five, unlike the previous four volumes, includes three treatises on the cryptanalysis of poetry, i.e. those of ibn ab ab , the Author of The Art of Poets, and al- urhum . This volume (Volume Six) consists of the following two treatises: 1. A treatise incorporating the Two Essays on Cryptanalysis by an author known only by these Essays that date back to the 4th or 5th century AH (10th or 11th AD); and 2. The treatise of ibn Wahab al-K tib, who is estimated to have lived during the late 3rd century AH (9th AD) and the better part of the 4th AH (10th AD). To be noted is that the first three volumes of this series are the English translation of Book One of our Arabic book entitled ilm at-ta miya wasti r al-mu amm ind al- Arab (Origins of Arab Cryptography and Cryptanalysis), published by the Arab Academy, Damascus, 1987.

ix

On the other hand, the second three volumes (i.e. Volumes Four, Five and Six) are the English version of Book Two of our afore-stated Arabic original, also published by the Arab Academy, Damascus, 1997. More Arab treatises, dealing mainly with ancient calligraphs, are currently in preparation in both Arabic and English.

*

*

*

Damascus, January 2007

Dr. M. Mrayati Dr. Y. Meer Alam

Dr. M. H. Tayyan

x

The First Treatise The Two Essays on Cryptanalysis

1

2

Chapter 1

Analytical Study of the Two Essays on Cryptanalysis

3

4

1.1. Preliminary The Two Essays constitute something of a compact treatise, addressing simple encipherment that is “easy to cryptanalyse,” as the author describes it, as well as “demanding and highly elaborate ciphers”. The manuscript has the distinction of including cryptological concepts of paramount importance, and also indications that the author was a seasoned old hand at the art of cryptography, who experienced encipherment and cryptanalysis through correspondence with dignitaries and state officials. A chronological approximation shows that the Two Essays must have been written prior to ibn Dunayn r (AD 1187-1229), who makes reference to them in his book Expositive 1 Chapters on Cryptanalysis. The likelihood is that they have been written after ibn ab ab (d. AD 934), on the basis that their author adopts for the term “encipherment” the term “rendering” or “tar ama”, which is the one ibn ab ab uses in his Treatise on Cryptanalysis. This is particularly sensible, given that the terms “encipherment” and “ciphers” were the common terms in use before him. This leads to the conclusion that the Two Essays are supposed to have been written sometime in the 4th and 5th centuries of the Hegira (10th and 11th AD). On the other hand, the identity of the author is still unknown. Except for a single indication by ibn Dunayn r to “the Author of the Two 2 Essays,” no reference whatsoever has been made to him in the sheer bulk of authoritative sources consulted. ibn Dunayn r‟s refrainment from explicitly stating the name of the Author of the Two Essays could be attributed to one of the following two reasons: 1. Some prominent early figures are better known by their major works than by their own names. This phenomenon is not uncommon in the Arabic literature; for example Ab Al al-F ris is widely known as “the author of al-' ”, and Ab al-Baq ' al- Ukbur is dubbed “the author of al-'I r b”. If this argument held good in our case, it would be an evidence of the

1 2

See ibn Dunayn r (Volume Four of this Series), p.54 and p.176. See ibn Dunayn r, p.176.

5

author‟s extensive knowledge in this science, and an expression of the importance of the Two Essays. 2. The Author of the Two Essays was anonymous. Failing to establish his name, ibn Dunayn r opted to identify him with his Two Essays. Apart from that, he refers in his book to other cryptological figures by name, such as al-Kind and ibn ab ab . Although there is not the slightest indication in the Two Essays as to the motive for writing them, the odds are that they have been drawn up at the instance of a then influential person, who seems to appreciate the use of cryptography in the state affairs. This tone is demonstrated towards the end of the First Essay, when the author cautions professional experts “in this invaluable science” against downgrading its worthy applications to unproductive ends, such as using it for fun and betting on trifles that serve no purpose, instead of employing it in pursuit of honourable objectives. This statement, in addition to the ciphertext given in the First Essay as a practical example, reflects the thriving activity of encipherment, and shows how far it was enjoying a boost in circulation at the time of the Author.

1.2. The First Essay on the Cryptanalysis of Straightforward Ciphers (Simple Encipherment)

This essay opens right with the words: “I tell you, may God 3 shepherd your steps” . By this the Author may be addressing himself to every reader in the tradition of early Arab writers, not that the discourse might be directed to the one for whom the Two Essays have been written. This practice, if anything, is not unfamiliar; it was observed before by al-Kind who addressed his treatise to Ab al4 Abb s ibn al-Mu ta im, and by ibn Adl n later addressing his work 5 to the King al-'A raf. However, this possibility is rather discounted 3

See p. 34. See al-Kind (Volume One of this series), p.118. 5 See ibn Adl n (Volume Two of this series), p.29. 4

6

by the fact that the formula of address used has nothing special, and falls short of the big honorific openings that are particularly cut out for personalities of high status.

1.2.1. Requisite Tools for the Cryptanalyst The Author turns straight to discuss the tools necessary for the cryptanalyst, and the attributes characteristic of him/her. These are: 1) Exercising the utmost degree of patience, and showing a real sense of commitment. 2) Quitting idleness and slackness. 3) Poring over the cipher symbols from beginning to end, in the interests of readjusting and learning by heart. 4) Applying the mind with wholehearted dedication. (This is a principle of special importance, probably unprecedented.) 5) Temporarily putting off elaborate ciphers to refresh the spirit before making an attempt again. 6) Familiarity with the algorithms typically utilized in cryptanalysing simple ciphers. If cryptanalysis proves to be impossible by the above, the following tools should be observed: 7) Acquaintance with the principles of elaborate encipherment that is impervious to solution. 8) Cryptanalysis of insolvable ciphers that do not seem to respond except by sheer coincidence, i.e. through an inadvertent omission of the encipherer. As the author puts it: “… possibly as a result of an error on the part of the cipherer. A cryptologue with cogent argument, sound intuition and genuine insight can 6 stand a chance of cracking it in consequence.” This is a major principle widely used in cryptanalysis; it is based on tracing encipherment errors and turning them to good account towards cryptanalysis. (To the best of our knowledge, this principle is also unprecedented, and peculiar to the Author of the Two Essays.) 9) The cipher length: The ciphertext “should be ten lines at the minimum, because less than that is nothing if not wearing and 6

See p. 34.

7

literally exacting. Letters, if not used frequently enough, would 7 turn out futile.” Determining the technique of processing or the algorithm of cryptanalysis is dependent on the length of the cryptogram. Unless the cryptogram exceeds ten lines (i.e. 400-500 letters), the statistical law of letter frequency would no longer be applicable to it, and the cryptogram is thus rendered quite difficult to handle by these quantitative expedients. In fact this reflection goes to show the Author‟s extensive grasp of the principles of encipherment in general, and letter frequencies and their relative connection in particular. To be noted is that al-Kind (d. AD 873) was the first to mention this statistical law. He says: “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 8 in cryptanalysing the letters.” Later on, ibn Adl n (d. AD 1268) came to determine the approximate minimum number of letters a ciphertext should include for successful cryptanalysis. “The length of the text to be cryptanalysed,” he argues, “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 9 certain cases.”

1.2.2. Algorithms Not Based on Statistical Analysis There are a number of simple algorithms for cryptanalysis that are more concerned with practice and experience than statistical analysis. Of these algorithms the Author of the Two Essays states the following: 7

See p. 36. See al-Kind ‟s treatise (Volume One of this series), pp.124-126. 9 See ibn Adl n‟s treatise (Volume Two of this series), p.52. 8

8

(1) Separation of letters with no spacers between words, such as: ٍٟ‫( ِؽّذ ع‬plain) = ٞ ‫( َ غ َ د ع ي‬cipher) (2) Transposition within each word, e.g. ٍٟ‫( ِؽّذ ع‬plain) = ‫ ي ع‬ٞ َ ‫( د َ غ‬cipher) 321 4321

1 2 3 1234

The numbers indicate the relative positions of letters within each word. (3) Concealment by letters: operative and inoperative letters, i.e. by introducing insignificant letters (nulls) in between the ciphertext letters, e.g. (plain) = (cipher) (4) Reversal of text with letters broken up, so that reading is conducted from left to right: (plain)

(cipher)

987654321

1 2 3 4 5 6 7 8

9

(5) Transposition of letters by splitting them into two lines, starting with the first. Example: Plain

Cipher =

(6) Concealment of letters within words; only one letter of each word (e.g. the first, second, third, fourth, or the last) is the target letter. Example: = (7) Concealment within words, the starting point being the edge of a page or the first letter of each line in it, so that these letters together form a group of words making up the cryptogram. Some later authors have taken a special interest in this kind of writing, and so compiled books on various fields such that different information comes out pursuant to the way pages are read: if a page is read widthways, a text in one field of science emerges; if it is read lengthways ab initio, another field of science develops; if read lengthways ab intra from a certain point, a third field of science appears; and so on. A typical

9

example on hand thereupon is a book entitled: Unw n a - araf al-W f (The Quintessence of Distinction) by 'Ism l ibn Ab Bakr al-Muqri' (d. AH 837/ AD 1434), covering the five sciences of Islamic jurisprudence, history, syntax, prosody and rhymes. Each page is divided into columns; reading it widthways, irrespective of the columns, emanates jurisprudence; the right-hand column concerns prosody; the next columns are on history, syntax and rhymes respectively. A sample page of the book is here quoted just for illustration. (8) Concealment by changing especially the letters of the highest frequency (i.e. ‫ا‬, ‫ي‬, َ, ْ, ‫٘ـ‬, ٞ), of which two, three, four, or five letters may be concealed. For instance, by concealing the two letters: ‫ )ٱ =( ا‬and ‫=( ي‬3), the cleartext ‫ ؼسثٕا اهلل‬becomes in cipher: ‫ ٘ـ‬3 3 ْ ‫ ٱ ٱ غ ط ب‬.

(9) Encipherment by arranging the letters of the alphabet in two aligned arrays as follows: ‫ط ش ظ‬ ‫ع ظ غ ض‬

‫ر س ص‬ ‫ق ؾ غ‬

‫د‬ ‫ن‬

‫ؾ‬ ‫ي‬

‫غ‬ َ

‫ض‬ ْ

‫ا ب خ ز‬ ‫ ٘ـ‬ٚ ‫ ال‬ٞ

and substituting reciprocally within the pairs ( ‫ ا‬and ٞ), ( ‫ ب‬and ‫)ال‬, ( ‫ خ‬and ٚ), etc. For example: ٍٟ‫( ِؽّذ ع‬plain) = ‫( غ َ غ ن ط ؾ ا‬cipher)

10

‫وعاخ اال اٌر‪ٛ‬ظ‪ ٗ١‬وم‪ٌٛ‬ه اٌععُ ـاٌّ‪ُ١‬‬

‫عش‪ٚ‬ض شُ اٌسش‪٠‬ع ‪ِ ٛ٘ٚ‬سرفعٍٓ ِسرفعً‬ ‫عش‬ ‫‪ٚ‬‬ ‫ض‬ ‫شُ‬ ‫ا‬ ‫ي‬ ‫ط‬ ‫س‬ ‫‪ٞ‬‬ ‫ع‬ ‫‪ٚ‬‬ ‫٘‪ٛ‬‬ ‫َ‬ ‫ط‬ ‫خ‬ ‫ؾ‬ ‫ع‬ ‫ي‬ ‫ْ‬ ‫َ‬ ‫ط‬ ‫خ‬ ‫ـعً‬

‫وزٌه‬ ‫‪ٚ‬عاض‪ٛ‬ساء‬ ‫عشـح‬ ‫‪ٚ‬لطع رٌه ظاص ‪ ٌٛٚ‬لع‪ٝ‬‬ ‫ظع‪١‬ؿ ‪ ِٓٚ‬دخً ـ‪ ٟ‬ذط‪ٛ‬ع‬ ‫شُ إْ صاِ‪ٙ‬ا ٌُ ‪٠‬صػ‬ ‫اال‪ٚ‬ا‬ ‫اٌعطش‬ ‫ـ‪ٟ‬‬ ‫أٗ‬ ‫ٌ‪ٍ١‬ح اٌؽاد‪ٚ ٞ‬اٌعطش‪ ٓ٠‬ال ‪٠‬خش‬ ‫س‪ٛ‬اء واْ ـ‪ ٟ‬ذط‪ٛ‬ع أ‪ٚ‬‬ ‫اٌّعرىؿ‬ ‫عٓ‬ ‫س‪ٚ‬اؼٗ‬ ‫‪٠‬عة عٍ‪ ٗ١‬اٌخش‪ٚ‬ض ٌؽ‪١‬ط ال ‪ّ٠‬ىٓ‬

‫عٍ‪ٚ ٗ١‬ال تطالْ ‪ٚ‬اْ خشض‬ ‫‪ ٌٛٚ‬خشض ِٓ اٌّسعذ اٌ‪ٝ‬‬ ‫اٌخاسظح‬ ‫إٌّاسج‬ ‫٘‪ٛ‬‬ ‫ِ‪ٚ ٌٝٛ‬ص‪ٚ‬ض ‪ٌٍّٚ‬ىاذة أْ ‪٠‬ش‬ ‫‪ٟ٘ٚ‬‬ ‫اٌ‪ٛ‬ظ‪ٛ‬ب‬ ‫سث‪ٍٙ١‬ا‬ ‫أدائٗ‬ ‫عٍ‪ٗ١‬‬ ‫ذ‪ٛ‬ظٗ‬ ‫‪ٕ٠‬صشؾ‬ ‫اٌؽىُ تً‬ ‫ـ‪ٟ‬‬ ‫سو‪ٛ‬ب‬ ‫عالً ‪٠ٚ‬عة ـ‪ٗ١‬‬ ‫الصَ ٌٍّشذذ ‪٠ٚ‬أذ‪ ٟ‬اٌصث‪ٟ‬‬ ‫ٔ‪١‬اتح عٕٗ ‪ٚ‬اٌصؽ‪١‬ػ اْ ِا‬ ‫اٌ‪ٌٟٛ‬‬ ‫ِاي‬ ‫ِٓ‬ ‫سائش ِا ‪٠‬ؽراض إٌ‪ ِٓ ٗ١‬صا‬ ‫‪ٚ‬ال ِذ‬ ‫اٌ‪ٛ‬ظ‪ٛ‬ب‬ ‫ذعزس‬ ‫وأد‬ ‫ـئْ‬ ‫ـعٍ‪ٙ‬ا‬

‫تص‪ َٛ‬أ‪ ٚ‬تشوعاخ‬ ‫‪ٚ‬ادا (ِرٗ ِسرؽثح ‪ٚ‬األ‪٠‬اَ اٌث‪١‬ط ‪ٚ‬سرح ِٓ ض‪ٛ‬اي ‪)ِٓٚ‬أصثػ ِرط‪ٛ‬عا‬ ‫‪٘ٚ‬زا‬ ‫رٌه‬ ‫‪٠‬ع‪ٛ‬ص‬ ‫ل‪ً١‬‬ ‫‪ٚ‬‬ ‫ـش‪٠‬عـح اٌص‪ َٛ‬أ‪ ٚ‬اٌصالج ؼشَ اٌمطع عٍ‪ٗ١‬‬ ‫ال ‪٠‬ؽً‬ ‫ذطش‪٠‬ك‬ ‫اٌؽــــــط ‪ٚ‬اٌعّشج ٌضِٗ اذّاِ‪ٙ‬ا ‪ٚ‬اٌص‪ َٛ‬ـ‪ َٛ٠ ٟ‬ـطش ‪ ٚ‬اظؽ‪ٚ ٝ‬أ‪٠‬اَ‬ ‫إال‬ ‫‪ٚ‬لد‬ ‫وً‬ ‫‪٠( ٚ‬ىشٖ ص‪ َٛ‬اٌعّعح ‪ٚ‬ؼذٖ (تاب االعرىاؾ) ٘‪ ِٓ ٛ‬إٌّذ(‪ٚ‬تاخ ‪٠ٚ‬سرؽة‬ ‫أٔ‪ٙ‬ا‬ ‫‪٠‬ش‪ٜ‬‬ ‫خـــــش ِٓ سِعاْ أـعً ٌطٍة ٌ‪ٍ١‬ح اٌمذس ‪ِٚ‬اصاي اٌطاـع‪ٟ‬‬ ‫واْ ِٕٗ تص‪ َٛ‬ـ‪ ٛٙ‬أـعً‬ ‫‪ِٚ‬ا‬ ‫ض (ِٕ‪ٙ‬ا ‪ٍ١ٌ ِٓٚ‬ح اٌصاٌس ‪ٚ‬اٌعطش‪ٚ ٓ٠‬ضشطٗ إٌ‪١‬ح‬ ‫أ‪ٚ‬ظثد‬ ‫ـئْ‬ ‫عٍ‪ٙ١‬ا‬ ‫تش‬ ‫ـ‪ٔ(ٟ‬زس ‪ٔ ِٓٚ‬زس اعرىاؾ ِذج ِرراتعح ٌضِٗ أْ ‪٠‬صا‬ ‫‪ٛ٘ٚ‬‬ ‫‪ٚ‬خشض‬ ‫اٌثشاص‬ ‫إٌ‪ٝ‬‬ ‫غ‬ ‫ؼً واٌّشض ‪ٚ‬االوً ‪ٚ‬اٌطشب ‪ٚ‬اٌش‪ٚ‬ا‬ ‫ض‪ٛ‬ا‬ ‫ؼشض‬ ‫ـال‬ ‫رٌه‬ ‫أضثٗ‬ ‫‪ِٚ‬ا‬ ‫ص‪ٚ‬ا(ي االعرىاؾ عٕٗ ا‪ ٚ‬عذج ا‪ ٚ‬اداء ض‪ٙ‬ادج ذع‪ٕ١‬د‬ ‫ـ‪ٗ١‬‬ ‫‪ٚ‬تطً‬ ‫اٌرراتع‬ ‫ؼىُ‬ ‫أفه‬ ‫أِش ٌٗ ِٕٗ تذ واٌض‪٠‬اسج ‪ٚ‬صالج اٌعّعح‬ ‫ـ‪ٟ‬‬ ‫واْ ـ‪ ٟ‬ؼذ اٌّسعذ ال ‪٠‬عش ‪ٚ‬رٌه‬ ‫‪ِٚ‬ا‬ ‫أ‪ ٚ‬ظاِع اِشأذٗ عاِذا تطً اعرىاـٗ‬ ‫اٌثش‬ ‫ل‪ٛ‬ي‬ ‫تؽ‪١‬ش‬ ‫ٍِّ‪ٛ‬ن‬ ‫ـر‪ٝ‬‬ ‫‪ٚ‬اٌّشا ل‪ ٟ‬عٍ‪ ٝ‬تاتٗ ‪ٔٚ‬ؽ‪٘ٛ‬ا ‪ٚ‬ال ذعرىؿ اِشأج ‪ٚ‬ال‬ ‫اٌعّشج وزٌه‬ ‫أْ‬ ‫اٌصؽ‪١‬ػ‬ ‫‪ٚ‬‬ ‫وـــة رٌه تال ارْ ( تاب اٌؽؽط ) ٘‪ ٛ‬ـشض‬ ‫تّا‬ ‫‪٠‬أخ‬ ‫ٌُ‬ ‫اإلٔساْ‬ ‫ِاداَ‬ ‫ذسا‪٠‬شٖ ـ‪ ٟ‬وص‪١‬ش ِٓ األؼىاَ ‪ٚ‬سٕزوش٘ا ‪ٚ‬‬ ‫تاطً‬ ‫تؽ‪١‬شٖ‬ ‫اؼشاِٗ‬ ‫اْ‬ ‫ٔم‪ٛ‬ي‬ ‫ـشظ‪ٙ‬ا ال ‪٠‬ع‪ٛ‬ص ٌٗ أْ ‪٠‬ؽشَ تؽ‪١‬شٖ ‪ٚ‬ال‬ ‫ـ‪ٟ‬‬ ‫٘‪ِ ٛ‬سٍُ تاٌػ ؼش ِسرط‪١‬ع‬ ‫ِٓ‬ ‫ؼشاِٗ إٌ‪ ٝ‬اٌفشض ‪ٚ‬ال ‪٠‬عثاْ اال عٍ‪ٝ‬‬ ‫ا‬ ‫ارا ؼٍثد ـ‪ ٗ١‬اٌسالِح ‪ٚ‬اٌؽط‬ ‫رٌه‬ ‫عٍ‪ ٝ‬االظ‪ٙ‬ش إرا ٌُ ‪٠‬عذ طش‪٠‬ما ‪ٚ‬‬ ‫ٌثؽش‬ ‫ؼ‪١‬ش ِّ‪١‬ض ـٍ‪ ٗ١ٌٛ‬اْ ‪٠‬ؽشَ‬ ‫واْ‬ ‫‪٠‬سرط‪١‬عٗ ‪ ٗ٠ٕٛ٠ٚ‬اٌ‪ ٌٟٛ‬ـّا ععض عٕٗ ‪ِٓٚ‬‬ ‫تّا‬ ‫ٔفمح اٌؽعش ‪٠‬صشؾ‬ ‫اعٍ‪ٝ‬‬ ‫ص‪٠‬ذ‬ ‫‪ٔٚ‬فمح‬ ‫‪ٚ‬وفاسج‬ ‫اٌؽط‬ ‫ِؤٔح‬ ‫‪٠‬ؽراض إٌ‪ِٓ ٗ١‬‬ ‫‪ٚ‬اظذا‬ ‫صؽ‪١‬ؽا‬ ‫تٕفسٗ‬ ‫لائّا‬ ‫االسرطاعح ٔ‪ٛ‬عاْ اؼذّ٘ا ِٓ واْ‬ ‫شُ‬ ‫اٌّصً‬ ‫شّٓ‬ ‫عٓ‬ ‫ل‪ّ١‬رٗ‬ ‫سـعد‬ ‫‪ٔٚ‬ؽ‪ ٖٛ‬ر٘اتا ‪ٚ‬ا‪٠‬اتا تصّٓ اٌّصً ـاْ‬ ‫د‬ ‫‪ٍ٠‬ضَ‬ ‫‪ٔٚ‬فمح‬ ‫د‪ٓ٠‬‬ ‫عٓ‬ ‫ص‪٠‬ذا‬ ‫ٌٍ‪ٛ‬ظ‪ٛ‬ب عٍ‪ ٗ١‬ؼر‪٠ ٝ‬ى‪ِ ْٛ‬ا ‪٠‬صشـٗ‬ ‫خً‬ ‫اٌّط‪ٚ ٟ‬اٌسم‪ُ١‬‬ ‫عٍ‪ٗ١‬‬ ‫‪٠‬طك‬ ‫الٔٗ‬ ‫ِٕٗ عٍ‪ِ ٝ‬ساـح اٌمصش ـالتذ ِٓ ساؼٍح‬ ‫ِىح‬

‫‪A sample page of the book Unw n a - araf al-W f‬‬

‫‪11‬‬

‫وعاخ‬ ‫ا‬ ‫ي‬ ‫ا‬ ‫ا‬ ‫ي‬ ‫خ‬ ‫‪ٚ‬‬ ‫ض‬ ‫‪ٗ٠‬‬ ‫ن‬ ‫ل‪ٛ‬ي‬ ‫ن‬ ‫ا‬ ‫ي‬ ‫ع‬ ‫ض‬ ‫َ‬ ‫ؾ‬ ‫ا‬ ‫ي‬ ‫َ‬ ‫‪ُ٠‬‬

(10) Substituting some letters of the alphabet according to a set key, such as that stated by the Author: “Then consider the 10 key often used in our days, i.e. ( ُ‫عصثى‬٠ ً٘ ٚ‫”)أ‬. Encipherment is done by substitution reciprocally only within these pairs: ( ‫ ا‬and ٚ), ( ‫ ٘ـ‬and ‫)ي‬, ( ٞ and ‫)ع‬, ( ‫ ظ‬and ‫)ب‬, and ( ‫ ن‬and َ); all other letters of the alphabet remain unchanged: ‫ن‬ َ

‫ظ‬ ‫ب‬

ٞ ‫ع‬

‫٘ـ‬ ‫ي‬

‫ا‬ ٚ

Thus, the name ٍٟ‫ ِؽّذ ع‬is ciphered: ‫ ٘ـ ع‬ٞ ‫ن غ ن د‬. (11) Encipherment utilizing the arithmetic of decimally-weighted numerical alphabet (ADWNA), giving the cryptogram the appearance of a financial register (accounting sheet). The Author invokes an example demonstrating a method for expressing the tens, hundreds and thousands in order to conceal the ADWNA numbers. He says: “Encipherment may be predicated on a special arithmetic [ADWNA]. You arrange the numbers denoting units from one to nine using whole [dinars]; under the tens you write fractions of quarters, and under the hundreds write fractions of halves. Under the thousand (standing for the letter ‫ )غ‬you write fractions of 11 halves and quarters.” This can be represented as follows:

10 11

See p. 38. See p. 38.

12

Nine ‫غ‬ 9 dinar ‫ظ‬ 90

Eight Seven ‫غ‬ ‫ص‬ 8 7 dinar dinar ‫ؾ‬ 80

‫ع‬ 70

Six ٚ 6 dinar

Five ‫٘ـ‬ 5 dinar

‫ط‬ 60

ْ 50

Four Three Two ‫د‬ ‫ض‬ ‫ب‬ 4 3 2 dinar dinar dinar َ 40

‫ي‬ 30

‫ن‬ 20

One ‫أ‬ 1 dinar ٞ 10

quarter quarter quarter quarter quarter quarter quarter quarter quarter

‫ظ‬ 900 half

‫ض‬ 800 half

‫ر‬ 700 half

‫ؾ‬ 600 half

‫ز‬ 500 half

‫خ‬ 400 half

‫ش‬ 300 half

‫س‬ 200 half

‫ق‬ 100 half ‫غ‬ 1000

quarter and half

Accordingly, the name ٍٟ‫أؼّذ تٓ ع‬, for instance, can be enciphered: ٞ one

‫ي‬ three

‫ع‬ seven

ْ five

‫ب‬ two

‫د‬ four

َ four

‫غ‬ eight

‫أ‬ one

quarter quarters quarters quarters dinars dinars quarters dinars

dinar

It is evident that ibn Dunayn r has taken this method from the Two Essays, and included it in his Expositive Chapters on Cryptanalysis 12 anonymously of any ascription.

12

See ibn Dunayn r's book (Vol. 4 of this series), p.138.

13

1.2.3. Algorithms Based on Statistical Analysis In case the method of encipherment used turns out to be none of the afore-mentioned or kindred ciphering methods, it is then supposed to be simple encipherment. Cryptanalysis is conducted through the following steps: 1. Counting up the cipher forms meticulously, “taking special care of the forms that are close in shape. Two closely similar forms may be mistaken for one form, such as: ‫ ع عـ‬or ‫ ع ع‬or the like; for in 13 that case cryptanalysis would become extremely taxing.” Here three cases can be distinguished: (a) “If the count is found to be twenty-eight forms, you decide that each letter of the alphabet has been assigned a single form, with (‫ )ال‬deemed as two individual letters [not as a 14 distinctive letter]. (b) “If the count adds up to twenty-nine forms, then (‫ )ال‬is 15 included as a stand-alone letter, too.” (c) “If, however, it amounts to thirty forms, you conclude that 16 a space recurs between words.” 2. Sorting out the cipherforms: “Then sort the forms out. The sorting process involves taking up the first form, computing its frequency of occurrence in the cipher, and affixing the frequency number to 17 it. Subsequent patterns are handled alike.” 3. Endorsement of cipherforms: “Next, you mull the forms over, and endorse them for good by marking them each with a point under 18 the number.” 4. “Seek for a cipherform of higher frequency than all other forms, making it the letter (‫ )ا‬in case the cryptogram is comprised of 19 twenty-nine letters.”

13

See See 15 See 16 See 17 See 18 See 19 See 14

p. 40. p. 40. p. 40. p. 40. p. 40. p. 40. p. 40.

14

5. Recording the letters of the alphabet against their respective cryptanalysed counterparts in tabular form, according to their relative frequencies. 6. Hunting for an adjacent element that seems to recur often with the most frequent letter, and approximates it in number, making it the letter (‫)ي‬. You can verify that by seeking for both forms together and consecutively to develop the definite article (‫)اي‬. 7. “If the cipher uses word-spacers [30 different cipherforms], you are getting along well towards cryptanalysis, given the fact that the spacer has a higher frequency than both (‫ )أ‬and (‫)ي‬. It might be extracted from within the cipher by sound intuition. If this proves difficult, try to assume the last form of the cipher to be the space, and estimate the context accordingly. Otherwise take up the first form and check up on it, since it is possible to start a cipher with a 20 spacer as a method of further deception.” 8. “Now that the space comes out right with both (‫ )أ‬and (‫)ي‬, look between two spaces for a light word such as: ٓ‫ع‬, ٟ‫ـ‬, ‫إرا‬,… or the like, on the basis of what goes before and after, which you should 21 adopt and build upon.” 9. Taking advantage of any possible words deliberately kept plain in the cryptogram, and using them as a vehicle for the intended goal. 10. Utilization of the “probable word” concept: “In case the cipher turns out to have been rendered without spaces, seek beside (‫)ا ي ي‬ a form which you can fairly guess as the letter ( ‫ )٘ـ‬and so read the name of God (‫)اهلل‬. Now consider preceding and following forms already known, and guess at such typical expressions as: ‫أطاي اهلل‬ ‫تماءن‬, ‫َذن اهلل‬٠‫أ‬, ‫أعضَن اهلل‬, ‫ؼشسه اهلل‬, ‫إْ ضاء اهلل‬, or the like as dictated by 22 the context.”

20

See p. 42. See p. 42. 22 See p. 42. 21

15

1.2.4. A Practical Example Having completed his discussion of the tools and algorithms of cryptanalysis, the Author turns to give an illustrative cipher of topical importance at the time. It is in fact a message describing the suffering of harassed peasants in the Town of Peace, and their abandonment of their farmlands as a result of the sharp increase in the number of claims made on them for payment. It is worth noting that the original version of the ciphertext is not without errors, additions and omissions. However, these have all been redressed and set right in light of the cleartext.

1.2.5. Conclusions The Author concludes his First Essay by considering the benefits of grasping this science, and regularly practising it to promote practical experience. Serious cryptanalysts do not content themselves just with the easy and straightforward, but show keen interest in pursuing the opaque and the formidable. The Author strongly advises against degrading this precious science, particularly on the part of those who have attained the dizzy heights of knowledge in it, by using it for unworthy intentions such as staking, entertainment, or fun in company. Instead, he suggests, it should be employed in far more serious purposes ––in activities that have to do with state affairs and the like. This statement of the Author clearly indicates that encipherment in his days was used for both objectives. The Author stakes out his position on the issue of employing this science for betting on solving ciphers, as this proves futile for two reasons: (a) that such ciphers are intended solely for sustained mental exertion, which is impractical; and (b) that they are unrealistic and not meant for live correspondence between two minds or souls.

16

1.3. The Second Essay on the Cryptanalysis of Elaborate and Demanding Ciphers (Advanced Cryptanalysis) This Second Essay incorporates advanced methods of encipherment and algorithms of cryptanalysis, as opposed to the contents of the First, which serves as an introduction to cryptanalysis. This one may be equivalent to what is termed „an advanced paper‟ in today‟s terminology, and can be divided into the following topics:

• Introduction It is a brief statement that lists types of advanced ciphers. These are: a) Ciphers responsive to cryptanalysis by deep insight and common sense. b) Ciphers that involve two or more types of encipherment, and are therefore misleading to the cryptanalyst, giving him/her a false impression of solution. c) Ciphers hard to cryptanalyse, although seemingly straightforward. d) Ciphers that defy cryptanalysis, even by dedicated professionals who might well, if at all, manage on mature reflection.

1.3.1. Algorithms for Cryptanalysis According to the Author, elaborate ciphers may be cryptanalysed along the following steps: 1. Attempting the tools and algorithms cited in the First Essay. The Author says: “If you are invited to solve a cipher that baffled other people‟s endeavours, consider it first by all the „weapons‟ 23 I have already given you.”

23

See p. 56.

17

2. Verifying the cipherforms are properly sorted out: “Make sure of the sort-out and the number of cipherforms, for that is the 24 backbone of the whole process.” 3. Seeking for letters of high frequency of occurrence: “Seek for 25 one of the „pillars‟, namely the letters (‫ )ا‬and (‫)ي‬.” 4. Utilizing the ten principles earlier mentioned in the First Essay, especially the last five. In the Author‟s own words: “Work out the rest by the algorithms already known to you. If [the cipher is] found still unresponsive to ordinary techniques of treatment, you should realize 26 that the letter (‫ )ا‬probably assumes two cipherforms.” This suggests a modification to the method of encipherment based on simple substitution.

1.3.2. Cryptanalysis of Simple-Substitution Ciphers Using Two Cipherforms for the Letter (‫)ا‬

Encipherment is here rendered by assigning two cipher symbols to the most frequent Arabic letter (‫)ا‬, rather than just one, as is typically the practice in simple substitution, “particularly if the cryptogram 27 consists of thirty of them”; thereupon: a) “Give up working on the letter (‫[ )ا‬for a while] and seek for the 28 letter (‫ ;)ي‬you will find more of it than all other forms.” b) “Now spot its exact image next to it, add another unknown form before it and guess at the word (‫)هلل‬, presuming the preceding letter to 29 be (‫ )ا‬by approximation,” denoting the utilization of the probable word ( ٗ‫)اٌٍـ‬, which was undoubtedly in common use in correspondence at the time. c) “Look at the word closely and reflect on it; if you manage to draw out the form of the letter (‫ )ا‬from this word, [ ٗ‫]اٌٍـ‬, then trace its other form with the adjoining (‫ )ي‬as they recur together in other 24

See See 26 See 27 See 28 See 29 See 25

p. 56. p. 56. p. 56 and p. 58. p. 58. p. 58. p. 58.

18

30

positions,” namely make use of two-letter words (bigrams) of higher frequency in general, and (‫ )اي‬in particular. d) “With the forms of the letters ‫ا‬, ‫ ي‬and ‫ ٘ـ‬coming out right, rack 31 your brains to resolve the rest.” Otherwise, quit this algorithm altogether and use another approach; the cipher could have been rendered by simple substitution but on a different variation. The following are further possible approaches.

1.3.3. Cryptanalysis of Ciphers Rendered Using Forms of Close Frequency The count of cipher characters may turn out to be in excess of thirty (the count of the alphabet and the space), and a statistical (quantitative) analysis of the cipher text may give comparable frequencies of the cipher forms. In this case the cryptologue can decide for sure that the letters (‫ )ا‬and (‫ )ي‬are made to assume two cipher forms each, and that “the cryptogram thus has its defects and 32 frailties blurred”. Note that the main defect of encipherment by simple substitution is the possibility for a cryptanalyst to arrive at the letters of higher frequency in the language through statistical analysis. It follows, the Author suggests, that cryptanalysis grows all the harder when high-frequency letters such as (‫ )ا‬and (‫ )ي‬are assigned more than one cipher symbol. Cryptanalysis of such ciphers is accomplished according to the following steps: 1. “Look for another technique; do not try to cryptanalyse the „pillars‟ [=the letters (‫ )أ‬and (‫ ])ي‬unless they emerge haphazardly upon 33 reflection.” 2. “Seek for a form that is higher in frequency than all others, and make it one of the abundant letters, i.e. َ, ْ, ٚ, ‫ ٘ـ‬and ٞ. Take the pattern of the letter (‫ )ا‬if it has been assigned two forms. In case the (‫)ا‬ assumes more forms than two, it certainly does not belong to the

30

See See 32 See 33 See 31

p. 58. p. 58. p. 60. p. 60.

19

34

group of „lucid‟ letters,” i.e. the abundant letters or the letters of highest frequency. Needless to say, this is an important indication of the Author‟s deep understanding of the fine points of letters and their frequency of occurrence. This idea can be elucidated by looking at the table of frequency of the abundant (high-frequency) and common 35 (moderate-frequency) letters, as observed by al-Kind : High-Frequency Letters

Moderate-Frequency Letters

Letter Rank Percentage of Occurrence Letter Rank Percentage of Occurrence

‫أ‬ ‫ي‬ َ ‫٘ـ‬ ٚ ٞ ْ

1 2 3 4 5 6 7

‫س‬ ‫ع‬ ‫ؾ‬ ‫خ‬ ‫ب‬ ‫ن‬ ‫د‬ ‫ط‬ ‫ق‬ ‫غ‬ ‫ض‬

16.36 11.91 8.72 7.44 7.14 6.87 6.02

8 9 10 11 12 13 14 15 16 17 18

4.22 3.57 3.32 3.27 3.05 3.05 2.50 2.48 1.71 1.55 1.25

Given that the letter (‫ )ا‬has two forms, the percentage of occurrence for each would be 16.36/2 = 8.18%, which falls within the range of abundant letters or „lucid‟ letters as the Author dubs them. If, however, the (‫ )ا‬assumes three forms, the percentage becomes 16.36/3 = 5.45%, which falls short of that of the last abundant letter (i.e. ْ = 6.02%), and therefore each of the forms representing the letter (‫ )ا‬is effectively outside the range of these letters. 3. If a form is entertained to be the letter (َ), for example, match it up where you find it, and look if it blends in well with its surroundings. Identify it with identical instances throughout the cipher. 4. “If it comes out right, you have achieved the goal; if not, then you have to retrace your steps straight from the beginning. Assume the selfsame form to be the letter (ْ), and manipulate it the way you have 34 35

See p. 60. See Volume One of this series, p. 58.

20

manipulated the (َ). You may this time fare well; otherwise, make it one or the other of the two forms representing the letter (‫ )ا‬and manage 36 it as before …until you are done with all the lucid letters.”

1.3.4. Unanswering Ciphers The Author of the Two Essays proceeds to advance a number of issues and ideas of paramount importance on encipherment methods and cryptanalysis algorithms. His argument is based on the following: (1) There are some intricate ciphers that defy cryptanalysis by the afore-mentioned algorithms; they might be resolved quite by chance. the Author says: “If the cipher proves so refractory that employing all these techniques of cryptanalysis is out of the question, you should recognize that it is irretrievable except by sheer chance, since it is 37 hermetically sealed from all sides.” (2) Other ciphers add nulls. The Author urges the cryptanalyst to “strain for tracing the nulls, now dropping one symbol, now including 38 another. On that you build, in the hope that it may respond.” (3) Some ciphers are intended to be communicated specifically between a sender and a recipient, and therefore they are impossible to pierce by a third party. (4) A wide knowledge of the algorithms of cryptanalysis and the various techniques of cipher manipulation is bound to help in the design of unattainable or inaccessible ciphers, through sealing up all the gaps. He says: “A retrievable cipher is typically positively definable and restricted to specific limits, of which the clues to cryptanalysis are often predictable. Stopping up these clues makes the 39 cipher impossible to solve, however great the toil is.” This is a general principle which is still effective even today: The encipherer should assume the role of the cryptanalyst, trying to close the gaps in his/her cipher and to offset the shortcomings therein, making it as tightly and as closely knit as to grow unresponsive to solution. 36

See See 38 See 39 See 37

p. 60. p. 62. p. 62. p. 62.

21

However, the belief of the existence of such an impregnable cipher does not, in fact, hold good all the way. Mathematically speaking, all ciphers are breakable somehow or other except the so-called one-time pad cipher, proposed in 1917 by Gilbert Vernam, and proved mathematically to be perfectly secure by Shannon in 1949. (5) There are ciphers based on simple substitution, in which several characters are used for each letter, thus increasing the count of cipherforms to, perhaps, as many as a hundred. Consequently, decipherment becomes a very complex and demanding task both to the sending encipherer, should he need to read his cryptogram some time later, and the receiving cryptologue, who has knowledge of the encipherment method used and also the key for decipherment. In fact carrying the cipher complexity to excess would necessarily lead to delays in deciphering the message –––a reality that can entail serious, indeed sometimes disastrous, adverse consequences when the cipher involves an urgent situation or a critical state of affairs that needs prompt action, such as war. This view of the Author of the Two Essays still holds true nowadays. For all the sophistication and state-of-the-art electronics of today, excessive complexity in the design of encryption algorithms has its own drawbacks in implementation and decryption, even though algorithms are known both to the sender and the recipient. Indeed any delay may incur the forfeiture of precious opportunities, the loss of which would cost dear. A case in point is the delay that occurred in breaking a highly complex cipher transmitted to the U.S.S. Pueblo on its maiden voyage to collect intelligence for the top-secret Operation Clickbeetle. The incident ended in the ship being attacked and captured by North Korean gunships on the high seas in January 1968 well before the completion of its first mission, showing how damaging 40 the intelligence loss is to national security. (6) Ciphering and cryptanalysis played an important role at the time of the Author. It was practised on a large scale in many state affairs among such personalities of high status as the king, leaders, ministers, governors, etc., with each employing a scribe

40

See Kahn, D. Kahn On Codes, New York: Macmillan, 1983, pp. 35, 181 & 188. See also Lerner, Mitchell B. The Pueblo Incident: A Spy Ship and the Failure of American Foreign Policy, University Press of Kansas, 2003.

22

responsible for tasks concerned with cryptography and cryptanalysis –––something similar to what is called today “black chambers”. (7) The Second Essay concludes with an example of setting up a cipher that is hard to retrieve and yet easy to read, given that the count of the cipherforms is no more than 28. The method is based on misleading the cryptanalyst into thinking that it is a simplesubstitution cipher, while it is really not. The letter (‫ )ا‬is here assigned three symbols ( ‫ظ‬, ‫ؾ‬, ‫ )س‬and the letter (‫ )ي‬three others ( ‫ط‬, ‫ع‬, ‫)د‬. Such a practice is bound to complicate the statistical analysis on tha part of the cryptanalyst. The four extra cipher symbols (i.e. ‫ؾ‬, ‫س‬, ‫ع‬, ‫ )د‬used for (‫ )أ‬and (‫ )ي‬are compensated for by reducing the total count of cipherforms to 28 through assuming a single symbol to at once represent three letters having the same orthographic pattern such as (‫ب‬, ‫خ‬, ‫ )ز‬and (‫د‬, ‫ )ر‬and (‫س‬, ‫)ص‬, thereby making the count of cleartext letters and ciphertext symbols equal. As a result the seemingly easy cryptanalysis would prove to be extremely difficult. A noteworthy feature in the frequency of cipherforms so rendered is the so-called “spectrum flattening” of the cipher symbols. A comparison of the frequency of cipherforms to the original frequency of letters shows a variation in the order of letters as well as bigrams in terms of their frequency. The bigram (‫ )أي‬turns to assume nine (3x3) possible forms, namely: ‫ظ ط‬, ‫ظ ع‬, ‫ظ د‬, ‫ؾ ط‬, ‫ؾ ع‬, ‫ؾ د‬, ‫س ط‬, ‫ س ع‬and ‫ س د‬. The same applies to bigrams consisting of letters having the same orthographic pattern, namely: ‫ر د‬, ‫ص س‬, ‫ ز خ ب‬. Such a variation in the order of letters and bigrams results in considerable difficulty in processing for statistical cryptanalysis. It should be pointed out that ibn Dunayn r in his Expositive Chapters on Cryptanalysis refers to this method of the Author, disapproving of his use of a single form to denote orthographically identical letters. This, ibn Dunayn r argues, is likely to confuse the legitimate decipherer and create ambiguity in determining which of 41 the identical letters is meant. Although initially sound, ibn Dunayn r‟s criticism would prove misplaced, given that the general context and word order would all but certainly help the astute legitimate decipherer to remove any possible ambiguity. This view is particularly substantiated by the fact that the Arabic letters were originally written undotted. It is not beyond the bounds of possibility, 41

See ibn Dunayn r‟s book (Vol.4 of this series), p. 54 and p. 176.

23

therefore, that this fact itself has prompted the Author of the Two Essays to develop this method of encipherment.

1.3.5. Annex The Two Essays, whole and complete, have been appended by a practical follow-up that comes in useful in statistical cryptanalysis. It covers the letters of the Arabic alphabet classified into three broad categories as per their frequency of occurrence. Order of letters Abundant (High Frequency)

Common (Medium Frequency)

Scarce (Low Frequency)

Total

Number

Letters

7

‫ ٘ـ‬ٚ ْ ٞ َ ‫ا ي‬

12

‫سع ؾبخندطقغضظ‬

9

‫رؾشزصغغظض‬

28

By analogy, it is interesting to recall ibn Adl n‟s classification of 42 Arabic letters into these three categories. Apart from the slight variation in the order of letters within each category, there is no other difference between ibn Adl n‟s classification and that of the Author of the Two Essays except for the letter (‫)ظ‬, which belongs under the „scarce‟ category according to the former‟s calculations, and under the „common‟ category according to the latter‟s. However, no significant effect ensues, as the letter (‫ )ظ‬often occupies a middle position between the two categories.

1.4. Originality of the Author of the Two Essays The Author attains the furthest limits of distinction in his precision of expression and profusion of information. He puts forward important ground-breaking ideas, unprecedented in other cryptological 42

See ibn Adl n‟s treatise (Vol. 2 of this series), p. 18 and p. 48.

24

compilations so far explored. The Two Essays are in many ways reminiscent of al-Kind ‟s treatise as regards their originality. The Author‟s contributions include: 1) The relative spectrum flattening in the frequency of the forms in the ciphertext, through the utilization of several symbols to represent one high-frequency letter. Note that the first use ever of this principle in the West dates from the reign of King Henry IV of France (15891610), that is at least four centuries later than the time of writing the 43 Two Essays. 2) Advising against inordinate complexity in cipher construction, as too much elaboration in encipherment can be dangerous, and may incur the loss of irrecoverable opportunities owing to delayed decryption. 3) Drawing attention to the importance of spotting potential errors, inadvertently incurred by the encipherer, and using them profitably toward cipher cryptanalysis. Note also that this principle has not been conveyed by cryptographers in the West until quite recently. 4) Restricting the use of encipherment to serious matters related to state affairs and military and diplomatic correspondence, cautioning against using the art for unworthy purposes such as staking, entertainment or the like. 5) Developing a method of encipherment that seems simple and easy to solve on the face of it, but actually quite involved. 6) Thorough and perceptive knowledge of cryptanalysis by statistical analysis of letters. 7) A clear distinction between simple and complex ciphers. 8) Highlighting the cryptanalytical experience and expertise required in cipher design, which contributes to sealing up the gaps, if any, to ensure a tightly-knit cipher. 9) The Two Essays include many cryptological terms, some of which are novel coinages; e.g. lucid letters, elaborate ciphers, ciphers that do not answer (unanswering ciphers), closely-knit ciphers, cipherforms, letter spotting, etc. 10) Stressing the psychological aspect in cryptanalysis. The Author says: “Then apply yourself to it wholeheartedly, undaunted and unflinchingly determined to solve it, never letting go of hope. Set your 43

See Treatise on Cryptography, A. Lange and E.A. Soudart; Laguna Hills, CA: Aegean Park Press, 1981,pp. 4-5.

25

mind at ease while exerting yourself all out for one day or so. Otherwise, just relax and refresh your soul. Do not overtax your mind 44 in pursuit, since it is unlikely to pay in that mood.” 11) The Two Essays have become a source for other later authors on cryptology to tap, such as ibn Dunayn r and probably ibn Adl n.

44

See p. 34.

26

Chapter 2

The Edited Two Essays On Cryptanalysis

27

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 individuals (in footnotes to Arabic text only), referring 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 individuals that could not be interpreted or identified 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 necessary, 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 and transliterating norms. We have enclosed requisite contextual additions -i.e. explanatory insertions and comments other than the writer's own wordswithin 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.45

45

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

28

2.2. Description of the Manuscript The manuscript of the Two Essays is part of the assemblage of cryptology, which is estimated to date back to the sixth century of the 46 Hegira (12th century AD). The Two Essays together occupy eleven sheets, i.e. the sheets 108/B- 118/B, with the sheet no. 115/B representing the end of the First Essay and the beginning of the Second. The following two Exhibits are photocopies of the first sheet of the First Essay, and the first sheet of the Second Essay (including the concluding lines of the First Essay).

46

See Volume Two of this series, p. 28 for a full description of the assemblage and its content. On the other hand, the identification number of the assemblage has turned out to be 5300, not 5359 as previously stated; we do apologize for this omission.

29

Exhibit 1: A photocopy of the first sheet of the First Essay (Document No. 5300, as-Sulaym niyya Ottoman Archives, Istanbul, Turkey)

30

Exhibit 2: A photocopy of the first sheet of the Second Essay, featuring the concluding lines of the First Essay (Document No. 5300, as-Sulaym niyya Ottoman Archives, Istanbul, Turkey)

31

32

2.3. The Texts (Arabic Original and English Translation)

33

In the name of God the Compassionate, the Merciful Sufficient unto me is He

2.3.1. The First Essay On the Cryptanalysis of Straightforward Ciphers

[1. Requisite Tools for the Cryptanalyst] I tell you, may God shepherd your steps, that the first things the cryptanalyst needs are: exercising the utmost degree of patience, quitting idleness and slackness, scrutinizing the cipherforms from beginning to end in the interests of readjusting and learning by heart. Then apply yourself to them wholeheartedly, undaunted and unflinchingly determined to solve the cipher, never letting go of hope. Set your mind at ease while exerting your self all out for one day or so. Otherwise, just relax and refresh your soul. Do not overtax your mind in pursuit, since it is unlikely to pay in that mood. Reconsider it later, keen to work it out according to the lights I have set for you and your mind. If your attempt does not come to fruition, put it off again, only to re-examine it yet again [later on]. If found anyway unresponsive, you should recognize it is one of the elaborate ciphers I am to describe in the Second Essay. In this case the cipher is calculated to be hermetically sealed and unlikely to yield to solution except haphazardly, possibly as a result of an error on the part of the cipherer. A cryptologue with cogent argument, sound intuition, and genuine insight can stand a chance of cracking it in consequence.

34

[2. Algorithms Not Based on Statistical Analysis] The ciphertext should be ten lines at the minimum, because less than that is nothing if not wearing and literally exacting. Letters, if not used frequently enough, would turn out futile. First try the simple algorithms, as the cipher might have been rendered by someone who thinks that separating the letters of words would make them difficult to read, such as: ٞ ‫َ غ َ د ع ي‬ Or by transposition within each word, writing each word in reverse: ٍٟ‫ٍع = ِؽّذ ع‬٠ ُ‫دِؽ‬ Or through concealment by letters: operative and inoperative, e.g. ٍٟ‫ د س ع ب ل ٘ـ ي = ِؽّذ ع‬ٞ ‫د م ع ح ي م‬ Or by inverting the text, with letters broken up: ٗ‫٘ـ ي ي ا ا ْ ب ط غ = ؼســثٕا اٌٍـ‬ Encipherment may also be accomplished by splitting the letters of the ciphertext into two lines, and then taking one letter from the first line, followed by the corresponding one from the other line alternately, such as:

ٗ‫ اٌٍـ‬ٍٝ‫وٍد ع‬ٛ‫ذ‬

=

{

‫ي‬

‫ا‬

‫ي‬

‫خ‬

‫ن‬

‫خ‬

‫٘ـ‬

‫ي‬

ٜ

‫ع‬

‫ي‬

ٚ

Or by concealing the letters within words, so that only one letter of each word –the first, second, third, fourth, or the last – is the intended letter. Example:

36

Another method involves selecting for encipherment certain letters –e.g. two, three, four, or five- such as the letters ‫ا‬, ‫ي‬, َ, ْ, ‫٘ـ‬, ٞ, and leaving the rest intact. Or by concealment within words, the starting point being the edge of the page or the first letter of each line in it. Or by systematically substituting for each letter another; thus substituting ‫ ا‬for ٞ, ‫ ب‬for ‫ال‬, etc. and vice versa after this fashion. Then consider the key often used in our days, i.e. ( ُ‫عصثى‬٠ ً٘ ٚ‫)أ‬. Encipherment is done by substitution reciprocally only within the pairs: ( ‫ ا‬and ٚ), ( ‫ ٘ـ‬and ‫)ي‬, (ٞ and ‫)ع‬, (‫ ظ‬and ‫)ب‬, and (‫ ن‬and َ); all other letters of the alphabet remain unaltered. Note that letters can be written joined or detached. Cryptanalysis is thereby achieved using the same rule. Encipherment may be predicated on a special arithmetic [ADWNA]. You arrange the numbers denoting units from one to nine using whole [dinars]; under the tens you write fractions of quarters, and under the hundreds write fractions of halves. Under the thousand (standing for the letter ‫ )غ‬you write fractions of halves and quarters, and so on. Accordingly, the name ٍٟ‫أؼّذ تٓ ع‬, for instance, can be enciphered thus:

one three seven five two quarter quarters quarters quarters dinars

four four eight dinars quarters dinars

one dinar

Treat all kindred cases likewise, and investigate this category of algorithms to its full potential.

38

39

[3. Algorithms Based on Statistical Analysis] You may get along perfectly well using the above algorithms. If so, you have practically attained your objective; otherwise, you set about counting the cipherforms meticulously, taking special care of the forms that are close in shape. Two closely similar forms may be mistaken for one form, such as: ‫ ع عـ‬or ‫ ع ع‬or the like; for in that case cryptanalysis would become extremely taxing. If the count is found to be twenty-eight forms, you decide that each letter of the alphabet has been assigned a single form, with (‫ )ال‬deemed as two individual letters [not as a distinctive letter]. If the count adds up to twenty-nine forms, then (‫ )ال‬is included as a distinctive letter, too. If, however, it amounts to thirty forms, you conclude that a spacer recurs between words. Then sort the forms out. The sorting process involves taking up the first form, computing its frequency of occurrence in the cipher, and affixing the frequency number to it. Subsequent patterns are handled alike. Next, you mull the forms over, and endorse them for good by marking them each with a point under the number. Seek for a cipherform of higher frequency than all other forms, making it the letter (‫ )ا‬in case the cryptogram is comprised of twenty-nine letters.

40

Now write down the letters of the alphabet. Under the letter (‫ )ا‬set down the form held to be the letter (‫)ا‬. Then hunt for an adjacent element that seems to recur often with it, and approximates it in number, making this cipher form stand for the letter (‫ )ي‬and affix it to the letter (‫)ي‬. You can seek for both forms together and consecutively to develop the definite article (‫ )اي‬in one place. If the cipher uses word-spacers [30 different cipher forms], you are getting along well towards cryptanalysis, given the fact that the spacer has a higher frequency than both (‫ )أ‬and (‫)ي‬. It might be extracted from within the cipher by sound intuition. If this proves difficult, try to assume the last form of the cipher to be the space, and estimate the context accordingly. Otherwise take up the first form and check up on it, since it is possible to start a cipher with a spacer as a method of further deception. Now that the space comes out right with both (‫ )أ‬and (‫)ي‬, look between two spaces for a light word such as: ٓ‫ع‬, ٟ‫ـ‬, ‫إرا‬, ‫لذ‬, ‫٘زا‬, ٌٛ, ٍٝ‫ع‬, ْ‫إ‬, ٌٓ, ُ‫ش‬, ‫إر‬, ٚ‫أ‬, or the like, on the basis of what goes before and after, which you should adopt and build upon. With such words laid clear, cryptanalysing the rest would be plain sailing, particulary if you take advantage of any possible words some encipherers deliberately leave plain, and which you can use as a vehicle for the intended goal, God willing.

42

In case the cipher turns out to have been rendered without spaces, seek beside (‫ )ا ي ي‬a form which you can fairly guess as the letter ( ‫)٘ـ‬ and so read the name of God ( ٗ‫)اٌٍـ‬. Now consider preceding and following forms already known, and guess at such typical expressions as: ‫أطاي اهلل تماءن‬, ‫َذن اهلل‬٠‫أ‬, ‫أعضَن اهلل‬, ‫ؼشسه اهلل‬, ‫إْ ضاء اهلل‬, or the like as dictated by the context. Indeed it is an agreed fact among encipherers that once the letters (‫ )ا‬and (‫ )ي‬come out right, they are all but sure to point to the rest, provided the cryptologue is endowed with patience. I would call on you to bear with me while I give you an illustrative example, so as to lend a helping hand to you and support to my own argument, with the good assistance of God. 47

[4. Practical Example: Cryptanalysing a Ciphertext]

And I have laid before you the following cipher to consider:

47

The cryptogram has suffered some errors, omissions and additions in the original manuscript. These, however, have been set right in light of the plaintext that follows shortly, and by making use of the cipherforms of the original as shown in the scribe‟s handwriting.

44

46

For cryptanalysis, you set out to approach the cipher using all the afore-mentioned simple methods. Or then you carefully compute its component cipherforms in line with that I have already shown you. Having found that their count adds up to thirty forms, you sort them out, indicating the occurrence frequency of each cipher element apart 48 as follows :

Examing them closely in conformity with the rules I have explained to you, you will find this form ( ‫ )عــ‬has higher frequency than others; it recurs 64 times, and is therefore held to be the space. You further support your belief sensibly by observing possible word limits according to what I have previously stated. Now you seek another form that occurs at the next higher frequency than other letters. No other than (‫ )ع‬presents itself; it recurs 30 times, and is consequently judged to be the letter (‫)ا‬. Then you look for a neighbouring and equally recurring form, to find this (‫ )ط‬and to establish accordingly that it stands for the plaintext letter (‫)ي‬. Set it down in place under the letters of the alphabet:

48

The cipher elements in fact exceed 30 in number, as some of them are repeated. In addition, they are not sorted out, nor are their frequencies indicated. However, they will soon be stated properly under their respective letters of the alphabet after cryptanalysis.

48

Subsequently hunt for two spaces enclosing the letters (‫)ا ي ي‬, plus another letter yet unknown. At first glance you recognize this: , the unknown form being . Considering preceding forms so far unfolded, you spot an (‫)ا‬, an unknown letter, followed by (‫ )ا‬and (‫)ي‬ respectively, thus: . You readily come to realize that this unknown letter is (‫)غ‬, and the first unknown is reasoned to be [the letter ‫]٘ـ‬, so that you read the statement: “ ‫”أطاي اٌٍـٗ تماءن‬. Your discerning choice is fixed on the letter (‫ )ن‬in the word ( ‫ )تماءن‬rather than the letter ( ‫( )٘ـ‬making ٖ‫ )تماء‬because ( ‫ )٘ـ‬has already been worked out in the word ( ٗ‫)اٌٍـ‬. Thus you can now designate the letters in their proper locations. In another location you come across two spacers with two forms in between ( ), one of which is still covert. But owing to its high occurrence frequency in the sort-out, you hold it to be the letter (ْ). In yet another location you find this: , of which two letters are known and another unknown. Guided by the context, you read it (‫)ٌَِّا‬. Elsewhere you pick out this pattern: , followed by this: , of which the letters (َ) and ( ‫ )٘ـ‬have previously been disclosed with the letter ( ٓ‫ )ع‬also uncovered already. On the spot it comes home to you that it is the word ( ‫)ســالِح‬. So you designate the 49 forms drawn. Then you observe these forms: , of which the letters ‫ا‬, ‫ي‬, and َ have been made clear by now. Later you spot this: , which is known, and you read it: ٗ‫اٌؽّذ ٌٍـ‬ٚ. This is followed by four known forms, namely , making the word (ٖ‫ؼذ‬ٚ).

49

i.e. of the newly emerging letters: ْ, َ, ‫ع‬, ‫ ط‬and ‫ال‬.

50

You keep on in the same vein outright, reflecting on the cipherforms and appropriately affixing them to their respective letters of the alphabet, until they are exhausted. Thereupon you get the 50 following arrangement of the letters and their cipher counterparts :

Thereby you can read the plaintext, fully developed. The space is ‫عـ‬

51

:

52

53 54

50

Note that the two letters ‫ ظ‬and ‫ غ‬have not been used in the cipher. The space symbol could have been better placed at the end of the arrangement. 52 So written in the original as well as in the ciphertext; it is typically written ٜ‫ظّاد‬. 53 Just so written in the ciphertext, instead of ‫شالز‬. 54 The square-bracketed statement has somehow been dropped from the original here, and redressed from the ciphertext. 51

52

[5. Conclusions and Tips] Having acquainted yourself with this amount of knowledge, practised it in cryptanalysing ciphers, and gained more and more interest and insight, the time is now ripe for you to open your mind to new prospects. You will feel confident of your ability and mental attitude not to be content just with easy and straightforward ciphers, but to embark on attacking vague and formidable ones. Always bear in mind that the more you practise, the more consummate and familiar with cryptanalysis you become. However, in this one respect you will need to concern yourself with issues form which you can benefit in more ways than one. When you attain such a high level of knowledge in this invaluable science, you might be tempted to use it in venturing bets on cracking ciphers among a company of friends. Should you give way, you are doomed to suffer failure on account of two reasons: the first is that such ciphers are intended solely for sustained mental exertion, and deliberately rendered so as to be impenetrable to you. [The other reason is that they are] not an outcome of mutual live communication between two minds, and therefore they are ultimately impractical and unrealistic. In no case does your success or failure contribute anything to your celebrity status on that score. I counsel you to spare yourself the pains of working out such pointless cipher, and not to overtax your talents by showing interest in them. Instead, you may be invited by a monarch or a high officer of state to break a cipher that has baffled their aides and scribes, and whose content relates to some state affairs, and for which they have expected to set credit and reward sooner and later. Such a worthy purpose is really a far cry from utilizing cryptanalysis for betting on trifling matters such as a hen or the like. Realizing the difference is bound to rid you of the failure to act properly and think soundly, God willing.

54

2.3.2. The Second Essay On the Cryptanalysis of Elaborate and Demanding Ciphers These include: [1] the difficult ciphers that are only responsive to cryptanalysis by deep insight and common sense, [2] those [composite] ciphers that mislead the cryptanalyst as to solution while in fact they are still far from it, [3] ciphers that are hard to cryptanalyse although they apparently seem straightforward, and [4] the ciphers that are inherently unresponsive to cryptanalysis even by dedicated professionals who might well, if at all, manage on mature reflection. [1. Algorithms for Cryptanalysing Elaborate Ciphers] I have already considered the straightforward ciphers, and wearied you with cryptanalysing the tough ones. I have also guided you to the special snags and hitches thereof. Be sure to make that your standard paradigm, and to take it as a basis of your knowledge and a prop to your intellect. Never neglect or despise the art in the mistaken belief that it is too easy for you to grasp, nor are you required to delve too far into the depths of what remains unknown to you of this science. Now that you got to grips with the better part of the foundations for cryptanalysis, all that remains are bits and pieces not of vital importance, and details too long to be discussed in a treatise the size of this, but are bound to be acquired through abundant first-hand involvement and enhanced by steady personal experience as time goes by. If you are invited to solve a cipher that baffled other people‟s endeavours, consider it first by all the „weapons‟ I have already given you. Retreat into privacy to concentrate and work undisturbed in a mood of peaceful mind. Make sure of the sort-out and the number of cipherforms, for that is the backbone of the whole process. Seek for one of the „pillars‟, namely the letters (‫ )ا‬and (‫ ;)ي‬extracting either of them would facilitate the cryptanalysis of the greater portion of the enciphered message. Work out the rest by the algorithms already known to you.

56

[2. Cryptanalysis of Simple-Substitution Ciphers Using Two Cipherforms for the Letter (‫])ا‬ If [the cipher is] found still unresponsive to ordinary techniques of treatment, you should realize that the letter (‫ )ا‬probably assumes two cipherforms, particularly if the cryptogram consists of thirty of them. Give up working on the letter (‫[ )ا‬for a while] and seek for the letter (‫ ;)ي‬you will find more of it than all other forms. Now spot its exact image next to it, add another unknown form before it and guess at the word (‫)هلل‬, presuming the preceding letter to be (‫ )ا‬by approximation. Look at the word closely and reflect on it; if you manage to draw out the form of the letter (‫ )ا‬from this word, [‫]اهلل‬, then trace its other form with the adjoining (‫ )ي‬as they recur together in other positions. Using careful handling, it will get out, God willing. With the forms of the letters ‫ا‬, ‫ ي‬and ‫ ٘ـ‬coming out right, rack your brains to resolve the rest. It will definitely come out.

58

[3. Cryptanalysis of Ciphers Rendered Using Forms of Close Frequency] Should you notice that the count of cipherforms exceeds thirty, and that they are of close frequency, then you decide for sure that the letter (‫ )ي‬also assumes two forms, and that the cryptogram thus has its defects and frailties blurred. So look for another technique; do not try to cryptanalyse the „pillars‟ unless they emerge haphazardly upon reflection. Instead, seek for a form that is higher in frequency than all others, and make it one of the abundant letters, i.e. َ, ْ, ٚ, ‫ ٘ـ‬and ٞ. Take the pattern of the letter (‫ )ا‬if it has been assigned two forms. In case the (‫ )ا‬assumes more forms than two, it certainly does not belong to the group of „lucid‟ letters. Match it against other forms. The matching is done such that if you entertain a given form to represent the letter (َ), for example, you start right from where you find it and reflect on it, guided by common sense and sound approximation. Keep identifying the form, namely the assumed (َ), in its positions with identical instances throughout the cipher. If it comes out right, you have achieved the goal; if not, then you have to retrace your steps straight from the beginning. Assume the selfsame form to be the letter (ْ), and manipulate it the way you have manipulated the (َ). You may this time fare well; otherwise, make it one or the other of the two forms representing the letter (‫ )ا‬and manage it as before. Carry on patiently until you are done with all the lucid letters.

60

[4. Unanswering Ciphers] If the cipher proves so refractory that employing all these techniques of cryptanalysis is out of the question, you should recognize that it is irretrievable except by sheer chance, since it is hermetically sealed from all sides. On the other hand, strain for tracing the nulls, now dropping one symbol, now including another. On that you build, in the hope that it may respond. Furthermore, not every cipher communicated strictly and exclusively between two persons is of necessity penetrable by a third party. A retrievable cipher is typically positively definable and restricted to specific limits, of which the clues to cryptanalysis are often predictable. Stopping up these clues makes the cipher impossible to solve, however great the toil is, particularly if more than one form are assumed for each letter, thus increasing the number of cipherforms to, perhaps, a hundred. Such ciphers, of course, would be hard to solve even for those immediately concerned; cryptanalysis would take quite a long precious time, and require serene frame of mind. Any delay in cryptanalysing an intricately forged message of sensitive nature can entail serious, if not disastrous consequences. Supposing the message is conveyed to a sovereign by an army commander in wartime demanding urgent military aid, defeat might be incurred in case of any delay in fulfilling the need. Let me now give you a typical example of a cipher the count of 55 whose forms does not go beyond twenty-eight letters .

55

i.e. with (‫ )ال‬excluded.

62

To set up a cipher that is the very devil to resolve and yet easy for you to read, assume for the letter (‫ )ا‬the letters of a light name such as ‫ظ[ ظفش‬, ‫ؾ‬, ‫ ]س‬and ‫ط [ سعذ‬, ‫ع‬, ‫]د‬, using them one by one. Do the same for the letter (‫)ي‬. On the other hand, assume a single form to at once 56 represent the letters ‫ب‬, ‫ خ‬and ‫ز‬, and the same for ‫ س‬and ‫ص‬, [and also for ‫ د‬and ‫]ر‬. The rest of the letters are each assigned one form, and (‫)ال‬ is given a distinctive pattern, so that the letters of the alphabet are represented as follows:

In this way, the letters are rendered thoroughly sealed and impossible to break, because the encipherer represents the letter (‫)ا‬ once as (‫)ظ‬, another time as (‫)ؾ‬, and a third time as (‫)س‬. And suchlike for the letter (‫)ي‬. If the letters (‫ )ا‬and (‫ )ي‬happen to occur together, you 57 use the set-up pattern that is unresponsive to solution, though seemingly easy to solve, Deo volente. End of the Two Essays. Praise belongs to God.

56 57

Since they share the same orthographic pattern. i.e. the letters (‫ )ا‬and (‫ )ي‬are enciphered each by one of 3 forms; the outcome is 9 possible bigrams to encipher (‫)اي‬.

64

[5. Annex] Letters of high frequency in rank order of occurrence: ‫ا‬, ‫ي‬, َ, ٞ, ْ, ٚ, ‫٘ـ‬ Letters of medium frequency in rank order of occurrence: ‫س‬, ‫ع‬, ‫ؾ‬, ‫ب‬, ‫خ‬, ‫ن‬, ‫د‬, ‫ط‬, ‫ق‬, ‫غ‬, ‫ض‬, ‫ظ‬ Letters of low frequency in rank order of occurrence: ‫ر‬, ‫ؾ‬, ‫ش‬, ‫ز‬, ‫ص‬, ‫غ‬, ‫غ‬, ‫ظ‬, and ‫ض‬.

66

1

1

2 3 4 5 6 7 8 9

35

2



1 2 3 4 5 6 7 8

37

1 2 3 4 5 6 7 8

39

3

1 2

394 1

3

293 1 81

454 3 4

41

1 2 3 4 5 6 7

43

4

1 2

45

47

1

2 3 4 5

49

1 2 3 4 5 6 7 8

51

1 2 3 4 5 6 7 8 9 10 11

53

5

2

1 2 3 4

5

55

1

1 2

3 4

57

2

1

59

3

1 2 3

4 5 6 7 8

61

4

1 2 3

63

1 2 3 4 5 6 7

8

65

5

67

68

The Second Treatise The Treatise of ibn Wahab al-Katib

69

70

Chapter 1

Analytical Study of ibn Wahab‟s Treatise

71

72

1.1. Preliminary ibn Wahab‟s treatise does not seem to fall in one single work. Rather, it appears in the assamblage of cryptology under the title: “From the book: al-Bay n Wattaby n (Eloquence and Elucidation) by Ab al- usayn 'Is q ibn 'Ibr h m ibn Sulaym n ibn Wahab alK tib”. Upon further investigation, it turned out that the treatise, whole and complete, is part of an edited book, also by ibn Wahab, entitled: “al-Burh n f Wu h al-Bay n (Demonstration of Eloquence Aspects)”, printed twice: in Baghdad (1967) and in Cairo (1969). However, compared to the book, the assemblage version is found to be broken and interrupted in two places: just prior to the manuscript text, and right after it. Therefore, the treatise has been here completed by making up the insufficiency from “al-Burh n”. The Wahabs were household names in the writing profession. It seems that this profession used to be passed down amongst them from generation to generation. Moreover, some of them were concerned in politics and high-powered government affairs, thus enjoying the best of both worlds. They were known to have been favoured more by the Abbasids than the Omayyads. To be noted is that the highly esteemed status of the Wahabs inspired great Abbasid poets, such as Ab Tamm m, al-Bu tur and ibn ar-R m , to make panegyrics on members of the family. ibn Wahab, the author of this treatise, is estimated to have lived the greater part of his life during the fourth century of the Hegira (10th AD).

1.2. Structure of the Treatise ibn Wahab‟s treatise can be divided into an introduction and five sections as follows: - Letter forms and representations - Methods of encipherment - Algorithms of cryptanalysis - An overview of poetry cryptanalysis - An encipherment method

73



Introduction: Motives for Using Secret Writing

ibn Wahab starts by summing up the motives for utilizing secret writing in general. He maintains that these are incorporated in the need to keep certain information confidential for reasons of having best interest properly safeguarded, so that such information can only be disclosed to the initiated. The author distinguishes between two states of such utilization, i.e. the written state, for which encipherment is the appropriate means; and the oral (spoken) state, for which signalling gesture is the suitable medium.

1.2.1. Letter Forms and Representations Given the constant change of writing styles everywhere according to the changing conditions of people, the author establishes that the letters of the Arabic alphabet in use are 29 in number. He differentiates between the two terms of a “letter” and a “letter image”. A letter, to him, is the uttered sound or contrastive sound unit ––the so-called “phoneme” in today‟s terminology; while the letter image is its written form or “grapheme”. A grapheme represents any of the letters of the Arabic alphabet. Indeed ibn Wahab‟s differentiation is bound to resolve the mistaken belief, held by latter-day and modern scholars, of considering (‫ )ال‬as one single stand-alone letter, making the count of letters thirty. The fact remains that the Arabic alphabet consists of 29 letters, of which 28 have fixed graphemes, with a distinctive articulation for each. The 29th letter, that is the “alif”, has no independent articulatory pattern because it is ever neutral (quiescent) and never vocalized (mobile). What appears to the laity as an “alif” pattern is in fact nothing more than a prolonged hamza (‫)ء‬. Since it is impossible for the alif to be enunciated on its own, there was a need to use it along with another voiced letter, ideally the letter (‫)ي‬, and thus (‫ )ال‬has originated. Oddly enough, this pattern (‫ )ال‬has become an independent, free-standing symbol on printers, typewriters and computer keyboards. It was not until the Arabic Standard ASMO 449 was

74

recently developed and internationally acknowledged that this symbol was dropped. It should be worth noting here that placing (‫ )ال‬before (ٚ) and (ٞ) in order testifies to the earlier scholars‟ awareness of the difference between consonant and vowel letters. They grouped the three vowels at the end of the alphabetical order, expressing the letter „alif‟ by (‫)ال‬, as stated above. Accordingly, the Arabic alphabet adds up to 29 letters, starting with the consonants ( ‫( ء‬hamza), ‫ب‬, ‫خ‬, …) and terminating with the vowels ( ‫( ا‬written ‫)ال‬, ٚ and ٞ). The author then points out to other nondescript letters –––letters with no distinctive pattern, that might occur in the Arabic language. These are: the hamza betwixt and between, the letter (‫ )ا‬slanted to (ٞ), the letter (‫ )ا‬intensified by (ٚ), the letter (‫ )ش‬pronounced like (‫)ض‬, the letter (‫ )ظ‬that resembles (‫)ص‬, and (‫ )ض‬resembling (‫ )ن‬in pronunciation. The following table shows these letters, associated with their international phonetic symbols each, and related to the respective Arab tribes known to have used them: Letter

International Phonetic Symbol

(‫ )ء‬betwixt and between

/Ɔ/

(‫ )ا‬slanted to (ٞ)

/ε/

(‫ )ا‬intensified by (ٚ)

/o/

(‫ )ش‬resembling (‫)ض‬ (‫ )ظ‬resembling (‫)ص‬ (‫ )ض‬resembling (‫)ن‬

/ŝ/ /z/ /g/

Dialect Typical of Tribes of Hejaz Region Typical of Tam m Tribe Typical of Tribes of Hejaz Region (Unknown) Typical of Qays Tribe Typical Yemeni Tribes

According to phonology there are no individual graphemes for each of these spin-off phonemes. Two or more phonemes may share the same graphemic representation when they happen to share the same function. The offshoots of a parent phoneme are called its allophones. Notice, for example, the cardinal (ْ) in words such as (‫اج‬ٛٔ) or ( ‫ )ٔاس‬and the assimilated (ْ) in words such as ( ‫ )ِٕه‬or ( ‫ ;)عٕه‬also the dark and light (‫)س‬, etc. Every such variant letter is regarded as an allophone of a parent letter; thus the hamza betwixt and between is an allophone of the parent hamza, the slanted (‫ )ا‬is an allophone of the parent letter (‫)ا‬, and so on. This is manifested by the fact that there is no difference, as

75

far as meaning is concerned, between reading the Koranic verse  ٝ‫اٌعؽ‬ٚ with a clear final (‫ )ا‬and an (‫ )ا‬slanted to (ٞ), or reading ‫ُصْذِس‬٠ with a clear (‫ )ظ‬and with the (‫ )ظ‬slanted to (‫)ص‬. By extension, ibn Wahab addresses the letters that share the same orthographical patterns, gathering that the 29-letter Arabic alphabet is basically made up of 18 patterns, since the letters ( ‫ب‬, ‫خ‬, ‫ )ز‬have the same pattern in common, as do the letters ( ‫ط‬, ‫ )ش‬and ( ‫ض‬, ‫غ‬, ‫)ؾ‬, etc. This typical feature has been put to good account by restricting encipherment exclusively to these 18 letter-patterns, as we shall see in the following paragraphs.

1.2.2. Methods of Encipherment ibn Wahab distinguishes between two types of encipherment: A) Encipherment by Substitution (at-Tar ama), i.e. by substituting for each letter or its pattern another pattern. B) Encipherment by Concealment and Transposition (at-Ta miya), i.e. by concealing letters in names of species and genera, or by changing their relative positions within the ciphertext (transposition). He then elaborates on two methods of the encipherment by at-tar ama: 1. With each letter assuming the form of another, such as using the form of the letter (‫ )ع‬to denote the letter (‫)ض‬, and (‫ )ا‬to indicate (ٚ), etc. This is a type of encipherment using simple substitution observed by al-Kind and his successors, and 1 exemplified by the Qumm and Bis m encipherment. 2. With letters assuming devised forms that do not pertain to letter forms, such as: ∂, ‫ٱ‬, γ …

1

The Qumm encipherment: i.e. employing the Qumm cipher alphabet in letter substitution according to its key: See Vol.3 of this series, p.10 ff and pp. 60-62. See also Vol.2, pp. 16-17 and pp. 42-44.

76

As for the encipherment by at-ta miya, ibn Wahab identifies three methods: 1. Encipherment by related conceptions –––what al-Kind calls the conceptual relationship and diffusion method, using generic or 1 species names to represent letters. 2. Encipherment by transposition, through changing the order of letters within a given cipher. This involves many approaches, of which the author restricts himself to three, although he points to a type of composite encipherment that utilizes transposition and substitution together, making cryptanalysis more and more difficult. “However,” ibn Wahab says, “this method of encipherment may be augmented either by letter substitution or 2 by pattern contrivance, thus intensifying obscurity.” –––a gesture of prime importance on the part of ibn Wahab. 3. Encipherment by letter addition and reduction, through the 3 inclusion of null letters, as has been stated earlier by al-Kind . ibn Wahab refers here to three different cases: (a) Addition of insignificant nulls; for example: ‫( ِؽّذ‬clear)= ‫( ِرؽىّعذي‬cipher), where a negligible null is added after each letter. ibn Wahab indicates the possibility of incorporating tar ama into nulls to obtain composite encipherment. (b) Reduction of letters through assigning common letter combinations (such as the bigrams: ‫ِع‬, ٓ‫ع‬, ِٓ, ً٘ and the like) single patterns in cipher, creating inconsistency between the letter count of the ciphertext and that of the plaintext. Given that such bigrams are normally extremely helpful in the cryptanalysis process, ciphering them in this way is bound to add to the difficulty of cryptanalysis, and to make encipherment even more complicated. Indeed this is another worthy gesture that is noted to ibn Wahab‟s credit. (c) Reduction of letters by giving a single pattern to letters that share the same orthographic image (e.g. ‫ض‬, ‫غ‬, ‫)ؾ‬. This implies the adoption of the 18 images of the letters, not the 29 letters proper, and also suggests non-observance of letter dotting. 1

See Vol.1, p. 93 and p. 132; Vol.3, pp. 27-28 and p. 76; and Vol.4, p.34 and p.110. See p. 100. 3 See Vol.1 of this series, p.92 and p.138. 2

77

Ibn Wahab concludes this section with the important notion that encipherment methods are too numerous to be reckoned, as they are the outcome of conventional experiences dictated by mainstream intellectual needs and typical usage, rather than an inherently established phenomenon. The following tree-diagram illustrates ibn Wahab‟s methods of encipherment.

78

ibn Wahab’s Methods of Encipherment

Simple encipherment

Composite Encipherment (Tar ama + Ta miya)

Ta miya (Encipherment by Concealment and Transposition)

Transposition + Tar ama Nulls + Tar ama

Assigning single pattern to orthographically identical letters (e.g. ‫ض‬, ‫غ‬, ‫= ؾ‬ ٍٟ‫)ع‬

By Addition and Reduction

Assigning single pattern to letter combinations (e.g. ‫ق = ِع‬ٚ‫ـاس‬ ِٓ = ٍٟ‫ع‬ ‫اسع‬ٚ = ‫)اهلل‬

By Transposition (Changing letter order within a given cipher)

Adding nulls (e.g. ‫= ِؽّذ‬ ‫ِرؽىّعذي‬

By Names (people or instruments) ‫ِؽّذ = ا‬ ‫أؼّذ = ب‬ ‫ = خ‬ِٟ‫سا‬ ‫ق = ز‬ٚ‫ـاس‬ . . .

By Genera ‫ = غ‬any bird ٚ = wild animals ‫ = ع‬perfumes

Tar ama Encipherment by Substitution Each letter assumes a devised form not pertaining to letter forms (e.g. ‫ =ا‬α ‫ڤ =ب‬ ‫)]=خ‬ . .

Each letter assumes the form of another

Some letters

All the letters (e.g. Qumm and Bis m encipherment)

79

1.2.3. Algorithms of Cryptanalysis Cryptanalysis according to ibn Wahab incorporates the following seven principles: 1) Form count 2) Statistical analysis of forms (their frequency of occurrence), used especially when the ciphertext is long enough 3) Combination of letters, used especially with short ciphertexts 4) Bigrams: Two-letter words and their frequency of occurrence 5) The probable-word principle 6) Outlets of letters (their points of articulation) 7) Word length These algorithms will be addressed one by one in some detail in the following paragraphs. 1) Form Count Counting up the numbers of forms or patterns in the cipher constitutes the first step towards cryptanalysis. ibn Wahab here identifies five possible cases: (a) The count of forms that comprise the cipher is found to be 29 forms in all: This indicates that the encipherment is rendered by simple substitution; one symbol for each letter. (b) The case of more than 29 forms signifies the use of nulls. (c) More than 29 forms in a short cipher suggests assigning a single pattern to stand for a letter combination, e.g. ِٓ = π and ‫ = اي‬δ. (d) Less than 29 forms implies giving a single pattern to some of the orthographically identical letters, e.g. ‫ڤ = ز خ ب‬. (e) 18-form count denotes giving a single pattern to all the orthographically identical letters, implying non-observance of letter dotting. 2) Statistical Analysis of Forms This involves matching the frequency of forms in the cipher against that of the letters of the language concerned. ibn Wahab classifies the Arabic letters according to their frequency of occurrence in descending order of precedence as follows:

80

‫ض‬

‫غ‬ ‫ظ‬

ْ ‫د ط ق‬ ‫ص غ غ‬

‫ ٘ـ‬ٚ ٞ َ ‫ي‬ ‫ع ؾ خ ب ن‬ ‫ظ ش ض ؾ ز‬

‫ا‬ ‫س‬ ‫ر‬ 1

Note how close this classification is to that of other cryptologists. The author maintains that this statistical (quantitative) principle applies particularly to those ciphertexts that are long enough, in which all letters circulate sufficiently, and where the order of letter frequency can be applied effectively. Applying the principle for cryptanalysing scanty ciphers proves, therefore, of no avail, and in this case another, 2 qualitative expedient must be used, i.e. that of letter combinability.

3) Combination of Letters This principle is used especially with short ciphertexts. A short ciphertext, according to ibn Wahab, is estimated at 1-2 lines or so. At this point he makes no mention of non-combinable letters, postponing this until later, where he presents a brief outline of the Arabic phonetic system. More important here, however, is highlighting his concept of letter association and non-association. He says: “if the guesstimate falls on two letters, see whether or not they admit combination; if found combinable, seek each of them in another place, checking at the same time that they associate well together.”3 It seems that letter combination to him is not the same as letter association. By association he may mean the occurrence in one word of two noncombinable letters, with a letter barrier in between, as in: ‫ة‬ٙ١‫ؼ‬, ‫ش‬ٙ‫عث‬ and ًٙ١‫ ؼ‬,in which the letters ‫غ‬, ‫ ع‬and ‫ غ‬do not normally combine with the letter ‫٘ـ‬, were it not for the occurrence of the letter barrier ٞ, ‫ ب‬and ٞ respectively in the above words. 4) Spotting Bigrams and Their Frequency of Occurrence Cryptologists often stress the importance of bigrams, such as ِٓ, ‫ِع‬, ‫ِا‬, etc., and their usefulness in cryptanalysis. ibn Wahab is no

1

See Vol.1 of this series, p.100; and Vol.5, p.129. See al-Kind ‟s treatise, Vol.1 of this series, p.124 and p.126. See also Vol.4, p.19 and p.88. 3 See p. 106. 2

81

exception in that respect. But he takes the idea a step further by stating the frequency of bigrams depending on their rate of occurrence in discourse. He cites as many as 29 typical bigrams. Notice that in his citation he takes care to use the conjunction (ٚ = and) to express coordinate bigrams, and the conjunction ( ُ‫ = ش‬then) to join bigrams of descending order of frequency –––a sign of his accuracy and precision. Furthermore, he points out the possibility of encipherment using just one symbol to represent a bigram. Given the fact that managing to deduce bigrams in a ciphertext is likely to make for eliciting other letter groups, cryptographers tend to employ this technique even today in the interest of making a cipher even more difficult for the cryptanalyst to break. 5) The Probable Word ibn Wahab emphasizes the significance of the probable word in the cryptanalysis of cipher messages, making it a vital clue thereto. He then cites a number of honorific opening statements and introductory expressions typically used in Arabic correspondence of the time, such as: In the name of God, the Merciful, the Compassionate; Praise be to God; Glory be to the Lord; From God‟s servant So-and-so to God‟s servant So-and-so; Sir, may God prolong your life, Minister or Prince. Considering such honorific openings, we are given to understand that encipherment was in use at the time for communicating messages with celebrities and personages of state. The author concludes by noting that the three Arabic vowels ( ‫ا‬, ٚ, ٞ) all combine with each of the Arabic letters. 6) Outlets of Letters ibn Wahab reviews a number of phonetic and phonological phenomena, with the aim of examining certain phonetic laws that are relevant to, and used in, cryptanalysis, such as letter assimilation (diphthongization) and non-combination. One of these phenomena is that concerning letter outlets in the human vocal mechanism, which the author classifies into 13 outlets, starting at the lips and ending at the throat. The following table depicts these outlets and the respective letters pertaining to each, as observed by ibn Wahab:

82

Outlet Number

Outlet of Articulation

Letters

Description

Number of Letters

1

Between the lips Tip of the tongue and front teeth Tongue locked on roots of teeth Slightly deeper on the tongue surface Blade of the tongue Either side of the tongue Between the middle and side of the tongue Further back towards root of the tongue The furthermost root of the tongue Forethroat next to the mouth Mid-throat Far end of throat in front of thorax The nasopharyngeal passages

ٚ‫ؾَب‬

Labial

4

‫رظز‬

Lingua - alveolar

3

‫غدخ‬

Cacuminal

3

‫صطظ‬

Sibilant

3

‫يْس‬ ‫ض‬

–– ––

3 1

ٞ‫شض‬

––

3

‫ن‬

––

1

‫ق‬

––

1

‫غؾ‬ ‫غع‬

Guttural Guttural

2 2

‫٘ـ ء‬

Guttural

2

Light ْ

––

1

2 3 4 5 6 7 8 9 10 11 12 13

It is well worth noting that ibn Wahab‟s survey of letter outlets has posed several phonetic laws that prove perfectly consistent with the latest phonetic theories such as: (a) The theory of letter dissonance “the closer the outlets of two letters, the heavier on the tongue in articulation,” says ibn Wahab.1 This proposition has been the subject of detailed discussion by many Arab linguists and rhetoricians, for example ibn inn , ar-Rumm n , and ibn Sin n al- af , among others.

1

See p. 110.

83

(b) The law of least effort “the Arabs tend by nature to use what is inherently light and easy to pronounce, and to avoid using all that is awkward. It follows that they hardly take up two letters of the same outlet or of two equal outlets.”1 In other words, languages generally have an innate tendency to put the least muscular effort in articulation. (c) The theory of assimilation “The general rule of assimilation is that in the case of the occurrence of two adjacent letters that belong to one and the same outlet or pattern, and provided that the preceding letter is diacritically neutral (suk n), those two letters should be assimilated to each other.”2 As a phonetic phenomenon, letter assimilation has been addressed by many Arab linguists. ibn Wahab reviews a few relevant cases and rules, and winds up featuring aspects of letter combination and noncombination that have been described earlier in outline, and minutely detailed in former treatises of this series. But then ibn Wahab‟s approach projects two distinguishing characteristics:  His distinction between the two terms of letter „proximity‟ and „adjacency‟, maintaining that whereas proximity relates only to the basic letters of a word, i.e. those forming an intrinsic part of it, adjacency relates to the affixing letters in words ordinarily used in discourse. For instance, the letter (‫ )ن‬in the word ( ٗ‫ٌـ‬ٛ‫ )وم‬is not proximate to the letter (‫ )ق‬but adjacent to it because it is an affixing letter employed here for comparison, and not a basic letter in the word.  His elaboration on certain cases of letter noncombination, and his accounting for some, such as his statement: “The letters ‫ض‬, ‫ ش‬and ‫ ض‬may combine in some cases by reason of the fact that the outlet of some of them is longer in extent than that of others, and also because the order of some, as regards their outlets, is lower than that of others.”3

1

See p. 110. See p. 110. 3 See p. 112. 2

84

7) Word Length The author suggests that considering word lengths is likely to reveal to the cryptologue the method of encipherment used. In case the cipher is found to be abundantly supplied with long words (words made up of more than four letters), it is most probably enciphered by the addition of null letters. If, on the other hand, it is found to be mainly composed of three- or four-letter words, it is then expected to be enciphered without the use of nulls. Next he points to an issue of paramount importance: “If you strongly believe that the letters [of the cipher message] have actually been correctly identified, but with their alignment still not fitting into place, you realize that the letter arrangement in that cipher has been altered. Thereupon you should utilize letter fronting, post-posing, transposition and substitution, keeping on until all is laid just right for you. Indeed this constitutes the most intricate cipher method.”1 Here he refers explicitly to composite encipherment where substitution and transposition are used simultaneously, and where cryptanalysis necessitates not only the extraction of symbol surrogates but also rearrangement of letters by way of fronting, post-posing, transposing and substituting, as needed for the letters to take form and turn out clear. This is in fact a genuinely interesting indication on the part of ibn Wahab because it is connected with one of the most important and widely applied methods of modern-day encipherment ––the international Data Encryption Standard (DES) and the Advanced Encryption Standard (AES).2 ibn Wahab concludes this section by calling attention to a statistical phonetic phenomenon: that no Arabic word of more than three letters is void of one of the so-called liquid letters (i.e. ‫ؾ‬, ‫س‬, َ, ْ, ‫ي‬, ‫)ب‬, which he dubs the letters of the tongue tip or the lips. Such letters, therefore, are to be carefully traced when considering words of 4 letters or more in cryptanalysis. However, this is conditional on whether spaces are used in the ciphertext to mark word limits. “Learning that well is an

1 2

See p. 116. See Chapter 13 of ibn Dunayn r‟s book, Vol.4 of this series, p.100. See also Henk, C.A. van Tilborg, An Introduction to Cryptology, pp. 55-62, Academic Pub., 3rd ed., 1989.

85

important guideline towards cipher cryptanalysis, provided that wordspacers are employed,”1 he asserts.

1.2.4. An Overview of Poetry Cryptanalysis Having concluded his discussion of cryptanalysing prose ciphers, ibn Wahab proceeds to address cryptanalysing poetry ciphers. In his treatment of poetry cryptanalysis there is actually nothing special that places him one up on his peers. Overall, he advances the following issues on the way to poetic cryptanalysis: 1) Considering the rhyme letter. 2) Counting the letters of the verse so as to identify its meter. In this connection he observes the following points: (a) the “mu arra ” verse: a line of poetry characterized by the phenomenon of “ta r ” (agreement between the last metrical units (feet) in both hemistichs of the verse). (b) the verse that is affected by the metrical variations arm (the measured omission of the first vocalized letter of a threeletter foot segment at the beginning of a verse), and zi f (an optional variation that affects the second of a two-letter metrical foot called sabab). (c) the verse that contains a prolonged or geminated letter. 3) Making use of the tools mentioned earlier with regard to the cryptanalysis of prose ciphers. 4) Experimenting with the various metrical feet, with a view to recognizing the verse meter. He covers all the types of Arabic metrical units, which are eight in number (two fivesomes and six sevensomes), demonstrating the possible meters derived from each. In this aspect ibn Wahab has perhaps an edge over other scholars concerned with poetry cryptanalysis.

1

1) See p. 116. 2) Apropos word length, it might be useful to make a passing reference to Zipf‟s “law of abbreviation”, to the effect that the word length relates inversely to its circulation, so that the shorter the word the commoner in usage. (Translator)

86

1.2.5. An Encipherment Method ibn Wahab brings his treatise to a close by presenting a method of encipherment that is unique to him in that it is a departure from what we have seen practised by others. It basically involves ciphering letters by pointing to their respective positions in the words of an agreed key verse that embraces all the letters of the alphabet (simple substitution). This key is: Thus, the name (‫ )ِؽّذ‬is enciphered: (1/6, 2/3, 1/6, 2/1), i.e. the first letter of the sixth word in the key, followed by the second letter of the third word, and so on. To be noted is that this method is the closest thing to the encipherment by the branched calligraph of ibn ad-Durayhim,1 except that the latter is based on the words of the numerical alphabet instead of the key verse, and that it uses drawing instead of writing.

1.3. Originality of ibn Wahab al-Katib The various aspects of ibn Wahab‟s originality can be summed up in the following points, as manifested in his treatise: 1. His demonstration and explanation of a number of terms, and distinction between those of a kind such as at-ta miya versus attar ama, the letter and its pattern or image, etc. 2. His description of important methods of composite encipherment using a combination of both transposition and substitution, or of substitution and nulls. 3. His coverage of Arabic bigrams, arranged according to their frequency of occurrence. 4. Highlighting the importance of representing bigrams of high frequency by means of one symbol. 5. His marked exploration in the treatise of such phonetic topics as the outlets of letters, letter assimilation, letter dissonance, and the law of least effort.

1

See Vol.3 of this series, p.27 and p.74.

87

88

Chapter 2

ibn Wahab‟s Edited Treatise

89

2.1. Description of the Manuscript ibn Wahab‟s treatise is part of the same assemblage of cryptology. A short treatise of no more than three pages, it occupies both sides of sheet No. 82, as well as one side of sheet No. 83. The following is a photocopy of the assemblage version of the treatise.

90

A photocopy of the first page (of two) of ibn Wahab‟s treatise (Document No. 5300, as-Sulaym niyya Ottoman Archives, Istanbul, Turkey)

91

A photocopy of the second (and last) page of ibn Wahab‟s treatise (Document No. 5300, as-Sulaym niyya Ottoman Archives, Istanbul, Turkey)

92

2.2. ibn Wahab’s Treatise (Original Arabic Text and English Translation)

93

From the book: al-Burh n f Wu h al-Bay n by Ab al- usayn 'Is q ibn 'Ibr h m ibn Sulaym n ibn Wahab al-K tib

[Introduction: Motives for Using Secret Writing] 1

[As for secret writing, we should say that there is information one needs to conceal or keep secret for some reason or intended advantage, so that it can be disclosed only to those who are eligible and trustworthy. Therefore, encipherment has been established in writing in place of oral signaling and indication, such that written material meant to be kept secret is enciphered, and spoken material intended for secrecy is likewise preserved.

1

From this point starts ibn Wahab‟s text in “al-Burh n f Wu h al-Bay n”.

94

[1. Letters: Their Forms and Representations] We say: Writing styles change everywhere with the changing conditions of people. The letters of the Arabic alphabet that are widely used are twenty-nine in all, of which twenty-eight ("alif" excepted) have fixed written images (patterns). Since the letter "alif" is ever diacritically neutral and therefore impossible to articulate on its own, the letter (‫ )ي‬has been prefixed to it as a key to pronouncing it, and thus (‫ )ال‬has originated. Note that the lexical (‫ )ا‬with which the alphabet opens is not literally an "alif", but in fact a "hamza" that is figuratively and by extension termed "alif". But then in some Arab dialects there are a few letters without a distinctive pattern, such as the hamza betwixt and between, the letter (‫ )ا‬slanted to (ٞ), the (‫ )ا‬intensified by (ٚ), the letter (‫ )ش‬that is pronounced like (‫)ض‬, the letter (‫ )ظ‬that resembles (‫)ص‬, and (‫)ض‬ resembling (‫ )ن‬in pronunciation. It would have been appropriate to assign each letter of the alphabet a distinctive pattern; but, finding that burdensome, they [the Arabs] have opted for giving just one pattern to represent letters of the same orthographical outline, for example the letters: ‫ ز خ ب‬and ‫ش ط‬, so that all such letters are distinguished by means of dots, and that has proved more convenient. Consequently, there go eighteen letter patterns to represent twenty-nine letters proper.

96

[2. Methods of Encipherment] Some people will base encipherment on the number of letters, some others will base it on the number of letter patterns, and others yet again seem to add to the number or otherwise reduce it. Here I mean to put forth what comes to my mind of the expedients of cipher cryptanalysis, God willing it. So I say: Ciphers might be either poetry or prose, achieved by the 1

"tar ama" or the "ta miya".] Encipherment by "tar ama" differs from that by "ta miya". On the one hand, encipherment by "tar ama" involves the expression of a letter by substituting for it the form of another letter, or a devised form that does not pertain to letter forms. As for a cipher rendered with a letter assuming the form of another, the letter (‫)ع‬, for example, may be used in place of the letter (‫ )ض‬and the letter (‫ )ا‬instead of (ٚ) –––a method which was used in the wellknown Qumm and Bis m encipherment. Take note that this type of ciphering can be applied to some or all of the letters. Regarding a cipher rendered with letters assuming devised forms or patterns, this approach is very common indeed, and anyone can create whichever forms he likes.

1

The end of ibn Wahab‟s paragraphs from “al-Burh n” that precede the manuscript text of the assemblage of cryptology.

98

On the other hand, encipherment by "ta miya" divides into three methods: One, encipherment by related conceptions, such as ciphering the letter (‫ )غ‬by the bird genus, the letter (ٚ) by the name of wild animals, the (‫ )ع‬by perfume. This encipherment uses generic names. Alternatively, by assigning each letter a name related to people, wild animals or birds, for example representing the letter (ْ) by a partridge, the letter (‫ )ض‬by a duck, (‫ )ن‬by a pomegranate, (‫ )ظ‬by the proper name Zayd, and the like. The first alternative, however, is harder to break. Two, enciphering a word by [measuredly] changing the order of its letters so that the last letter is rendered first and the first last. Other letters are accordingly arranged. For example, the name of God (‫ )اهلل‬is enciphered by this method as ( ‫)ٍ٘ال‬. Such encipherment by changing the positions of letters has several methods apart from the above, such as placing the first letter of a word at the beginning of a line, the second at the end, the third next to the first, the fourth next to the second, and so forth until the letters are over, meeting in the middle of 1 the line. Encipherment may also be accomplished by placing the last letter of the word next to the first, the second follows. The last letter but one is placed next to the third, and so on until all the letters are used. Example: ‫( أؼّذ‬clear)= ُ‫( أدؼ‬cipher). However, this method of encipherment may be augmented either by letter substitution or by pattern (form) contrivance, thus intensifying obscurity. Letter orders are liable to be changed as the case may be.

1

See Vol.1 of this series, p.91 and p.136, and Vol.3, p.9 and p.56 ff.

100

Three, encipherment by letter addition and reduction. Addition involves the inclusion, in between the ciphered letters, of inconsiderable null letters that are meant to enhance the cryptanalyst‟s uncertainty, such as the addition, in ciphering the name ( ‫)ِؽّذ‬, of the letter (‫ )خ‬next to the initial (َ),(‫ )ن‬next to the (‫)غ‬, (‫ )ض‬after the other (َ), and (‫ )ظ‬next to the (‫)د‬, so as to get: ‫( ِؽّذ‬plain) = ‫ِرؽىّعذظ‬ (cipher). This method can possibly be incorporated into the two methods of encipherment by "tar ama". Or else, each letter of the alphabet is assigned an individual pattern, without necessarily being committed to the letter patterns that have the same orthographic outline in common. Reduction, however, entails enciphering letter combinations, such as: ‫ِع‬, ِٓ, ‫ِا‬, ً٘ and the like, by means of one pattern for each, and assigning the name of God the Great and Almighty one single pattern too, not a pattern for each letter thereof. This would enable the encipherer to enhance complication and make life even more difficult for the cryptanalyst, since it is through such [bigrams] that a cipher often comes out. Moreover, letter reduction in encipherment is achieved through making use of those letters [of the alphabet] that are orthographically identical, by giving them a single pattern, the like of ( ‫ض‬, ‫غ‬, ‫ )ؾ‬, ( ‫ع‬, ‫)غ‬, etc. Remember that encipherment methods are in fact inexhaustibly numerous, as they are not an inherently established phenomenon, but rather the outcome of design and convention, alternatives of which are 1 not naturally limited, but infinite.

1

Thus far ends ibn Wahab‟s manuscript text. The remainder of the treatise has been extracted from "al-Burh n".

102

[3. Algorithms of Cryptanalysis] Among the expedients towards cryptanalysing a cipher, if long enough, is to count up all its forms or letter patterns, and write down the frequency of occurrence of each form. If the total count of forms is found to be twenty-nine, you decide that each letter has been assigned one form. If found in excess of twenty-nine, nulls are understood to have been used. Less than twenty-nine and more than eighteen count indicates that some two and three [orthographically identical] letters in it are given one single form each. In case, however, the number is exactly eighteen forms, the indication is that a single pattern is assigned to [each and] all the letters that share an orthographically identical pattern in the alphabet. You then proceed to consider the forms of highest frequency, and those progressively lower and lower in frequency until all are exhausted. You will find for yourself what has been established by experiment: that the most highly frequent letters are ‫ا‬, then ‫ي‬, then َ, then ٞ, then ٚ, then ‫٘ـ‬, then ْ, then ‫س‬, then ‫ع‬, 1

then ‫ؾ‬, [then ‫ خ‬, then ‫]ب‬, and ‫ن‬, then ‫د‬, then ‫ط‬, then ‫ق‬, then ‫غ‬, then ‫ض‬, then ‫ر‬, then ‫ظ‬, then ‫ش‬, then ‫ض‬, then ‫ؾ‬, then ‫ز‬, then ‫ص‬, then ‫غ‬, and ‫غ‬, then ‫ظ‬.

1

These two letters have been dropped from the original, but their normal place is between (‫ )ؾ‬and (‫)ن‬. See Vol.2 of this series, p.18 and p.48.

104

This [statistical/quantitative] rule holds good particularly in a ciphertext that is long enough, so that all letters occur and circulate sufficiently in it. It does not, however, apply to very short ciphers of one or two lines, in which case you should seek to utilize another [qualitative] expedient that involves knowledge of combinable and non-combinable letters in the Arabic language. If the guesstimate falls on two letters, see whether or not they admit combination; if found combinable, seek each of them in another place, checking at the same time that they associate well together. Keep on matching until words do make sense. To be noted in this context is the frequent occurrence of such two-letter words [bigrams] in the [Arabic] tongue as: ِٓ, ‫ِع‬, ٓ‫ع‬, ‫ِا‬, ٟ‫ ـ‬and ‫ اي‬whose patterns all-often come together in many places, giving further indications of working out the letters. What contributes towards drawing out such bigrams -when they are sought in their individual patterns or when assigning a single pattern to represent a bigram- is the acquaintance with their rate of occurrence frequency in this tongue. Bigrams of highest frequency [in descending order] are: ‫ال‬, then ِٓ, then ْ‫إ‬, then ‫ِا‬, then ٟ‫ـ‬, then ٌُ, then ٓ‫ع‬, then ٛ٘, then ُ٘, then ‫إر‬, then ُ‫ش‬, then ٟ٘, then ٚ‫أ‬, then ٌٛ, then ً‫ت‬, then ً٘, then ً‫و‬, then ٞ‫أ‬, then ٌٓ, then ُ‫و‬, then ‫ ِع‬and َ‫ أ‬and ٞ‫ر‬, then ‫را‬, then ٌٟ and ٚ‫ ر‬and ‫سب‬, then ‫ ِز‬and ٓ٘. These are the frequency orders of associative letters. Another vital clue towards cryptanalysis is the opening statements of correspondence, such as commencing a message by the name of God (In the name of God, Most Gracious, Most Merciful), and using typical honorifics, titles, and standard expressions gaining wide currency nowadays, e.g. May God prolong your life; Sir, May God prolong your life; May God prolong the life of the Vizier/Emir; From God‟s servant So-and-so to God‟s servant So-and-so; and the like. If, through repetition, these expressions were found reasonably sound, then you could decide for certain the authenticity of your conjecture, considering that this kind of cipher is in all probability identified by fair guesswork. Bear in mind that the letters in this language which admit association and combination with each letter [of the alphabet] are the three vowels, i.e. ‫ا‬, ٚ and ٞ.

106

Outlets of Letters The articulatory outlets of letters are thirteen in number, starting between the lips to form the outlet of the letters ٚ, ‫ب‬, َ and ‫ؾ‬, called the labial letters. The tip of the tongue and front teeth mark the outlet of ‫ز‬, ‫ ظ‬and ‫ر‬, which are the lingua-alveolar letters. With the tongue locked on the roots of the teeth the outlet of ‫خ‬, ‫ د‬and ‫( غ‬cacuminal letters) is formed. Slightly deeper on the tongue surface constitutes the outlet of ‫ظ‬, ‫ ط‬and ‫( ص‬the sibilant letters). From the blade of the tongue is the outlet of ‫س‬, ْ and ‫ي‬. The outlet of the letter ‫ ض‬is from either side of the tongue (right or left). Between the middle and side of the tongue the letters ٞ, ‫ ض‬and ‫ ش‬are released. Further back towards the root of the tongue is the outlet of the letter ‫ن‬. The furthermost root of the tongue marks the release of the letter ‫ق‬. The guttural letters have three outlets: 1. The forethroat next to the mouth (‫ ؾ‬and ‫;)غ‬ 2. Mid-throat (‫ ع‬and ‫;)غ‬ 3. The far end of throat in front of the thorax ( ‫( ء‬hamza) and ‫)٘ـ‬. The light ْ is released through the nasopharyngeal passages.

108

[It is interesting to note that] the closer the outlets of two letters, the heavier on the tongue in articulation. The Arabs tend by nature to use what is inherently light and easy to pronounce, and to avoid using all that is awkward. It follows that they hardly take up two letters of the same outlet or of two equal outlets. If, however, such letters happen to occur together, they tend to assimilate the one into the other. The general rue of such assimilation is that in the case of the occurrence of two adjacent letters that belong to one and the same outlet or pattern, and provided that the preceding letter is diacritically neutral (suk n), those two letters should be assimilated to each other, for example 

 [= So We said, „Strike with thy

staff the rock‟] and 

 [= They were rebels and transgressors].

If they occur in one word, then assimilation is mandatory, as in 

 [= Why then do you dispute a matter of

which you know not anything?]. If the second is diacritically neutral (i.e. marked with suk n), assimilation is impermissible, as in 

 [= Ha, you are the ones who dispute..], and in

words such as

,

,

, etc. However, in the case of two

adjacent letters which are both diacritically vocalized, and which share the same outlet or pattern, it is your choice to either assimilate or not, e.g. 

and

are equally correct. Likewise,

 may be recited 

.

110

Should the two diacritically vocalized letters happen to occur in one word, they are both voiced distinctly in nouns, e.g. ‫اٌعذد‬, ‫اٌّذد‬, and 

 [= or then we had spoken outrage], and are assimilated

in verbs, e.g. َ‫ ِذ‬and َ‫( سد‬Do not say: َ‫ ِذَد‬and َ‫)سدَد‬. That is perhaps due to that nouns are lighter than verbs in articulation. The same applies to the letters (‫ )ي‬and (‫ )س‬regarding assimilation because they are of the same articulatory outlet, and also to the letters (‫ )د‬and (‫)ط‬, as in 

 [= God has heard], for the closeness of their respective

outlets. The guttural letters do not combine. As gutturals, the „hamza‟ and the „alif‟ do not associate because they are affixing letters, and one of them is part of the three vowels, so they combine with all other letters of the alphabet. In addition, the letters (‫ )ق‬and (‫ )ن‬never combine in any root word unless the (‫ )ن‬is added [to the word] for comparison, as in the word ( ‫ٌه‬ٛ‫)وم‬, where the [first] (‫ )ن‬is not proximate, but in adjacency. The letters ‫ض‬, ‫ ش‬and ‫ ض‬may combine in some cases by reason of the fact that the outlet of some of them is longer in extent than that of others, and also because the order of some, as regards their outlets, is lower than that of others. Thus (‫ )ض‬combines with (‫ )ض‬in the word ( ‫ع‬١‫ )اٌعع‬posteriorly but not anteriorly, and (‫ )ش‬does combine with (‫)ض‬ in both anterior and posterior positions, as in (‫ )ظص‬and ( ‫)ضط‬. The letter (‫)ض‬, however, is not possibly combinable with (‫ )ش‬anteriorly nor posteriorly by reason of the closeness of their respective outlets.

112

On the other hand, the sibilant letters never combine with one another, and neither do the lingua-alveolar letters. Quite the contrary is the case with the cacuminals, which are combinable owing to the fact that their outlets, though considered equal, are varying. Most Arab speakers tend to say, for example, ‫ِش‬َٙ‫ ِط‬for ‫ِش‬ٙ‫ ِرط‬and ُ‫ عٕد‬for . Examples

from

the

Holy Koran

include:

1



 [=Truly, God loves those who repent, and

He loves those who cleanse themselves] and 



[=If he obeyed you in much of the affair, you would suffer]. At the same time, there are those letters articulated using the tip of the

ْ

tongue. Hardly any two such letters occur together without assimilating them to each other, for example

and

. But

should the (‫ )ي‬be shifted on, then both letters may be uttered distinctly; alternatively, the first is dropped. People say, for example, or

;

or

. Note also that the labial letters

combine with each other in view of their lightness in articulation. These are the letter outlets and the letter combinability for each outlet put in a nutshell, as handling them individually would entail prolixity. You can try your hand at that yourself. If you start on the letter (‫ )خ‬of the alphabet, you experiment with all the letters in both pre- and post-positions. Do the same with the following letters of the alphabet in order to identify those that combine and those that do not, instead of dragging out our discussion, God willing.

1

As a matter of fact, this is not a case in point, since the ( ) of ( ) is not assiilated to the (‫)غ‬. Another more relevant example is   [= Therein are men who would keep pure; and God loves those who purify themselves].

114

Should you find the cipher to contain a series of continuous letters, you realize it is rendered by letter substitution. If it is mostly made up of three- and four-letter words, with sporadic longer words, it is calculated to be rendered without the employment of nulls. When, conversely, the cipher is composed mainly of long words (i.e. four-, six-, and eight-letter words), it is most probably rendered by the addition of nulls. This is so because root (unaugmented) Arabic nouns are primarily of five letters, and root (bare) verbs are mainly of four letters. Any extra letters are affixings. If you strongly believe that the letters [of the cipher message] have actually been correctly identified, but with their alignment still not fitting into place, you realize that the letter arrangement in that cipher has been altered. Thereupon you should

utilize

letter

fronting,

post-posing,

transposition

and

substitution, keeping on until all is laid just right for you. Indeed this constitutes the most intricate cipher method. Note that the greater portion of Arabic speech involves those letters that are easily articulated with the tongue tip or the lips. There is hardly any noun or verb made up of four letters and more without one or two of these letters, except for rare anomalies such as ‫إسؽاق‬. Learning that well is an important guideline towards cipher cryptanalysis, provided that word-spacers are employed. Check spaces and look into the words to trace such [liquid] letters. The most abundantly supplied letters in the cipher are reckoned to be those of highest frequency in the Arabic tongue as I have mentioned earlier, then the next abundant, and so on till the end of the cipher. And that is the long and short of [cryptanalysing] prose ciphers.

116

[4. An Overview of Poetry Cryptanalysis] By contrast, cryptanalysing poetry ciphers is easier because poetry is rhymed and metrically measured. Rhyme and meter of poetry are useful aids to its cryptanalysis. The technique lies in locating the rhyme letter within the cipher before counting all the letters of the verse. Having found the count to be fourteen letters more or less, you assert it belongs to the ra az and short meters. A little higher count indicates a verse of medium length. In case the rhyme letter seems to be repeated in fronting or post-posing, and not too far within the cipher, that verse is held to be “mu arra ”. The letter count of one verse might be found less than that of another, in which case you realize that it might be affected by the arm and zi f phenomena, both involving letter omission. Be mindful of letters that are lengthened or geminated; such a letter, though one in writing, is in fact considered two in poetry. This is perhaps why one line of verse is less in letter count than another [of the same meter]. If the words are separated, calculate the constituent letters, matching them against the different poetic meters. Should they be in proportion, you work out the letters by the afore-stated expedients. If the outcome was metrically sound, with identical letters recurring coherently in all lines, then you are sure to have hit the mark in cryptanalysis. The poetic meters fall into eight groups, of which two are pentameters (i.e. fa lun and f ilun) and six heptameters (i.e. maf lun, mustaf ilun, f il tun, muf alatun, mutaf ilun, and maf l tu). Consequently, in order to decide to what meter a given verse belongs, reflect on the first metrical foot in it:

118

If it is fa lun or any of its variations, the stich belongs to the aw l or mutaq rib meter. The deciding factor is to consider the second foot (that follows fa lun): if it is also fa lun or its variations, the verse is of al-mutaq rib meter; if it is maf

lun or its variations, the meter is

the aw l, seeing that there is no such meter starting with f ilun. If it is maf

lun or its variations, the meter is haza or mu ra .

A look into the metrical foot that follows will determine: maf

lun or

its variations indicates the haza , and f il tun or its variations reveals the mu ra . Care should be taken, however, to that the foot maf

lun

is also a possible variation of al-w fir meter, which entails looking at the verse: if its feet are all maf

lun, without fa lun in either

hemistich, it is determined to belong to the haza meter, otherwise it is associated with the w fir. If it is mustaf ilun or its variations, the verse might possibly be of the bas , ra az, sar , munsari

or mu ta . The next foot decides

exactly which meter the verse belongs to: f ilun (or its variations) indicates the basi ; mustaf ilun signifies ra az or sa . (Identification here calls for considering the third foot, which is f ilun in the sar meter, and mustaf ilun in the ra az); maf l tu designates the munsari ; while f il tun marks the mu ta . If the first metrical unit is f il tun (or its variations), the possibilities are the meters of the mad d, ramal, af f or muqta ab. To fix on the exact meter look at the next metrical unit: f ilun (or variations) marks the mad d meter, f il tun (or variations) identifies the ramal, mustaf ilun characterizes the af f, and mufta ilun labels the muqta ab.

120

If it is muf alatun (or variations), the verse is composed on the w fir meter. If it is mutaf ilun (or variations), the meter there is k mil. After all, these are handy hints that should be quite sufficient to the wise veterans in metrics, who are keen to observe our aims and intentions of tackling poetry cryptanalysis, God willing. [5. An Encipherment Method] Circulating among people is the following line of poetry that covers all the letters of the alphabet:

They have used it for encipherment. [To convey the name ( ‫])أؼّذ‬, for example, in cipher they say: the fourth letter of the fourth [word], to indicate (‫ ;)ا‬the second of the third, to suggest (‫ ;)غ‬the first of the sixth, for (َ); and the second of the first for (‫ ;)د‬and suchlike for other letters. Any other similar verse or expression could actually serve as a feasible scheme of communication with one‟s correspondents. I have plumped for this verse in particular because of its wide popularity and utilization in this day and age. All in all, these chapters on cryptanalysis are intended as no mean signposts to whoever needs instruction therein. They constitute an adequate supply to those who have the attention and patience to investigate in earnest. With constant practice and perseverance many other methods might be discovered, or new ground broken quite unprompted, but yet based on the broad lines of approach we have laid out, if God wills it.

122

Now that we conclude our discussion, the hope is that we have not gone contrary to the principle of brevity we undertook to observe right from the beginning. However, for a field of such diversity, a little dilation might probably be warranted. Praised be God, the Great and Almighty at all times. May His blessings and peace be upon Muhammad the Prophet, as well as his fellow prophets and their noble folks, and all the rightly-guided believers. Sufficient unto us is God, the best Guardian, the Supreme, the Almighty in Whom we trust and from Whom we seek guidance.

124

1

1967 1969

2

350 350 350

95

3 4

1

351 351

97

1 2

2

1

432 4

51 1 2

351 351

351

99

3 4

1

352 352 352

2 3 4

352

5

352 352 352

6 7 8

352 352

9

352 352

101

10 11

1

353 353 353

2 3 *

353 353 353 353 353 353 353

103

4 5 6 7 8 9 10

3

1

362 353

353

2 3

354 354

4

274 1 5

274 1 354

6 7

8

274 1 354

105

9

354

107

1

356

109

1

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 

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

 



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

60 61 66 66

2 3 4 5

22 20 91

111

1

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14 181

113

1 2

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1

222

2

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115

3

1 2 3

117

4

1 2

119

1

94

121

154 152

5

123

125