Arabic Origins Of Cryptology Vol. 5

Series on Arabic Origins of Cryptology Volume Five

Three Treatises on Cryptanalysis of Poetry

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

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

Published by KFCRIS & KACST

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

Series on Arabic Origins of Cryptology Volume 5

Translated by Said M. al-Asaad

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

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

The First Treatise ibn ab ab ’s Treatise on Cryptanalysis

Chapter 1: Analytical Study of ibn ab ab ’s Treatise on Cryptanalysis ............................................................. 3 1.1. Biography of ibn ab ab .................................................... 5 1.2. Study and Analysis of ibn ab ab ‟s Treatise ...................... 6 1.3. Structure of the Treatise .......................................................... 7 1.3.1. Tools for Cryptanalysing Prose and Poetry ...................... 7 1.3.2. Cryptanalysis of Poetry Ciphers ....................................... 8 1.3.3. Methods of Encipherment by Simple Substitution ..........11 1.3.4. An Example of Poetry Encipherment .............................. 12 1.3.5. Management of Poetry Encipherment ............................. 13

Chapter 2: ibn ab ab 's Edited Treatise................................ 17 2.1. Editing Methodology ............................................................ 18 2.2. Description of the Manuscript .............................................. 19 2.3. ibn ab ab 's Treatise on Cryptanalysis (Original Arabic Text and English Translation) ................... 23

The Second Treatise A Treatise on Cryptanalysis of Poetry by the Author of Adab a - u ar '

Chapter 1: Analytical Study of the Treatise on Cryptanalysis of Poetry by the Author of Adab a - u ar ' ........... 51 1.1. Preliminary ......................….................................................. 53 1.2. Structure of the Treatise ........................................................ 53 1.2.1. Definitions ...................................................................... 54 v

1.2.2. Requisites and tools for poetry cryptanalysis ................. 1.2.3. Prosody and rhyme ......................................................... 1.2.4. Insight into the knack of writing .................................... 1.2.5. The importance of metrical measures ............................ 1.2.6. Impediments to cryptanalysis ........................................ 1.2.7. Examples ........................................................................ 1.2.8. Annexes ..........................................................................

55 55 56 59 59 60 61

Chapter 2: The Edited Treatise on Cryptanalysis of Poetry, by the Author of Adab a - u ar ' .......................... 63 2.1. Description of the Manuscript ............................................. 64 2.2. The Treatise (Original Arabic Text and English Translation) .................... 67

The Third Treatise al- urhum ’s Two Manuscripts

Chapter 1: Analytical Study of al- urhum ’s Two Manuscripts ............................................................ 121 1.1. A Text from al- urhum ‟s Book ........…............................ 123 1.2. A Text from al- urhum ‟s Treatise .................................... 127 1.2.1. Frequency Reversal ...................................................... 127 1.2.2. Classification of Letters As Per Their Frequencies ..... 128 1.2.3. Biliterals Occurring Initially and Terminally in Words ... 129 1.2.4. Manipulation of Bigrams and Trigrams (Combinatorics) . 130 1.2.5. Utilization of Bigrams and Trigrams in Cryptanalysis ..134 1.2.6. The Importance of Ciphertext Length ......................... 136 1.3. Originality of al- urhum ................................................... 140

Chapter 2: al- urhum ’s Edited Manuscripts .......................141 2.1. Description of the Manuscripts ........................................... 142 2.2. The Texts (Arabic Original and English Translation) ........ 147 2.2.1. From al- urhum ‟s Book .…........................................ 148 2.2.2. From al- urhum ‟s Treatise ….................................... 152

vi

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 ‫ت‬ ‫خ‬ ‫ج‬ ‫ذ‬ ‫خ‬ ‫د‬ ‫ر‬ ‫س‬ ‫ص‬

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 z

as r in red. as z in zoo.

vii

‫ط‬ ‫ش‬ ‫ص‬ ‫ع‬ ‫ط‬ ‫ظ‬ ‫ع‬ ‫ؽ‬ ‫ف‬ ‫ق‬ ‫ن‬ ‫ل‬ ‫و‬ ٌ ‫ْـ‬ ٔ ٘

s

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.

viii

Preface This is the fifth 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 of this series are each dedicated to one treatise. Volume One has been devoted to the oldest treatise ever found on cryptanalysis, written by al-Kind , the well-known Arab philosopher, about 1200 years ago. This 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 lilmalik 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 (this one), unlike the previous volumes, includes the following works by three Arab scholars of cryptology: 1. Treatise on Cryptanalysis of Poetry, by the Author of Adab a u ar ' (The Art of Poets) 2. A Treatise on Cryptanalysis, by Ab al- asan ibn ab ab 3. Two texts on cryptanalysis of poetry by Ab al- asan alurhum : a) From his Book b) From his Treatise These treatises study, first and foremost, the cryptanalysis of poetry, over against the previous treatises which are concerned mainly with the encipherment and cryptanalysis of prose, though occasionally touching on some aspects of poetry. In point of fact, poetry has enjoyed a remarkable and highly prized standing during the days of the authors of these treatises. Considering the Islamic state, at the time present over extensive areas from Spain to China through North Africa, Arabic was the official language. ix

Poetry, besides being an important literary genre, it was at one time a valuable medium for disseminating sciences; indeed Arab scholars were given to composing the principles of their sciences in poetical form, with a view to promoting easy methods of learning and rapid diffusion. Examples include ibn M lik's Alfiyya (Thousand verses) on syntax, a - ibiyya on the Koranic modes of recitation, ar- a abiyya on the Islamic law of statutory heirship, al- awhara (The gem) on monotheism, as-Suy 's Alfiyya on Prophetic tradition, Nih yat attadr b (The utmost practice) on a - fi Islamic jurisprudence, ibn Ra q's poem on the Prophet's battles, and ibn ad-Durayhim's Poem on Cryptology. 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. On the other hand, the second three volumes (of which this one is Volume Five) are the English version of Book Two of our afore-stated Arabic original, also published by the Arab Academy, Damascus, 1997.

*

*

*

Damascus, May 2006

Dr. M. Mrayati Dr. Y. Meer Alam

Dr. M. H. Tayyan

x

The First Treatise ibn ab ab ’s Treatise on Cryptanalysis

1

2

Chapter 1

Analytical Study of ibn ab ab 's Treatise on Cryptanalysis

4

1.1. Biography of ibn ab ab Mu ammad ibn 'A mad ibn Mu ammad ibn 'A mad ibn 'Ibr h m ab ab al- Alaw Ab al- asan was born in Ispahan and died there in AH 322/AD 934. Sources do not give detailed accounts of his life, but they are agreed that he was a leading literary authority, and a great poet and researcher. A renowned personality of widely-circulating poetry, he was well known for his intelligence, sagacity, serenity of mind, and seriousness of purpose. His Works ibn ab ab has left a number of works that tend primarily towards poetry, literature and the like. The following are the most important of his books:  Iy r a - i r (The Standard of Poetry): A book on literary criticism. Hailed by editors as significant, it has been printed and published several times, the most recent of which was in Riyadh 1985.  Tah b a - ab (Refinement of Taste): Includes an interesting poetic anthology, of his own selection, of the works of other poets.  Kit b al- ar (The Book of Prosody): Described by Y q t al- amaw of Mu am al-'udab ' as “unprecedented”, and no wonder, as the treatise in hand is a typical case in point; it involves metrical issues that demonstrate ibn ab ab 's extent of knowledge in the art of prosody.  His own poetical collection (divan), which has not reached us for some reason. It may have been lost in the mists of time. However, a fair bit of his poetry is strewn about in literary and biographical compilations ––a fact which has motivated quite a few researchers to collect these bits up into a so-called divan.  Treatise on cryptanalysis, the subject of our present discussion.

5

1.2. Study and Analysis of ibn Treatise

ab ab ’s

In keeping with the standard practice of writers on this science, ibn ab ab starts his treatise right by addressing the personage at whose behest the treatise has been written. He says he seeks ease and clarity, shortcutting the route to cryptanalysis, and making every effort to meet his main objective thereof. In his own words: “I went out of my way to [tersely] expound the subject, in the hope that it would turn out 1 of great advantage.” Before entering into the details of the treatise, an indication to three issues would be in order: 1. The author‟s statement at the outset of the treatise gives the impression that he is to tackle prose as well as poetry encipherment: “Bear in mind that all that is enciphered of prose or poetry is restricted 2 to twenty-eight letters,” while, in fact, the treatise is dedicated almost entirely to the encipherment of poetry, as we shall see soon. 2. The originality of the work stems, first and foremost, from its close consideration of the minutiae of poetry encipherment, so much so that it has become an important authority quoted by many later writers on the subject. Among the major books that have drawn upon it or made reference to it are the following: - At-tanb h al ud at-ta f (Alerting to the occurrence of misstatement), by amza ibn asan al-A fah n (AH 360/AD 971). - D w n al-ma n wan-na m wan-na r (Divan of meanings, poetry and prose), by Ab Hil l al- Askar (AH 395/AD 1005). - Maq id al-fu l al-mutar ima an all at-tar ama (Expositive chapters on cryptanalysis) by ibn Dunayn r (AH 627/AD 1229). It should be pointed out that, of these three books, the first is the most to tap ibn ab ab ‟s treatise. In fact the last chapter of At-tanb h includes the bulk of the treatise, with no mention of ibn ab ab whatsoever, suggesting that this chapter may have been appended to the book and is not an essential part of it.

1 2

See his treatise, p.24. Ibid., p.26.

6

3. ibn ab ab , the author of this treatise, is a poet of great note who practised the art of encipherment in his poetry, and was reported to have left special poetic selections in cipher.

1.3. Structure of the Treatise ibn ab ab ‟s Treatise on Cryptanalysis can be divided into five chapters as follows: 1. Tools for cryptanalysing prose and poetry. 2. Cryptanalysis of poetry ciphers. 3. Methods of encipherment by simple substitution. 4. An example of poetry encipherment. 5. Management of poetry encipherment.

The reader will immediately realize that this treatise is so straightforward and brief that it only just needs any further elaboration. It is sufficient therefore to state the most remarkable views covered by ibn ab ab in each chapter, highlighting the relevant technical terms in the edited text.

1.3.1. Tools for Cryptanalysing Prose and Poetry The author starts out by considering a few issues that are common to cryptanalysing ciphers rendered in prose and poetry alike, before he expands on the cryptanalysis of poetry ciphers in particular. These general issues are: a) The number of letters: ibn ab ab holds the Arabic alphabet to be made up of 28 letters, after the pattern of al-Mubarrid [an eminent Arabic-language figure, d. AH 286/ AD899], and counter to the view 1 of the predominant majority of language scholars. To be noted is that he does not touch on the idea of nulls, advanced by al-Kind and his successors, which augment the number of cipher forms, making the cipher even more complicated. b) The space or word-spacer: The symbol used to denote a blank between every two words in a cipher, i.e. the end of a word and the 1

This view regards the letters as 29 in the aggregate, including the "hamza".

7

beginning of the next. The difficulty, however, consists in the so1 called no-word-spacer encipherment, mentioned by ibn Adl n and overlooked by ibn ab ab . c) Combination and noncombination of letters: This phenomenon has been tackled by most of those engaged in this art, with al-Kind leading. Detailed tables of noncombinable letters can be referred to in 2 several places of our Series. d) Letter frequency of occurrence: According to ibn ab ab , the high-frequency letters, in order of precedence, are: ‫ا‬, ‫ل‬, ‫و‬, ٌ, ٘, ‫ب‬, ‫ع‬, ‫ْـ‬, ‫ ت‬and ٔ. Note that he places the letters ( ‫ )ْـ‬and (ٔ) towards the end, in contrast with the mainstream trend of relatively arranging these letters 3 as they appear in the word (ًٍٕٚٓ‫)ان‬, i.e. ‫ا‬, ‫ل‬, ‫و‬, ‫ْـ‬, ٔ, ٘ and ٌ.

1.3.2. Cryptanalysis of Poetry Ciphers This chapter, the longest and most important, discusses the algorithms of cryptanalysing poetry ciphers. The author surveys the poetic features that aid in cryptanalysis, and for that matter mentions fifteen issues, mainly related to poetry. These are: (1) Extensive knowledge of prosody. (2) Refined appreciation of poetry. (3) Letter count of a verse for identifying metrical variations. (4) Utilization of the phenomenon of "ta r " in a verse, i.e. the agreement between the last metrical units in both hemistichs of a line 4 of poetry. A line of poetry so characterized is called "mu arra ". Here ibn ab ab observes four possibilities in such an agreement: (a) agreement effecting ta r , as in: in which the number of letters in one hemistich equals that in the other. 1

See ibn Adl n‟s treatise, pp. 19, 21, 58 & 80. See, for example, Vol. 3, p. 32 and Vol. 4, pp. 22-25. 3 See Vol. 1 (of this series), p. 100. 4 See the treatise extracted from Adab a - u ar ' in this volume, p.76. 2

8

(b) agreement not effecting ta r , as in: in which the count of letters is also the same in either 1 hemistich. This kind of verse is called "muqaff ". (c) agreement effecting ta r , as in the following verse: in which the number of letters is not equal between the two hemistichs, and which contains geminated letters. (d) disagreement effecting ta r , as in: in which the ta r is prompted by lengthening the letter ( ) of ( ) in delivery to sound like ( ), and thus correspond to ( ). (5) Looking out for letters that go together, such as (‫ )ا‬and (‫)ل‬. For example, a message ciphered using bird names, in which the letter (‫)ا‬ is represented by "sparrow" and the (‫ )ل‬by "crow", would have the twosome "sparrow crow" recurring more often than any else. (6) Seeking three-letter and four-letter words (trigrams and tetragrams) with the letters (‫ )ا‬and (‫)ل‬, for the identification of these letters in a word would probably lead to the identification of the whole word. (7) Pursuing two-letter words (bigrams), such as the particles: ٍ‫ي‬, ٔ‫أ‬, ‫يز‬, ٍ‫ػ‬, etc. ; and imperative verbs, e.g. ‫خز‬, ‫دع‬, ‫سم‬, etc. Note here that al-Kind has already indicated the importance of the occurrence frequency of bigrams or the so-called contact count. (8) Tracing long words along the lines of long poetic meters such as ‫اسحفؼال‬, ‫يفاػالت‬, and the like.

1

See the treatise extracted from Adab a - u ar ' in this volume, p.76.

9

(9) Making use of the beginning of the second hemistich, so far made out, in determining the conjunctions (ٔ) and (‫ )ف‬if the context suggests words joined by means of conjunctions. (10) Approximation of vocalized and neutral beats, based on the letters already identified, thus establishing a criterion for assessing the metrical measure of the cipher verse. The criterion is supposed to be equal to the letter count; otherwise the analogy should be changed over until the criterion fits the cipher exactly and evenly. By the criterion ibn ab ab probably means scansion, i.e. the practice of marking off lines of poetry into metrical units known as feet, expressing the foot segments of a verse in terms of their metrically corresponding vocalized and neutral beats (e.g. ٍ‫ فؼٕن‬ //o/o). (11) Applying the previous criterion in revealing intractable letters, through matching it up against the letters of the alphabet until it accords closely with the intended meter, and the word is written accordingly. ibn ab ab warns the cryptanalyst here not to focus all his/her attention on certain letters at the expense of other letters, because “that is likely to protract your toil and disrupt your execution,” he says, maintaining that “cracking one letter often serves as a key by which to pierce through other letters that are still 1 unresolved.” (12) Making full use of the Arabic syntax, which calls for certain succession that is sine qua non for correct wording in Arabic. For example:  A relative pronoun (e.g. ٘‫ )انز‬requires an antecedent.  Letters specific to verbs are not followed by nouns.  Letters specific to nouns are not followed by verbs.  Adverbs of time and place require the nouns by which they are governed, or to which they are annexed.  Positions of nouns, verbs, and particles should be observed in context. ibn ab ab notes that confusion of meaning and structure in poetic ciphers, as well as non-observance of what is easy and familiar, would in all probability lead to difficult cryptanalysis. 1

See his treatise, p.34.

10

(13) Utilization of the special order of letters dictated by unusual poetic necessities. This is what is termed by Arabic language scholars "poetic licence" –––the acceptable deviation, on the part of the poet, from rule or conventional form of poetry to produce the desired effect, such as the use of triptote where diptote is typically appropriate; e.g. where the word is used instead of the syntactically correct form , to set up the meter. Another example is the use of a prolonged "alif" where a shortened one ought to be used, or vice versa: in which the word (

) should have been ( ), in proper Arabic.

(14) Trying all over again in case one letter only remains obscure of the cipher verse. (15) ibn ab ab sums up three requisites for efficacy in poetry cryptanalysis, i.e.: a. acquaintance with the general texture and constitution of the Arabic word (letter combinability), the frequently used words and those less or never used. b. familiarity with the Arabic syntax and grammar. c. adequate knowledge of versification and metrical patterns.

1.3.3. Methods

of

Encipherment

by

Simple

Substitution Although ibn ab ab ‟s treatment of encipherment does not generally cut across a single type, i.e. simple substitution, it can be classified into three categories: a) Substitution of certain generic names for letters: Of these genera he mentions birds, beasts, people, aromatic plants, tools and instruments, jewellery, etc. b) Encipherment by bead threading, mentioned later by ibn 1 Dunayn r . ibn ab ab ‟s reference to this method here is an 1

See Chapter 30 of ibn Dunayn r‟s book (Vol.4 of this series), p.44 and p.134.

11

indication to its popularity in the fourth century of the Hegira (Ninth AD), i.e. two centuries prior to ibn Dunayn r. c) Picturing different marks, through devising special signs and symbols substituted for letters, such as those used by ibn ad-Durayhim 1 in his two practical examples . To be noted is that ibn ab ab never touches upon any of the many encipherment methods treated by his predecessor al-Kind ; he rather restricts himself to simple substitution in its simplest varieties, with the employment of word-spacers.

1.3.4. An Example of Poetry Encipherment The example given by ibn ab ab concerns itself with the encipherment of a well-known line of poetry by 'Imru' al-Qays:

by simple substitution (category (a) above). Encipherment has been performed as follows: Letter

1

Bird Name peacock

Letter

Bird Name Buzzard

pheasant

Crow

hawk

Raven

falcon

Francolin

harrier

Grouse

merlin

Bobwhite

eagle

Ringdove

saker

Pigeon

vulture

Duck

See ibn ad-Durayhim‟s treatise (Vol.3 of this series), p.102 and p.116.

12

It is worthy to remark that the arrangement of bird names has suffered confusion in the ciphertext of the original manuscript, probably owing to a scribe‟s omission. However, the arrangement has been set right here in light of the plaintext as follows: peacock pheasant hawk falcon harrier merlin eagle falcon saker merlin vulture buzzard crow harrier buzzard harrier raven eagle falcon francolin grouse harrier bobwhite peacock ringdove hawk grouse grouse raven buzzard harrier buzzard falcon hawk grouse pigeon duck raven grouse pheasant crow raven eagle grouse.

Note that the number of names is identical to the number of letters of the verse (i.e. 44).

1.3.5. Management of Poetry Encipherment By this management is meant the placement of cipher words on an endless circle, from which all poetical meters relevant to that circle disengage themselves, provided that those words are capable of such disengagement. Also the first word of the cipher verse is not identified ––each word of it is a potential start. ibn ab ab illustrates his point with a verse whose composition and metrical units fit in quite harmoniously with the meters peculiar to the circle of the similar. This is the third of the metrical circles, so named because all its parts are similar seven-bit feet adding up to 21 bits in all. Three meters develop or emanate from this circle, i.e. haza , ra az and ramal, as shown in the following figure:

13

Accordingly, the circle has been divided into 21 equal parts serially numbered. Against the numbers are placed the corresponding strokes (denoting vocalized letters - arak t-) or bubbles (denoting neutral letters -suk ns-). If we start from the number (1), al-haza meter emanates with its feet ٍ‫ه‬ٛ‫هٍ يفاػ‬ٛ‫هٍ يفاػ‬ٛ‫يفاػ‬. If we start from the number (4), i.e. leaving out the first syllable ( ‫ )يفا‬of al-haza foot, ar- ra az meter emerges with its feet ٍ‫يسحفؼهٍ يسحفؼهٍ يسحفؼه‬. If, however, we start from the number (6), i.e. skipping the second syllable ( ‫ـ‬ٛ‫ )ػ‬of the foregoing haza foot, ar-ramal meter disengages itself: ٍ‫فاػالجٍ فاػالج‬ ٍ‫فاػالج‬. Given that ibn ab ab ‟s illustrative example is: (a brachycatalectic ra az), it is interesting to distinguish the possible alternatives, represented by the following model.

14

Let us start with the second word ( ‫ى‬ٚ‫)كش‬, from which emerges the haza meter. Notice how the letters of the haza verse are written (inside the circle) against the corresponding scansion represented by strokes and bubbles (outside the circle). The verse is:

But the circle has room for no more than 3 feet, interrupting the verse at ( ‫)سا‬. With the first syllable left out, the second alternative (ra az) emanates, the letters of which are written next to the first starting from the second syllable. The verse is:

Likewise, skipping the second syllable prompts the emergence of the third alternative (ramal) whose letters are written next to the second starting from the third syllable. This verse is:

ibn ab ab stresses the point that in this type of cipher, letter cryptanalysis should be performed before looking out for the meter. He maintains that meter may straighten by whatever word it starts ––something likely to cause ambiguity to the cryptologue through driving him/her to mistakenly believe that their cryptanalysis is correct as long as the meter is sound, while in fact it is not. The previous example is a case in point.

15

16

Chapter 2

ibn ab ab ‟s Edited Treatise

17

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.1

1

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

18

2.2. Description of the Manuscript ibn ab ab ‟s manuscript is the first in the order of treatises included in the assemblage of cryptology. It occupies some 5 sheets thereof, i.e. the sheets 48/A-53/A. The title of the treatise and the name of its author appear on the first page of the manuscript in this wording: “Ris lat Ab al- asan ibn ab ab al- Alaw f 'isti r almu amm (The treatise of Ab al- asan ibn ab ab al- Alaw on cryptanalysis)”, followed by: “In the name of God, the Most Gracious, the Most Merciful”.

19

A photocopy of the title page of ibn ab ab ‟s Treatise (Document No. 5300, as-Sulaym niyya Ottoman Archives, Istanbul, Turkey)

20

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

21

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

22

2.3. ibn ab ab ‟s Treatise on Cryptanalysis (Original Arabic Text and English Translation)

23

ibn ab ab ’s Treatise on Cryptanalysis

In the name of God the Most Gracious, the Most Merciful

You have asked [me] -may God honour you- to draw up an outline of the principles of cryptanalysis, by which to augment your intelligence, stimulate your spirit, and engage your intellect ––an outline that facilitates your comprehension of the concealed and promotes the elicitation of the ambiguous. Your special request is also to shorten the path to cryptanalysis, cultivating the rough work of it, so that you can proceed smoothly without toil or boredom to your goal that is made easy of access on reflection. I did my best to [tersely] expound the subject, in the hope that it would turn out to be of great advantage.

24

Bear in mind that all that is enciphered of prose or poetry is restricted to twenty-eight letters, assuming various cipher forms invariably repeated. Recurrence of letters and identification of wordspacers are likely to gesture towards what is enciphered in prose and poetry alike. Professional users of the Arabic language were acutely aware of the combinability of letters in words, the letters that are not combinable, and also operative and inoperative letters in the language, all according to the account of al- al l ibn 'A mad [al-Far h d ] in his book al- Ayn. Of the twenty-eight letters [that constitute the Arabic alphabet],

scholars recognized the highly frequent and the less frequent.

We say, by way of elucidation, a brief statement that is instrumental in cryptanalysis: You should know that the letters (‫ )ا‬and (‫ )ل‬are of highest frequency in usage; the next highest are: (‫و‬, ٌ, ٘,‫) ب‬, followed by (‫ع‬, ‫ْـ‬, ‫ت‬, ٔ), and then the rest of the alphabet. If you encounter a poetry cipher, approach it in the way I am going to explain, and thus you are in line for cryptanalysis, God willing.

26

Among the tools to be used in poetry cryptanalysis are profound knowledge of, and involvement in, prosody [poetic meters and versification], refined appreciation of poetry, and counting the letters of a cipher verse, thereby identifying metrical variation in it. Ponder upon the verse meter and letters on the basis of the verse length. Having known that, you set out to calculate the number of cipher forms of the verse, and then you divide the sum into two equal halves. If the dividing point happens to be a word-spacer, consider the last form in the first hemistich and compare it with the last form of the verse. If found in agreement, the verse is known to be “mu arra ”. However, agreement may occur without the verse being “mu arra ” [in which case the verse is “muqaff ”]. Now if the last word in the first hemistich overflows half the total number or falls short of it, with one hemistich exceeding the other by one or two or three letters, you establish that one hemistich contains geminated letters, and that the end of the first hemistich is where the word interruption occurs. Another possibility is that the verse may be “mu arra ” although the last letter of the first hemistich looks in disagreement with the last letter of the verse (the rhyme). That is to have, for example, ( (

), or to have (

) with (

) with

) for the feminine, in which case both

hemistichs agree in meter and differ in cipher form and the addition of a letter.

28

Then you examine letters that go together. For example, in a verse ciphered using bird names, if you find the form “crow” recurring with “sparrow”, and “sparrow” recurring with “crow”, you can positively gather that the one is the letter (‫)ا‬, the other (‫)ل‬. You move on to search for a three-letter or four-letter word incorporating the letters (‫ )ا‬and (‫)ل‬. If these two letters are found to take initial and terminal positions in the word, you are likely to assume the letter(s) in between. If, however, they both occur at either side of the word (initially or terminally), you are bound to presume the preceding or the following letter(s), and so to make up the word. Next you work out a two-letter word and suppose that it is any of the following [particles]:

,

,

, , , ,

, ,

,

, , , or such

similar words exacted by the preceding word or the following one. Two-letter words might be imperative verbs such as: , ,

1

,

,

,

1

,

, , etc.

Note: To cryptologists, what counts is the graphical representation only. Thus, the gemination in ( ّ‫ )يذ‬does not make a difference, while it does by the standards of lexicographers.

30

You then proceed to seek long words after long metrical patterns such as (

); and if such word was governed or annexed by a

feminine it would still be longer, and is inflected accordingly into ,

,

,

or

, both in the construct and absolute

states. Investigate the possibility of the second hemistich starting with the conjunction (ٔ) in some cases. The same applies to most initial letters of words in the context if you get an indication that the word connection is liable to be joined properly by means of conjunctions like (ٔ) and (‫)ف‬.

32

Having worked out a few letters of the verse, you are now poised to assess its meter. Using a criterion of your own, you seek scansion through approximate vocalized and neutral beats. Your scanning criterion is supposed to be completed right when the letters of the verse are all used up. In case this criterion proved in excess of the letters, or vice versa, you would have to change the criterion and the analogy, and take up a different approach to letter manipulation in order to attain the meter. Try to match the beginning of the verse with its middle and end, beating your brains out on it from beginning to end. Do not seek to work out certain letters at the expense of other letters because that is likely to protract your toil and disrupt your progress. Bear in mind that cracking one letter often serves as a key by which to pierce through other letters that are still unresolved. Intractable letters that respond to the scanning criterion without showing their true structure are matched up against the letters of the alphabet (‫ت ب ا‬

‫ )… خ‬until you hit upon the meter that closely

match your estimation, and thus you spell out that word accordingly, as all the Arabic language is of necessity composed of the 28-letter alphabet.

34

It should be pointed out that correct word composition [in Arabic] involves giving letters their due meanings by adhering to a certain order. You should therefore know that the relative pronoun ( ٘‫)انز‬ requires an antecedent; that letters peculiar to verbs are not followed by nouns; that letters peculiar to nouns are not followed by verbs; that adverbs of time and place call for the nouns by which they are governed, or to which they are annexed, as is dictated by word composition; and that positions of nouns, verbs and particles are observed in context: Do not focus your attention on manipulating a word after a noun pattern while it is in fact a verb, or after a verb pattern while it is a noun; or otherwise confusing an uninflected (mabn ) particle with a noun, or a noun with an uninflected particle. What makes cryptanalysis all the harder is the encipherment of an out-of-the-way verse that is confused in meaning and structure, and that deviates from what is typical, familiar and comprehensible. The more unsteady and incomprehensible the verse, the more trying and difficult its cryptanalysis.

36

Of the most robust algorithms for cryptanalysing [poetry] ciphers is the utilization of the artistic licence of using a special order of letters made necessary to set up a sound meter. In cryptanalysing a cipher verse, if you fail to arrive at the meter by your means, you might as well change the order of certain letters, prolong them, or shorten their utterance. Managing thereby to get the meter of the verse, it would be now easier for you to seek its letters towards cryptanalysis, God willing. You may have managed to work out the best part of the cipher verse and determine its meter and word uniformity, with only a single letter still obscure. The search for that letter would lead you to undo all your manipulation and to try all over again, adopting a different approach. It is important, therefore to exercise a high degree of persistence and forbearance in dealing with difficult ciphers; brainwaves often come all of a sudden subsequent to long patience. To make it clear to poets and to people of letters and intellect, there are three requisites for effective poetry cryptanalysis, namely:

38

 Acquaintance with the constitution of the Arabic letters, which is limited and well known as regards letter combinability and non-combinability, words frequently used and those less or never used.  Proper use of words (nouns, adjectives, verbs, particles, adverbs, antecedents) in their appropriate places in context through the assimilation of Arabic syntax.  Cognizance of the fact that poetry composition is a restricted art, strictly governed by meter and therefore has no room for any addition, deduction, vocalization of a neutral letter or neutralization of a vocalized one, except within the bounds of metrical variations. Keep in mind that sound and authentic truths readily appeal to the mind and persist until they manifest themselves. On the other hand flimsily-based judgements are sure to boggle the mind and are soon dismissed as unacceptable. Below we are stating names of birds that exhaust the number of letters, followed by a typical cipher to be taken as an illustrative example [of encipherment by simple substitution], God willing. Peacock, pheasant, hawk, falcon, harrier, merlin, eagle, saker, vulture, buzzard, crow, raven, francolin, grouse, bobwhite, ringdove, pigeon, duck, shrike, partridge, lark, crane, magpie cock, hen, nightingale, (babbler), phoenix, kite, woodpigeon, dove, ostrich, turtledove, rail, rhea, wren.

40

You may opt to do encipherment not by substituting for letters names of birds, but names of beasts, people, perfumes, fruits, aromatic plants, tooling or jewellery. You may also encipher by threading beads the same way as you encipher by names; or otherwise by picturing different marks (signs and symbols), each to serve as a substitute for a letter of your choice. Accordingly, if you engage in enciphering a line of poetry, you start substituting for every letter the name of, say, a bird. Use that name every time that particular letter recurs. At the end of a word you place a space such as a circle, dots, or any other signs indicating word spacers. For example, to encipher the following verse:

1

we write : Peacock pheasant hawk falcon harrier merlin eagle falcon harrier buzzard falcon hawk grouse pigeon duck raven grouse pheasant crow raven falcon saker merlin vulture buzzard crow harrier buzzard harrier raven eagle falcon francolin grouse harrier bobwhite peacock ringdove hawk grouse raven grouse buzzard eagle.

1

The arrangement of bird names is mixed up here, probably owing to a scribe‟s oversight. However, it has been set right in the analytical study; see p. 12.

42

Encipherment may be done by placing the cipher verse on an endless circle without any indication as to where the verse begins. Each word in it would be fancied as the first, which makes cryptanalysis more and more complicated. If you are challenged with such a cipher, you start right by working out its letters before manipulating its meter. If, however, the beginning of the cipher is already known, then start resolving the meter first. That is so because starting on the meter of a cipher verse without knowing its beginning may result in a perfectly sound meter but other than the correct one for the cipher in hand. In that case it is treated like the metrical circles from which relevant meters disengage. Every cipher verse whose beginning is not designated is apt to develop meters associated with the category to which it belongs. Note that word spacers often chance to coincide with the beginnings of metrical measures. Suppose that you are to cryptanalyse a verse of the haza meter, and that you figure it out as ra az or ramal. The letters would not help you unless you happen on a verse whose composition and metrical measures quite match the meters peculiar to the appropriate circle, without losing any of its letters or meaning. Example:

44

If you are to encipher this verse, you will soon realize that it makes sense and stands metrically correct from whichever word you start reading it. As it stands, it belongs to the ra az meter. By some word permutation it may be made into haza :

Also you could say:

or you might say: 1

These are just examples against which to match and judge by analogy. Given a poetry cipher whose beginning is obscure, make sure that you start by trying to work out its letters before you try its meter. If the beginning is overt, you handle its meter before letters, or both in parallel, God willing.

End of treatise

1

Further permutation produces the following two verses:

46

‫ن بنِ طَباطَبا العلويّ‬ ‫رسال ُة أبي الحس ِ‬

‫‪1‬‬ ‫‪2‬‬

‫‪79‬‬ ‫‪79‬‬

‫‪25‬‬

1

54 41

61 47

2

349 343 254 238 1 60 59

3

343 342 293 290 1

27

1

196 71

1

32 2

196

3 4

196

5

196 196

6 7

81

196 81

29

196

8

1

197 81

2

197

3

197 197

5

197 82

4

197 197 197

6 7 8 9

197

10

197

31

11

1

197 197

2 3

197

4

197 197

33

5 6

197

1 2

197

3

197

4

84 198

35

5 6

1

198 198

2 3

198 198 198

37

4 5

198

1 2

198

3

198

4

198 85

198 198

5 6 7

199

8

86

9

199 86

39

199

10

1

200 199 87 86

2

307 303 1 199

87

3 4 5

41

1 2

200

3

304

43

1 2

201 201

4

201 201 90

3

5 6

201 201

7 8 9

201 90

10

201 201 90

201 201

90

45

11 12 13

74

74

91

202

1 2 3 4 5

6

203

47

7

48

The Second Treatise A Treatise on Cryptanalysis of Poetry by the Author of Adab a - u ar '

49

50

Chapter 1

Analytical Study of the Treatise on Cryptanalysis of Poetry by the Author of Adab a - u ar ' (The Art of Poets)

51

52

1.1. Preliminary We could not track down the name of the author of this treatise, nor has his book got a mention in any of the numerous references consulted. However, the following points can be drawn right from the beginning of the treatise: a) It is entitled: “Treatise on the Cryptanalysis of Poetry”. b) It is extracted from an earlier book by the same author, known as Adab a - u ar ' (The Art of Poets), which he sometimes dubs the Large Book. c) It has been seemingly extracted at the behest of an official in power or a notability who was seeking to learn this art. Compared with other treatises, this one is estimated to have been written after ibn ab ab ‟s treatise (AH 322/AD 934), and prior to ibn Dunayn r‟s (AH 627/AD 1229), since it has made use of the first, 1 and was one source of the other .

1.2.

Structure of the treatise

For ease of handling, the treatise can be divided into the following sections: - Definitions - Requisites and tools for poetry cryptanalysis - Prosody and rhyme - Insight into the knack of writing - The importance of metrical measures - Impediments to cryptanalysis - Examples - Annexes It should be pointed out, before proceeding to study these sections in depth, that we have had recourse to ibn Dunayn r‟s book, just the way we turned to this treatise upon addressing ibn Dunayn r. That is 1

See Volume Four, pp.5-8.

53

so because both works have some decent material in common. To avoid repetition, passing references should often be sufficient to elucidate particularly knotty aspects and fine distinctions.

1.2.1. Definitions The author opens his treatise by demonstrating what is meant by saying that someone cryptanalyses cipher poetry. He maintains that enciphering poetry relates primarily to converting the forms of letters into names of birds, flowers or people, or representing letters by Persian or Syriac configurations or other symbols. This process clearly belongs under encipherment by substitution. Yet he qualifies it by the employment of word-spacers. As he puts it: “Words are separated by 1 an element that is not part of the cryptogram…” . To him, the idea of encipherment and cryptanalysis is perceived to involve mental exercise and fun in company as its main objective: “Then he [the encipherer] turns the cipher over to the cryptologue saying: „What do 2 you think have I enciphered for you?‟ ” . According to the author, then, it is hardly more than a brainteaser that is placed for solution in literary entertainment sessions, as he plainly states later in the treatise: “... because this science is meant for good fun and [the exhibition] of literary subtleties in the company of notables and in the 3 communication with peers.” It is no wonder that the author is so oriented, since he is after all a poet and a man of letters, on the evidence of his above-mentioned book, and also his advice to the cryptanalyst: “Having succeeded in working out the cryptogram, the best to do, if he [the cryptologue] is a poet, is to incorporate the cryptanalysed verse into a few lines of poetry he composes along the 4 same metric pattern” . This type of poetical encipherment that is intended for mental exercise was, in fact, well known among many poets, who used to

1

See p.70. See p.70. 3 See p.104. 4 See p.70. 2

54

compete for developing it and showing skill in ever more diversifying its presentation.

1.2.2. Requisites and tools for poetry cryptanalysis The author entitles this section "An algorithm of cryptanalysis". He states a number of characteristics typical of a cryptanalyst, most of them are in effect sciences or skills that ought to be mastered in order to gain the ability to cryptanalyse. Some of these characteristics are acquired through experiencing the sciences proper. The sciences are: - Prosody (Metrics) - Rhymes - Insight into the art of writing - Poetry. The characteristics are: - Perspicacity - Keen intuition - Resourcefulness - Promptitude. To be able to cope with ciphers, irrespective of their degree of complexity, the cryptanalyst should have a good practical grasp of all the sciences and characteristics stated above, or at least most of them. Otherwise, he is not likely to lend himself to this profession, or stand a chance in cryptanalysis. The author then explores the individual sciences under a single heading, i.e. “The use of each of the afore-stated sciences”.

1.2.3. Prosody and rhyme The author gives a brief account of prosody, pointing out to the five metrical circles of Arabic poetry, the fifteen poetic meters with the related foot variations of az-zi f, al- arm and al- azm, also the number of letters for each meter, as well as other relevant issues 1 discussed at great length in ibn Dunayn r's book. Next he approaches rhymes, indicating some types and expanding on a number of terms thereof. He considers the so-called al-mu arra 1

Q.v., p. 49 and pp. 144-46.

55

verse the same as the so-called al-muqaff , in contrast with ibn ab ab who draws a fine distinction between the two after the fashion of Arab prosody scholars, who argue that al-mu arra is a line of verse in which the last foot of its first hemistich (i.e. its ar ) is made to agree with the last foot of its second hemistich (i.e. its arb) in rhyme and meter, by adding to, or omitting from its ar . They maintain, on the other hand, that al-muqaff is a line of poetry whose ar agrees exactly with its arb, as far as meter and rhyme are concerned, without any additions or omissions made. To be noted is that ibn Dunayn r‟s stock-in-trade in prosody and rhyme outruns that of the author of this treatise, although they have a lot in common ––a fact which demonstrates clearly their adoption of a common source, tapped extensively by ibn Dunayn r, and more sparingly by the author of this treatise. The source is most probably the author's Adab a - u ar ' itself, the parent work of our subject of discussion.

1.2.4. Insight into the knack of writing The author here states a number of rules and principles relevant to the art of writing, and at the same time beneficial to cryptanalysis. According to their order of citation in the treatise, these are the following: 1. Spotting the letters ‫ ) ( ا‬and ‫( ل‬l). 2. Checking two-letter words (bigrams) such as: ‫لذ‬, ٍ‫ي‬, ‫ذ‬ٚ, etc. 3. Watching out for silent letters: letters written but not pronounced (e.g. the terminal ٔ in the proper name ٔ‫ [ ػًش‬Amr], and the functional ‫ ا‬of differentiation added to verbs denoting plurality such as ‫)لانٕا‬. 4. Attending to voiced letters: letters pronounced but not written (mainly the letter ‫ ا‬in such proper names as ‫ى‬ْٛ‫ إتش‬and ‫)إسحك‬. 5. Identifying the so-called "six nouns" and the potential changes that they undergo by declensional parsing. 6. Seeing to the letters ٔ ( /w) and ٘ ( /y) in all their modes and settings (i.e. being diacritically neutral, vocalized, geminated, at end-position, and as rhyme letters). 7. Spotting glottal stops (hamzas). 8. Tracing prefixes (conjunctions, prepositions, etc.)

56

9. Marking the letters ‫( ت‬t) and ‫( ْـ‬h) at end-positions (e.g. ‫لايث‬, ‫سحًة‬, ّ‫)فؼهح‬. 10. Scrutinizing doubled and geminated letters (e.g. ‫لهم‬, ‫ِذ‬ٛ‫)س‬. 11. Guessing probable words and using them as a vehicle for uncovering other words. 12. Observing noun structures defined with (‫ )ال‬and their different variations. 13. Special cases (with words). Any further discussion of the above principles will prove redundant, as most items have already been exhaustively analysed in ibn Dunayn r's book. Moreover, they are lucidly presented in the edited treatise that will follow, such that, with the additional annotations, they are made unmistakably intelligible. It has been found necessary, however, to make a specific reference to the twelfth item on account of its own significance on the one hand, and to demonstrate fresh aspects in it not raised by ibn Dunayn r on the other hand. Noun Structures Defined With (‫ )ال‬And Their Different Variations The author mentions a group of words defined with (‫)ال‬, in which the letters (‫ )ا‬and (‫ )ل‬are of frequent occurrence, and of which three or more letters are known of each word, with the rest still covert. The words mentioned here exceed in number those mentioned by ibn Dunayn r for that matter. The author poses possibilities and alternatives for cryptanalysing a certain letter depending on its relative position in a word, and also on the word‟s structure and measure. The following is a list of these words, with the unknown letters indicated by the symbols: v,w,x,y & z. 

Word Structure x‫الل‬ ‫ ل‬x‫الل‬ ‫ ا‬x‫ال‬ y‫ا‬x‫ال‬ x‫ا‬x‫ال‬

Examples ‫اهلل‬, ‫انهة‬, ‫انهح‬, ‫انهف‬, ‫انهز‬, … ‫م‬ٛ‫انه‬, … )‫انًا(ء‬, )‫انذا(ء‬, )‫انٓا(ء‬, … ‫انذاس‬, ‫انُاس‬, ‫انساق‬, ‫انؼاس‬, ِ‫انثا‬,… ‫انثاب‬, ٔ‫انٕا‬, ‫انشاش‬, ‫إنًاو‬, ‫إنحاذ‬, ِ‫أنٓا‬, ‫أنثاب‬,...

57

z‫ا‬yx‫ال‬ wz‫ا‬yx‫ال‬ z y‫ ا‬x‫ال‬ wv‫ا‬zyx‫ال‬

‫انضشاب‬, ‫انظٕاب‬, ‫انثٕاب‬, ‫انؼماب‬,... ‫انًماَة‬, ‫انًُالة‬, ‫انضشاغى‬, ‫انظٕاسو‬, ‫انٕسائم‬,... ‫انغائة‬, ‫انضاسب‬, ‫انمادو‬, ٙ‫انشاي‬, ْٙ‫انضا‬, ٙ‫انكاف‬, ‫انحادخ‬,...

zyx‫الا‬ ‫ا‬yx‫الا‬ ‫ا‬zyx‫الا‬ y‫ا‬x‫الا‬ z‫ا‬yx‫الا‬ zy‫ا‬x‫الا‬ wzy‫ا‬x‫الا‬ ‫ ا‬x‫ا‬

ٖٕ‫األل‬, ‫األكثش‬, ‫األػظى‬, ‫األفضم‬,... )‫اإلػطا(ء‬, )‫اإلغضا(ء‬,... )‫ا(ء‬ٛ‫األدػ‬, )‫ا(ء‬ٛ‫األٔح‬, )‫ا(ء‬ٛ‫األَث‬,... ‫يال‬ٜ‫ا‬, ‫خاو‬ٜ‫ا‬,... ‫األػًال‬, ‫األحٕال‬, ‫األػًاو‬, ‫األفؼال‬, ‫األطًاس‬,... ‫األػاخى‬, ‫ة‬ٚ‫األطا‬, ‫ة‬ٚ‫األخا‬, ‫األطاغش‬, ‫األكاتش‬,... ‫ة‬ٛ‫األػاخ‬, ‫ة‬ٛ‫األَات‬, ‫د‬ٚ‫األحاد‬,... ‫إرا‬,...

1

‫انًحماسب‬, ٘‫انًحؼاد‬, ‫انًحماطش‬, ٍٚ‫انًحثا‬,... w v z ‫ ا‬y x ‫م ا ل‬ٚ‫انمُاد‬, ‫م‬ٚ‫انًُاد‬, ‫ز‬ٚٔ‫انحؼا‬,… v ‫ ا‬z y x ‫انًُحاب ا ل‬, ‫انًغحاب‬, ‫انًؼحاو‬, ‫اس‬ٛ‫انًؼ‬, ‫انًغٕاس‬,... v ‫ ا‬w z y x ‫انًسحؼاس ا ل‬, ٌ‫انًسحؼا‬, ‫انًسحفاد‬,...2

These are followed in the treatise by helpful observations towards cryptanalysis. These are: 1. The letters of lower frequency of occurrence are: ‫خ‬, ‫خ‬, ‫ر‬, ‫ص‬, ‫ؽ‬, ‫ظ‬, ‫ط‬, ‫ ط‬and ‫ش‬. 2. It is unlikely in poetry the occurrence of a geminate (doubled) letter immediately after the letter (‫)ا‬, such as: ‫داتّة‬, ّ‫دٔاب‬. 3. No two consecutive neutral letters are likely to occur in Arabic poetry except in a rhyme characterized by relief such as: ْ‫ اندٕاد‬in the following verse: ْ‫فانساتك انساتك يُٓا اندٕاد‬ ْ‫م انطشاد‬ٛ‫انُاط نهًٕت كخ‬ 4. There are a few long Arabic words that are devoid of the letters (‫ )ا‬and (‫)ل‬, e.g. ‫كٓى‬ٛ‫كف‬ٛ‫فس‬, ‫سُسحذسخٓى‬. 1

This is true for words of this rhythmical measure having two initial affixing letters; otherwise words of different beats, without the letters (‫ )و‬and (‫)ت‬, are also possible such as ٙ‫شاف‬ٛ‫انس‬, َٙ‫انؼثًا‬, ٙ‫اندغشاف‬, ‫انًشخاَة‬, etc. 2 Similarly, this holds good for words of this rhythmical measure having three initial affixing letters; otherwise words of different beats, without the letters (‫)و‬, (‫ )ط‬and (‫)ت‬, are also conceivable possibilities, e.g. ‫اء‬ٚ‫انكثش‬, ‫شاء‬ًٛ‫انح‬, ‫ات‬ٚ‫انححذ‬, etc.

58

1.2.5. The importance of metrical measures The author reiterates the importance of meter in the process of cryptanalysing poetry ciphers. He draws attention particularly to meters which do not belong under the classical measures of Arabic poetry, and which are in wide circulation among postclassical neo-poets. To illustrate his point, the author quotes one example of such types of meter, highlighting the futility of observing a sound meter in producing nonsensical verse. This practice virtually amounts to the same thing as raving, the author says.

1.2.6. Impediments to cryptanalysis The author surveys special problems that could impede, or unduly slow down the cryptanalyst's endeavour towards solution, or even make it impossible. The following is a brief summary of these hindrances, inasmuch as they have already been dealt with in ibn Dunayn r's book: - Using undotted letters. - Using separate letters that do not link with other letters. - Deliberately employing dotted and undotted letters alternately. This can be exemplified by two verses attributed to the poet 1 af ad-D n al- ill , in which he expertly alternates one undotted word with another dotted one:

- Infrequency of letter occurrence in the cryptogram. - Using previously unknown or unheared-of poetry in cipher. - The verse sought for cryptanalysis being very short or very long: A very short cipher is most likely to indicate one of the meters: 2 split ra az, manh k ra az, curtailed sar , or curtailed munsari . A poetical cipher rendered using any of these meters would turn out hard to cryptanalyse because of the infrequency of letter occurrence in it. A very long verse, on the other hand, will 1 2

d. AD 1349. See p.110.

59

probably contain plenty of the letters (ٔ) and ( ‫ )ْـ‬as dependant (or inseparable) pronouns, and also of the functional (‫ )ا‬of differentiation that appear in the written spelling of past verbs 1 denoting plurality, as in: ‫ لانٕا‬and ‫فؼهٕا‬. - Unsound meter, language and syntax. - The meter used breaching the established measures of Arabic poetry. - Problematic peculiarities such as the occurrence of the so-called phenomena of al-qab and al-kaff simultaneously, which is 2 unacceptable in Arabic poetry. - The first hemistich of a verse of the aw l meter being affected by the arm phenomenon, making it into the k mil meter. - The cryptogram being affected by errors in encipherment. - The verse being drawn from the circle of the “different”. - Dealing with nonsensical poetry. In the course of the treatise the author often makes reference to the "Large Book" where he further develops his argument on prosody. This book may probably be Adab a - u ar ' itself. The likelihood is that ibn Dunayn r has drawn from the “Large Book” itself, not only from the extracted treatise, because his treatment of the subject actually transcends its contents, yet conforms to it in many ways. The author concludes this section by stating the purpose of poetry encipherment, which is barely a sort of intellectual luxury meant for good fun in the company of prominent personalities convoked on special occasions, or in friendly communications. This, in fact, stands in marked contrast to prose encipherment, which involves far more serious applications, sometimes of vital and urgent strategic implications (military, political, etc.).

1.2.7. Examples The author works out three illustrative poetical examples, which he describes as accessible and easy to solve. A perceptive look shows that he utilizes the simple substitution method of encipherment all 1 2

See p.96. See ibn Dunayn r's book, p.53 and p.170.

60

through, substituting for each letter a proper name associated with it, and employing a distinctive space between words. For each example the author traces special peculiarities, and names the metrical measure of individual verses. His comments make these examples too obvious to need any further explanation.

1.2.8. Annexes The treatise ends with lines of poetry that fall into two groups: the one contains verses intended for sustained mental exertion in pursuit of cryptanalysis; the other covers verses rounding up the Arabic alphabet, and so serving as cipher alphabets or cryptographic keys. Examples of both groups appear in ibn Dunayn r's book, most of which are here repeated. It is particularly interesting, however, to point out the three lines of verse that the author cites first. The three lines markedly differ from all else in nature, form and characteristics. Here he expresses the intended purport by spelling out the constituent letters of the target words in full, with each resultant word thereof bracketed beside the respective verse. This type of poetry has later become popular among recent poets. The following is an example of such poetry:

The treatise, has been appended by a table of the Arabic letters classified in groups according to their places of articulation in the human vocal apparatus, to be followed by a line of verse embracing all the letters of the Arabic alphabet.

61

62

Chapter 2

The Edited Treatise on Cryptanalysis of Poetry by the Author of Adab a - u ar ' (The Art of Poets) 63

2.1. Description of the Manuscript This manuscript is the last in the order of treatises included in the assemblage of cryptology. It occupies some 15 sheets thereof, i.e. from sheet 119/B to sheet 133/A, with no specific title, but starting right with the name of God. There follows a brief introduction, and then a title in the middle of the page that reads: "What is meant by saying someone cryptanalyses cipher poetry". The treatise thence proceeds. Following are photocopies of the first and last sheets of the handwritten manuscript.

64

A photocopy of the first sheet of the Treatise on the Cryptanalysis of Poetry (Document No. 5359, as-Sulaym niyya Ottoman Archives, Istanbul, Turkey)

65

A photocopy of the last sheet of the Treatise on the Cryptanalysis of Poetry (Document No. 5359, as-Sulaym niyya Ottoman Archives, Istanbul, Turkey)

66

2.2. The Treatise (Original Arabic Text and English Translation)

67

A Treatise on Cryptanalysis of Poetry By the Author of Adab a - u ar '

68

69

In the name of God the Most Compassionate, the Most Merciful In Him trust is reposed You have asked me, may God protect you and back your motives, to extract for you my treatise on the cryptanalysis of poetry from my book that is known as Adab a - u ar ' [The Art of Poets]. I thereupon hastened to undertake the task of committing it to paper, in compliance with your request. Carefully scrutinize it, following the procedure I have given you, and you will hit the mark, Deo volente.

What is meant by saying someone cryptanalyses cipher poetry It means to turn to a line of poetry, and convert the forms of its letters into names of birds, flowers, people, or suchlike; or representing letters by Persian or Syriac configurations or other symbols, as he [the encipherer] pleases until all the letters of the verse are exhausted. Words are separated by an element that is not part of the cryptogram, nor is it a replacement for any letter. The encipherer can also use as spacers circular shapes that he draws with a pen, or even leave the space blank, indicating separate words. Then he turns the cipher over to the cryptologue saying: „What do you think have I enciphered for you?‟ Having succeeded in working out the cryptogram, the best to do, if he [the cryptologue] is a poet, is to incorporate the cryptanalysed verse into a few lines of poetry he composes along the same metric pattern.

70

Algorithm of cryptanalysis A cryptanalyst should be knowledgeable about prosody and metrical structures, well-informed on rhymes and the knack of writing. He is also supposed to be a poet of perspicacity, keen intuition, resourcefulness, promptitude, with a large reserve of poetry committed to memory. If the cryptanalyst comes up to fulfil these attributes combined, he is bound to succeed in cryptanalysing complicated as well as easy ciphers. Failure to be conversant with prosody will reduce his chances of success. Similarly, insufficient knowledge of [Arabic] rhymes is another shortcoming that can make against his ability to cryptanalyse. Moreover, his efforts may well come to grief if he is not a poet himself. What I mean by being a poet is not only the decent capacity for versification, but also the impeccable sensitivity to identify sound and broken meters, and a reasonable appreciation of poetry even when he is not an established poet. Failing these skills, he should observe the other indispensable requirements, or else he would not be worthy nor able to do cryptanalysis.

72

The use of each of the afore-stated sciences As to prosody1, the cryptanalyst should be aware that the metrical circles are five, and that the poetic meters are fifteen. He has to be acquainted with the content of each circle, as well as with such metrical variations as az-zi f, al- arm and al- azm. He should also know the approximate number of letters for each meter, considering the slight distinctions thereof. If the letters [of a verse] turn up to be in excess of forty, up to fifty-five in number, the verse would most probably belong to a - aw l or al-bas meters of the first circle. It is most unlikely to belong to al-mad d meter as it is brachycatalectic, with two metrical units (feet) dropped from its original structure2. Alternatively, the encipherer's verse may be deliberately intended for sustained mental exertion by presenting it in its original form ––a feature not known to have been used before in Arabic poetry. However, the verse may still belong to the perfect k mil meter.

1

2

See also ibn Adl n's treatise, of which the 16th rule has been devoted to prosody and the 17th to rhyme. Readers interested in deeper and more detailed treatment of prosody (poetic measures, metrical circles, foot variations, etc.) and rhyme (its letters, types, flaws and defects, etc.) are referred to ibn Dunayn r's book Maq id al-fu l, p.49 and pp.144-152. These omitted units are specifically the last foot of the first hemistich (i.e. the ar ) and the last foot of the second hemistich (i.e. the arb).

74

In cryptanalysing a poetic cipher pay special heed to the positions [in the cipher] I am to state for you. Count up the letters of the cipher verse and see whether the two constituent hemistichs are equally lettered. The letter count in the one hemistich may be found exceeding that in the other by a letter, two, three, four, or even five. Consider also the terminal letter of the verse and the last letter of the first hemistich; if found the same, the verse is held to be “mu arra / muqaff ” 1. Next you check the letters located prior to each of these two; if found identical, the verse is taken for “murdaf” 2. When the last letter but two in both hemistichs also turns out to be the same letter, it is then assumed to be a "mu'assas" verse3. These positions are of particular interest to prosodists in order to establish the rhyme and the meter in pursuit of solution. But after all, the person with deep insight into the art of writing and spelling is the one who stands a fair chance of success in cryptanalysis. The most highly spotted letters in writing are ‫ ) ( ا‬and ‫( ل‬l) that occur for definition [i.e. to form the definite article] in such words as:

,

,

,

,

and

. When

you observe this form frequently repeated, you conclude that it would be the definite article. Other scattered ‫'ا‬s and ‫'ل‬s are then sought, and the rest of the cipher is now apt to get easier to crack.

1 2 3

See p.55. i.e. of which the letter preceding the rhyme letter is a neutral ‫ا‬, ٔ or ٘. i.e. of which the letter (‫ )ا‬is located prior to the rhyme letter but one.

76

Next you engage in working out two-letter words such as: , ,

,

,

,

,

,… . Such are worth pondering, reflection and sound

conjecture. They might be any of the following: - bigrams with geminated letters, such as: , ,

, , ,

,

, ,

, , and the like.

- two-letter nouns, e.g. , ,

,

,

, ,

- pronouns governed by prepositions, e.g.

- imperative verbal nouns, e.g.

- imperative verbs, e.g.

,

,

,

, , ,

.

.

, .

, , etc.

These serve as the most effective clues towards cryptanalysis.

78

What also should be manipulated with care is the terminal letter ( ) of differentiation subjoined to such past verbs as:

,

,

,

,

, etc. to denote plurality. This ( ) is not metrically counted, and therefore can be very problematical [in cryptanalysis] indeed. Equally confusing are verbs [with an intrinsic ( )] such as: , and that are sometimes wrongly written with a terminal ( ) 1. You should watch out for hamza's in phrases such as: 

[= He bought wine],

 [=I have come to thee from Sheba with a sure

tiding], and

[=wrong]. Yet some writers [mistakenly] drop the

functional ( ) in verbs like:

,

and

extra ( ) added to the proper name

. Be equally heedful of the (= Amr) to differentiate it

from another name, i.e. (= Umar). My view is that it should be dropped altogether in cipher poetry because poetry is usually diacritically vocalized, thus removing the ambiguity, whereas correspondence is not often provided with diacritics. This is particularly true in rhymes, which I never tend to approve. Be also aware of the letter ( ) that is dropped in writing for damping the vocalization, while it is established in articulation, such as the ( ) of the names

[for

],

[for

],

[for

],

[for ] and [for ]. I favour that it be shown in poetry since poetry calls for its retention to put up the meter. Some write the name ( ) in this way as ( ) and ( ) as ( ), making life extremely difficult, particularly if the encipherment is intended for sustained mental exertion.

1

Following the practice of some earlier writers. However, modern-day writers opt out of writing it.

80

Bear in mind that there exist [in Arabic] a few nouns that end in the letter (ٔ) in the nominative; the nouns being: , , , , and

. This final (ٔ) transforms into ( ) in the objective, and into

( ) in the genitive and prepositional cases. Thus you say nominative,

in the objective, and

in the

in the genitive. If used

with the letter ( ) of comparison it becomes ( ) as in: [=He is as brave as a lion], and suchlike. There is another different noun, the demonstrative ( ), which assumes one unchangeable form in all inflectional functions. It is often linked with ( calling attention, so that together they form ( (

), a particle for

), commonly written

) without ( ), which is also problematic in cipher solving. Many people wrongly write the word (

) using ( ) in place of the

terminal ( ), which can easily be mistaken for the letter ( ). Reflect on that, as you may happen upon a cipher rendered to you by someone who is ignorant of its right spelling. On the other hand, the word ( ) can mean

(=who) according to some Arab dialect. They say, for

example: (=who did so and so). The use of such dialect in cipher poetry can be extremely baffling to the cryptanalyst unless he/she is dialectally aware and cognizant thereof. The letters ( ) and ( ) must be the focus of attention because they can be diacritically neutral, vocalized, and geminated; they often take end-positions of words, and also occur as rhyme letters. Their occurrence as neutral is more than can be enumerated; e.g. , , , ; , , , , , , , .

82

They may occur at end-positions; e.g. ,

,

,

,

,

,

1

,

;

,

, . They may occur geminated; e.g. ,

,

,

,

,

(dialect);

.

As for their occurrence as a rhyme letter, they may occur diacritically neutral (e.g. (e.g.

,

,

,

, ;

, ,

, ,

,

,

, ,

,

, ,

; ,

,

,

2

); geminated

); or vocalized (e.g.

,

).

You should also see to glottal stops (hamzas) in words such as: ,

,

, which might prove extremely problematic in cipher

solving.

1

As previously indicated, it is the graphic representation rather than the pronunciation that counts by cryptanalytical standards; hence, undotted ( ) is condidered ( ), not a special variant of ( ). See ibn ad-Durayhim's treatise, Vol.3 of this series, p. 122.

2

So in the Arabic original, without the functional ( ) of differentiation. The author has just attributed this mode of writing such verbs to some writers. See also ibn Dunayn r's book, Chapter 44, p. 160.

84

What should also be spotted, among other things, are the conjunction ( ), the letter ( ), the superfluous ( ), and the similative ( ) that is used for comparison. For instance:

,

, , , and . I am particularly recommending the spotting of these letters since the definite (‫ )ال‬is in fact a major guideline towards cryptanalysis. When it occurs frequently in a line of poetry, preceeded by the conjunction ( ), the letter ( ), the superfluous ( ) or the similative ( ), it is likely to pose problems, and accordingly I must alert you thereto. Attend to the letter ( ) [denoting femininity] in such verbs as: , and

; and to the letter (

words as:

,

and

) [as a pronominal suffix] in such

. Both can occur immediately prior to a

terminal ( ) as in: ‫فؼهحا‬, , ; and as in: and respectively. Look closely into letters repeated consecutively [doubled letters] like the letter ( ) in words such as: , , ; the letter ( ) in words such as:

,

,

; and the letter (‫ )و‬in words such as:

. Also consider geminated letters in words such as: and

,

,

,

,

,

,

.

If you encounter the letter ( ) followed by a double ( ), and then another letter next to the double ( ), the resultant word is held to be the name of God ( ) ––and with good reason; that is in the mainstream of speech for such formula. Otherwise, it can be one of these words: , , , or ––a typical Arab dialect for ٘‫انز‬, such as the verse:

86

In case the letter ( ) is followed by a double ( ), plus another letter, and then another ( ), you guess the word to be ( ) and make sure you are right in your conjectures, as it can hardly be any other word; I personally do not know any other word as such. Thereupon the letter ( ) becomes known, together with the letters ( ) and ( ). Once the letter (٘) is known, whenever you encounter a two-letter word (bigram), you should try the letters of the alphabet one by one until it shows right. Note that working out parts of the verse will promise to facilitate solving the rest of it. Having positively spotted the letters ( ) and ( ), you should give your undivided attention to the following aspects in the process of cryptanalysis: Possible words with initial ( ) and terminal ( ) are: , , , , and the like. Possible words with a letter after ( ), followed by ( ) and then another letter are:

,

,

,

,

, and the like.

In case the letter next to the [definite] ( ) and the final letter were identical, the word produced would possibly be: ,

,

(plural of

,

,

,

,

), etc.

If two letters are found next to [the definite] ( ), followed by the letter ( ), plus a final letter, then you may guess at words like: ,

,

,

,

, and suchlike.

88

,

If two letters are there next to [the definite] ( ), followed by the letter ( ), plus two letters, take a guess at words like: ,

,

,

,

,

, and so forth.

If one letter exists immediately after [the definite] ( ), and then an ( ) followed by two letters, this would generate words like: ,

,

,

,

,

,

,

, and the like.

In the case of having three letters next to the initial [definite] ( ), followed by ( ) and then two more letters, the outcome is words like: , , , , and so on. Note that the letters ( ) and ( ) are essential in this rhythmical pattern. 1 If the [definite] ( ) is followed consecutively by two letters, the letter ( ), and then three other letters, the outcome is words of the pattern:

,

,

, etc.

But if the [definite] ( ) is followed consecutively by three letters, then the letter ( ), and one more letter, the product is words of the pattern:

,

,

,

,

, and such.

When four letters come after the [definite] ( ), followed by the letter ( ), plus one other letter, the resulting word should be something like:

,

,

,

, and the like. Note here that the letters

( ), ( ) and ( ) are essential in this rhythmical pattern2. A poetry cipher containing such a pattern is typically easy to cryptanalyse.

1 2

See footnote No. 7, p.58. See footnote No. 8, p.58.

90

If the [definite] ( ) is followed by another ( ) and then three other letters, the word produced would possibly be:

,

,

,

, or something of the kind. If the [definite] ( ) is followed consecutively by another ( ), two letters, and a terminal ( ), this brings forth words like:

,

, etc.

If, however, three letters occur between ( ) and the terminal ( ), words such as:

,

,

,

, etc. flow out.

If the order was: the [definite] ( ), ( ), another letter, ( ), [and one more letter], the outcome would be words like:

,

, etc.

If, however, the order was like this: the [definite] ( ), ( ), two letters,

( ), plus one more letter, then the outcome would be words of

the pattern:

,

,

,

,

, etc.

In case the [definite] ( ) is followed consecutively by: ( ), one letter, ( ), plus two more letters, then the word sought would be conformable with the pattern:

,

,

,

,

, etc.

If the letters were in the order: the [definite] ( ), ( ), a letter, ( ), three other letters, they would make up such words as:

,

,

,… If you come across two s (alifs) (so judged definitely or hypothetically), interposed by another letter of low recurrence, you can positively hold this intervening letter to be ( ) (making the word ) or ( ).

92

Bear in mind that the low-frequency letters that occur at endpositions of words are: , , , , , , , and .1 Fully comprehend that. You should also know that, in poetry, words such as: , , , 2

[i.e. gemination following the letter ] are not possible. It is likewise unlikely the occurrence of two consecutive neutral letters except in a relief rhyme, in which case one of the two neutrals is the rhyme letter, the other is relief. That is so since, after a pause on a neutral letter in delivery, there is no need to resume by a vocalized letter; thus their occurrence in such position is justified in terms of the macron (madd) inherent in vowel letters. You should be alert to that, as it is purposely elaborated here. Furthermore, you should be fully cognizant of the fact that there exist such long words that are devoid of the letters ( ) and ( ) as in : 

 [= God will suffice you from them], and   [=We will draw them on little by little whence they

know not],

1

2

, and the like.

From this statement one can observe that the low-frequency (scarce) letters are nine in number, whereas in fact they are ten, with the letters ( ) and ( ) dropped. Moreover, the list includes the letter ( ), which is of medium (common) frequency. See the order of letter frequency in ibn Adl n's treatise (Volume Two of this series), p. 48. Just so in the Arabic original; but this word does not seem to answer the rule applicable to the other words, as the ( ) is not geminated after the ( ).

94

A verse may be made to be no more than a load of nonsense, though prefectly sound in meter. That is what the neo-poets call ar-r 'i .1 This type of nonsensical but metrically-sound poetry virtually amounts to the same thing as raving, and is known by the Arabs as al-mat n, which is futile, hollow and aimed only at establishing a metrical measure that encompasses the letters of the cipher. Knowledge of the meter to which the verse in hand belongs soon leads to defining the vowels and the letters ( ) and ( ). Through practice you are sure to verify the authenticity of that I have just pointed out. Some poetic cipher may pose problems that are likely to make the progress of cryptanalysis so difficult as to delay, or even preclude solution. This is rendered in poetry intended for sustained mental exertion, and is accomplished through methods like the [deliberate] utilization of undotted or non-combinable letters, or letters dotted alternately, or through the stinted employment of high-frequency letters, or by otherwise choosing new or unheard-of verse for a cipher. Other barriers towards cryptanalysis include the following: - the verse sought for cryptanalysis being very short or very long. A very long verse will contain plenty of the letters ( ) and ( ) as pronominal suffixes, and also of the functional ( ) of differentiation appended to the written spelling of past verbs denoting plurality, as in: and . - Encipherment may be the product of a versifier with good knowledge of poetic meters but utter ignorance of parsing and language. Subsequently he comes up with a syntactically erroneous poetry which overtaxes you. Encipherment might be done by someone who produces verses incompatible with the recognized orthodox meters of Arabic poetry. Example:

1

Not among the types of poetry mentioned by post-classical poets.

96

Poetical measures, as those developed by the poet Ab alAt hiya1, among others, defy solution by any metrical number. Another example: - The occurrence of the so-called al-kaff and al-qa phenomena at the end of a verse. al-q involves curtailing the seven-unit metric foot ( ) by dropping the fifth unit. al-kaff, on the other hand, entails dropping the seventh unit. Consequently, the foot ( ), when affected by qab , becomes (

), and the foot (

when affected by kaff, becomes ( (

) undergoes qab , it becomes (

),

). If the foot ). The effect of

al-qa phenomenon is not much of a problem as alkaff, but their occurrence simultaneously creates an unpleasant impact indeed. To be noted is that the occurrence of the qa phenomenon is truly abundant, especially when the so-called alm, arm, arm, or azm occurs at the beginning of a line of poetry2. The following is an example of a verse subjected to al-kaff: ('Imru' al-Qays) (*) And this: which belongs to the aw l poetic meter.

1

d. A.D. 826.

2

These terms have already been tackled in ibn Dunayn r‟s book (Volume Four of this series), p.146 and p.170. (*) A great pre-Islamic poet.

98

The so-called al- abl is a metric phenomenon that calls for the dropping of the second and fourth neutral letters of a foot; e.g.

becomes [

, then transformed into]

. However,

four vocalized letters in a row are of rare occurrence in [Arabic] poetry. Words such as: forms of which are:

and and

are distortions, the genuine .

- Besides, the first hemistich of a verse that belongs to the aw l meter may undergo the arm phenomenon, making it into the k mil meter. In the following verse: 1

the first hemistich in its present form is of al-k mil meter; the other hemistich is of a - aw l. Had the poet said

or

…..

, the measure would have straightened to a - aw l. But it seems that the poet has been more attentive to meaning than to measure. The same applies to the following verse of the poetess al- ans ':

1

See footnote No. 111, p.172 in ibn Dunayn r‟s book (Volume Four of this series).

100

If you study prosody from my Large Book, you will see quaint niceties of the science and draw knowledge galore, with the result that you will find prosody a relatively easy topic to cope with. Deeper professional expertise in poetic cryptanalysis requires familiarity with prosody and rhymes, and a rich store of poetry learnt off by heart. Cryptanalysis is thus made easier, God willing. - An erroneously rendered cipher would probably complicate cryptanalysis. - The verse being drawn from the circle of the different (al-mu talif), which is the fourth1 of the metrical circles. I am to cite to you only some of what comes to my mind of the poetry that is intended for mental exertion, lest the treatise could become unduly long and boring. - The verse being nonsensical ––a sheer raving, though sound in meter, as I have already stated. Someone had enciphered to me the following verse: 2

which took me over a month's toil to break3. It belongs to the aw l meter. The complication and delay in cryptanalysis stem from the fact that it is meaningless raving ––the so-called r 'i , mentioned earlier.

1 2

3

So in the Arabic original; it is in fact the first, as he states later in the treatise. Mentioned by ibn Dunayn r with slight variation in wording, i.e. , instead of , , respectively. See Vol.4 of this series, p.174.

,

This bears evidence of the author's personal experience in cryptanalysis. It also demonstrates that ibn Dunayn r lived at a later time than the author of Adab a u ar ', and that he tapped into the treatise extracted from it. What corroborates this belief is the fact that ibn Dunayn r just mentions the above line of verse without the slightest indication to any attempt on his part to break it.

102

This kind of verse is not deemed a standard criterion by which to measure the competence of the cryptanalyst. Such a competence is judged through the ability of cryptanalysing meaningful verse ciphers, because this science is meant for good fun and [the exhibition] of literary subtleties in the company of notables and in the communication with peers. It is likely, however, that nonsensical ciphers are used by envious people as a vehicle to compromise the cryptanalyst's knowledge, and to show him/her helpless or otherwise incompetent. Besides, you have to approach the cipher verse with much care and reason. Do not overtask your mental powers if it proved inextricable, but leave it for some time before you give it another try when you are all-set for it. You may need to leave it for as long as a whole year. But if, after trying your hardest, you still fail to crack it, consult with the encipherer, for the cipher might be erroneously rendered, or in some way affected by one or more impediments to cryptanalysis that I have mentioned to you. Otherwise, your failure in cryptanalysis is surely due to reasons related to some deficiency or weakness on your part as a cryptanalyst. Yet, some may insist on stickling for feasibility of cryptanalysing close ciphers. When you are troubled by such an encipherer, never mind what he says. Had his cipher been properly rendered, it would have cracked. Ignore the encipherer, but keep his cipher, and present it to anyone who claims experience in cipher solving. If they managed to cryptanalyse it, they would prove more proficient than yourself; if not, then both of you have the same problem in common.

104

I have enciphered a few verses, which are accessible and easy to cryptanalyse, for you to explore the problem areas and to practise cryptanalysis. Of these are the following: 1) A verse of the bas meter: 2



1





 

 3



This is a line of poetry4 in which the letters ( ), ( ) and the conjunctive (ٔ) are highly frequent. The peculiarity lies in the conjunction, owing to the high frequency of occurrence of its form and the form that follows, so that [the conjunctive (ٔ)] can be mistaken for the letter (‫)ا‬, and the (‫ )ا‬can be mistaken for (‫)ل‬. That is why I have already stated the conjunctions and their orders of frequency.

1 2 3 4

A word-spacer observed throughout the three cryptograms. Not in the original. Not in the original. By al-Mutanabb . Its wording here is as follows:

106

Another verse which belongs to the aw l meter:









 

 



This verse1 is also easy, owing to the high frequency of the letters ( ) and ( ). Moreover, the bigrams ( ) and ( ) in it give signal clues towards cryptanalysis. Note that it is a typical "mu arra ", "muqaff ", and "mu'assas", line of poetry. 2) And yet another verse of the k mil meter:





 

 

 

1

Its wording in full is:

108

This is a widely-known verse1 in which the letters ( ) and ( ) are highly frequent. Con it. Remember that a very short cipher verse is most likely to indicate one of the following meters: split ra az, manh k ra az, curtailed sar , or curtailed munsari . You need not work it out unless it is fortified with another line to increase the number of letters, and so allow the letter order of frequency to be reasonably applied. You have no claim to ask what meter it is in the interests of facilitating cryptanalysis one way or another. Also you may encounter a cipher of the type that embraces all the letters of the alphabet. I am going to give you some soon. Limited in number, such verses are unmistakably indicated by their constituent forms and symbols, given that a verse of this type may possibly contain some letters of the alphabet stated more than once. The following are examples of poetry intended for sustained mental exertion, using undotted letters only, or systematically dotted and undotted ones. Of the first type is this line: 2

Also related to the poetry of mental exertion are the following [interesting] verses by Rab a ar-Raqq 3

1

2

3

By Antara al- Abs , a well-known gallant pre-Islamic poet:

1) Just so in the original Arabic manuscript. The dotted ( ) in the word ( ) is actually inconsistent with the author's statement above, that the verse is all made up of undotted letters. 2) For an example of the other type concerning the systematic use of dotted and undotted letters, see p.59. d. AD 814.

110

Encipherment for mental exertion is also achieved through purposely using separate letters that do not admit linking with one another, such as:

Of the verses that embrace the letters of the alphabet, here are typical examples: a) b) 1 And the following line covers the alphabet, with a few letters recurring several times: 2

1

Note that this verse lacks the

(hamza). Also note that the letter ( ) recurs four

times; the letters ( ) and ( ) three times each; the letters ( ), ( ), ( ), ( ) and ( ) twice each. 2

In fact this line does not exhaust all the letters of the alphabet as he states. However, this can be redressed by making the letter ( ) in the word ( ) into ( ), and the final ( ) of

into ( ).

112

A different type of encipherment may be rendered [by repeating in the second hemistich the same words of the first, but in different order]. Example:

And yet another type of cipher may be made [by adroitly writing the verse such that the first hemistich is read forward as the second is read backward]. Example:

Of the poetry that is particularly tough to crack is that composed on al-mad d meter in its original, rather than catalectic, version. Another such type is a special reversed form of al-mutaq rib meter (called bad ), not reported to have been ever used in the Arabic standard poetry. In a poem by an-Na

r al-Faq as , he says:

It is worth considering that some poetry does not in the slightest conform to the established rules of prosody. In fact this art is basically meant for common sense and fine intuition. So be mindful.

114

Following this treatise, I am reserving a space for the verses of mental exertion so as to be close at hand for you to go over time after time. The End of the Treatise on Cryptanalysis [of Poetry] [Classification of Letters According to Their Points of Articulation] 1 Letters Guttural

Uvular

Orificial

Apical

Liquid

Labial

Vocalic

Cacuminal

(hamza) Letters Gingival

Another verse consuming the Arabic letters: 2

1

2

An addition to the original, indicating the content of the table which, together with the verse that follows, is subjoined to the treatise in the same penmanship as the manuscript. This verse, as it appears in the original, suffers from the absence of some letters and the repetition of some others. It is, however, set right here from ibn adDurayhim‟s treatise Mift al-kun z (Vol. 3 of this series, p.62), where it is included under the substitution section as an anonymous cipher alphabet between the Qumm and the Fahlaw cipher alphabets.

116

1 2 3 4

71

1

2 3 4

73

1

2

1

300 295 1 72

70 54 2

75

1 2

3

1

2 3

77

79

1 5

4



3

2

1

104 103 2 3

22 27

4 5

81

1

1

83

1

2

3 5

4

6

1

363 1 2 3

74 4 5 6

85

2

1

3

5

4

6 7

1 2 3 4 5

76

6 7

87

1

2

3

1

111 2

113 112 3

89

1

2

3

4

6

5

1 2 3

4 5 6

91

1 2

3

5

4

1

2 3 4 5

93

1 2 3 5

4 6 7

9





8





1 2

274 1 3

4 5 6 7

137 2 182 7

95

8 9

1 2

4

3

1 2

91 90

3 4

97

1

3

2

4

5

77

1 2 3

77 12

4

71

32

10

99

5

1

2 3

4

5 6

7

1

236 6 2 3

1 58

4

333

5 6 7

124 370 3

101

1

2 3 4

1

248 6

11 18 251 6 77

2 3

4

103

1

2

1

117

2

105

1







 

 2

 

4

3

5

1 2 3

286

4

123

107

5









 

 



1





 

 

 

1

109

1

2 3

4 6

5

1

486 1

56 1

210 51 4

446 2 3

16 3

198 4 5 6

37 36

111

1 2 3 4

5

6 7

1 2

79

3 4

327 272 1 79 5

79

6

79

113

7

1

2 3 4 5 6

1

79 79

2 3

120

4 5

24 8 6

199 7 146 1

115

‫‪1‬‬

‫انحهم‪ٛ‬ة‬

‫‪2‬‬

‫‪1‬‬

‫‪2‬‬

‫‪117‬‬

118

The Third Treatise al- urhum 's Two Manuscripts

119

120

Chapter 1

Analytical Study of al- urhum ‟s Two Manuscripts

122

1.1. A Text from al- urhum ’s1 Book al- urhum addresses poetry cryptanalysis on the basis of a solid knowledge of rhyme and its component letters. He restricts his interest to the two patterns a line of verse ends with, which are identical to their counterparts in a previous line. That is so because one of the patterns is of necessity the rhyme letter (raw ); the other may be the 2 relief (ridf) if it precedes raw , or linkage (wa l) if it follows . The determinant factor lies in the ability to identify the letters of these three terms. The letters that occur as relief are the three vowel letters (‫ا‬, ٔ and ٘); those that occur as raw are all the letters of the alphabet; while those that occur as linkage are the three vowels besides the letter (‫)ْـ‬. The author then presents a wide variety of cases that cover most of the rhyme possible occurrences, and add up to fine algorithms for cryptanalysing poetry ciphers. The cases are each illustrated in the following paragraphs: 1. “If you are to distinguish the rhyme letter from the relief and linkage letters, see which of the two patterns is less frequently used and make it the rhyme letter. This is typical of people‟s ordinary speech, not that other possibilities are inconceivable. If the first pattern is found less frequent, the other must be the linkage; if the 3 second is the less frequent pattern, then the first must be the relief.” al- urhum here relies on the principle of letter frequency in the identification of the rhyme letter, and distinguishing it from the relief and linkage letters. While the rhyme letter may assume any letter, the relief and linkage are restricted to the vowel letters, as already stated. Thus the more frequently occurring pattern should be either relief or linkage, whereas the less frequently occurring one the rhyme letter. If the less frequent pattern comes first, it is determined to be the rhyme letter, and the one that follows linkage. Example:

1

He is Ab al- asan Mu ammad ibn al- asan al- urhum , of unknown date of birth and death. No biography of him has been hit, try as we might. 2 See ibn Dunayn r's book (Volume Four of this series), p.150. 3 See p.148.

123

where the letter (‫ )ب‬is the rhyme letter, and the following (‫ )ا‬the linkage letter. If, however, the more frequent pattern precedes the other (less frequent), then the first is relief, the other rhyme, as in: where the letter (ٔ) is the relief, and the following (‫ )ل‬is the rhyme letter. 2. “Should two patterns [of letters] at the end of two verses be identical, with the preceding letter in both being different and anteceded by one and the same letter, this last is fixed to be the letter 1 (‫ ـــــ)ا‬the so-called basal alif or ta's s.” Example:

The two identical patterns in both verses are the terminal (‫ )ل‬and ( ‫( )ْـ‬rhyme and linkage respectively), preceded by the letter (‫ )ذ‬in the first line and the letter (‫ )د‬in the second (both are called the extraneous letter or da l), then anteceded by the one basal (ta's s) letter (‫ )ا‬in both. The above can be represented thus: zyx (‫)ا‬ zyv (‫)ا‬ 3. “If the verse ends in three repeated patterns, the first of which is the least frequent, then it is positively the rhyme letter, always followed by the linkage ( ‫ )ْـ‬and then by any of the three vowels: ‫ا‬, ٔ 2 and ٘ immediately after, which is the exit or ur .” The exit or ur in rhymes is a mandatory vowel letter that results from lengthening the sound value of the linkage (‫)ْـ‬, as in:

so that the last syllable of each line is voiced: ْٙ‫ س‬- through the impletion (saturation) of the diacritic kasra of the linkage letter ( ‫ )ْـ‬in and . The last syllable can be represented: zyx, where x is the 1 2

See p.148. See p.150.

124

least frequent of the three letters and therefore it is the rhyme letter (the ‫ س‬here). The following y=‫ ْـ‬is linkage, and the last z=٘ exit. 4. “If the second pattern is found to be the least frequent, it is unmistakably the rhyme letter; the first is relief, the third linkage. The first and the third may equally be ‫ا‬, ٔ or ٘; the third only may also be 1 the letter ‫ْـ‬.” This case is similar to the one before, except that the least frequent pattern is the second, i.e. the symbol y in the above representation. Therefore it should be the rhyme letter; x is the relief, and z the linkage. These last two (x and z) may be any one of the vowels ‫ا‬, ٔ or ٘. Example: where the relief and linkage letters are both (‫)ا‬, with the rhyme letter (‫ )ب‬in between. However, the pattern z in particular may possibly be the letter ( ‫)ْـ‬. Example: where the rhyme letter is (‫)د‬, the relief (ٔ), and the linkage (‫)ْـ‬. 5. “If [each of] the two verses ends in four repeated patterns, then the first and the last may be any one of the vowels: ‫ا‬, ٔ or ٘; the second is the rhyme letter, and the third must be the letter ( ‫ )ْـ‬beyond 2 a shadow of doubt.” Example:

In each verse of the above, the repeated patterns are the last four letters ( ‫)ايٓا‬, of which the first (relief ) and final (exit) are one and the same letter (‫)ا‬. The second (i.e. ‫ )و‬is the rhyme letter, and the third pattern (i.e. the linkage) is ipso facto the letter (‫)ْـ‬. 6. “Suppose you are to address a two-line cipher, of which the pattern at the end of one line is incompatible with that at the end of the other. In this case seek a match for the last pattern in the first verse in 1 2

See p.150. See p.150.

125

the last pattern but one or two in the other verse. Failing this, you decide the last of the one verse is the letter (‫)ا‬, and the last of the other verse is an undotted (ٖ) that is pronounced as (‫ )ا‬in spoken discourse, 1 but assumes the shape of (ٖ) in writing.” The following example is a case in point:

7. “If, however, the last pattern of one verse is found to be the identical last pattern but one of the other verse, then the last pattern of this is decidedly the letter (٘), such as in: 2

”

where the lengthened diacritical ٘ (kasra) of ( ) is the linkage to the rhyme letter (‫ )و‬without establishing it in writing. The (٘), in contrast, materializes in (ٙ‫ )دي‬because it is the first-person (٘). 8. “In a single position the last pattern turns out to be the letter (ٔ); 3 that is if the final word of a verse is [the proper name] ٔ‫ػًش‬.” That is so because the (ٔ) subjoined to this name is not vocalized, though established in writing. Example: 9. “If it happens to be in agreement with the last pattern but two, then the first of these two is necessarily the letter (ٔ), the other [the functional] (‫[ )ا‬of differentiation denoting plurality], such as in: 4

”

1

See p.150. See p.150. 3 See p.152. 4 See p.152. 2

126

1.2. A Text from al- urhum ’s Treatise This is the second of al- urhum ‟s texts. It takes about seven pages, treating the encipherment of prose, but illustrating his points with examples of poetry. It is clear right from the title and the opening that the text is an excerpt from a larger parent treatise, most likely on cryptography. This proposition is vindicated by the fact that the text proves so advanced in complexity and elaboration it seems virtually inconceivable for the author to take it as a point of departure; it is probably preceded by easier introductory material. The text deals with cryptanalysis. It involves the following important aspects: 1. Deliberate non-observance, on the part of encipherer, of the standard and normal orders of letter frequency in a ciphertext (frequency reversal). 2. Classification of letters into five groups according to their frequency of occurrence in spoken and written discourse. 3. Recourse, in cryptanalysis, to biliteral prefixes and suffixes in words. 4. Experience in manipulating bigrams and trigrams as a means of working out letters (combinatorics). 5. Algorithms for cryptanalysis through bigrams and trigrams. 6. Significance of ciphertext length. The following paragraphs will cast light on each of the above topics.

1.2.1. Frequency Reversal al- urhum states that the encipherer may intend to make an excessive use of letters that are normally infrequently used (i.e. scarce and common letters), or to make a scanty utilization of letters that are 1 normally of high frequency of occurrence (i.e. abundant letters). He 1

The orders of letters and their frequency count have already been mentioned in several treatises. See al-Kind (Vol.1 of this series), pp.98-100 and pp. 166-170; ibn Adl n (Vol.2), p.18 and pp.48-50; ibn ad-Durayhim (Vol.3), p.33 and pp.98100; ibn Dunayn r (Vol.4), p.11 and p.70.

127

cites the following example of how the letters (‫ )ع‬and (‫ )ج‬are overused: He argues that this practice “makes cryptanalysis more 1 strenuous” , and indeed it does, because the principle that is still in use nowadays requires evenness of distribution of cipher patterns against the count of letters in the language. The expression that is used in today‟s terminology to denote al- urhum ‟s above reasoning is “frequency reversal” ‫ـــــ‬an indication which only attests to his deep understanding of the ways and techniques of cryptanalysis.

1.2.2. Classification of Letters As Per Their Frequenies al- urhum divides the letters of the alphabet into five classes according to their frequency in usage as follows: Class I includes the letters: ‫ا‬, ‫ل‬, ‫و‬, ٌ, ‫ْـ‬, ٔ and ٘. Class II includes the letters: ‫ب‬, ‫د‬, ‫س‬, ‫ف‬, ‫ ق‬and ‫ن‬. Class III includes the letters: ‫ت‬, ‫ج‬, ‫ذ‬, ‫ ط‬and ‫ع‬. Class IV includes the letters: ‫ص‬, ‫ ش‬and ‫ط‬. 2 Class V includes the letters: ‫خ‬, ‫خ‬, ‫ر‬, ‫ص‬, ‫ع‬, ‫ ظ‬and ‫ؽ‬. It seems that this division of letters into five classes is unique to alurhum ; other scholars in this art, such as the Author of the Two Essays and ibn Adl n, fix on three classes, i.e. - Abundant letters, incorporation al- urhum ‟s Class I letters. - Common letters, approximately incorporating his second and third classes. - Scarce letters, approximately incorporating his fourth and fifth classes. The following is a comparative table of the letters of the alphabet, classified according to their frequency of occurrence, as given by alurhum the Author of the Two Essays, and ibn Adl n: 1 2

See p.152. Cf. Volume One (of this series), p.100.

128

Letter Classes Class I (Abundant Letters) Class II (Common Letters) Class III (Scarce Letters)

Author of the Two Essays ‫ٔ ٌ ٘ و ل ا ٘ ْـ ٔ و ل ا‬ ٌ ‫ْـ‬ 7 7 ‫ب ت ف ع س ب ت ف ع س‬ ‫ج ذ ق ط د ن ج ذ ق ط د ن‬ ‫ص‬ 11 12 ‫ط ص خ ش خ ر خ خ ص ط ؽ ظ‬ ‫ر ص ش ع‬ ‫ع ظ ؽ‬ ibn Adl n

10

9

Class IV Class V

al- urhum ‫ٔ ْـ ٌ و ل ا‬ ٘ 7 ‫ن ق ف س د ب‬

6 ‫ع ط ذ ج ت‬

5 ‫ط ش ص‬ 3 ‫ع ص ر خ خ‬ ‫ؽ ظ‬ 7

1.2.3. Biliterals Occurring Initially and Terminally in Words Familiarity with biliterals occurring at front- and end-positions in words has substantial advantage in cryptanalysis. In terms of importance, such familiarity comes second only to the requisite knowledge of letter frequencies and orders. The letter (‫)ل‬, all too often, goes next to (‫ )ا‬which is by far the highest frequent letter. Together they form the definite article. Therefore (‫ )ل‬is spotted after (‫ )ا‬at the beginning of words. In a three-letter word (trigram) beginning with (‫ )ا‬plus (‫)ل‬, the third will most likely be one of the letters: (٘), (‫ )و‬or ( ‫)ْـ‬, such as in: ٗ‫إن‬, ‫أنى‬, ّ‫ إن‬. Biliterals often occur suffixed to verbs, nouns, pronouns, and particles. Examples of such biliteral suffixes are: ‫( ْى‬as in: ‫حفظٓى‬, ‫ٕفٓى‬ٛ‫( ٔا ;)س‬as in: ‫كحثٕا‬, ‫ٍ ;)اكحثٕا‬ٚ (e.g. ٍٛ‫جذسس‬, ٍٛ‫نهُاخح‬, ٍُٛ‫( ٌٔ ;)ت‬e.g. ٌٕ‫كاجث‬,

129

ًٌٕ‫حشخ‬ٚ, ٌُٕ‫( اٌ ;)ت‬e.g. ٌ‫( ات ;)لهًا‬e.g. ‫( ًْا ;)أدٔات‬e.g. ‫ًٓا‬ٛ‫ؼط‬ٚ, ‫حًٓا‬ٛ‫ت‬, ‫ًٓا‬ٛ‫;)ػه‬ ٍّْ (e.g. ًٍّٓ‫ؼه‬ٚ, ٍّٓ‫دسٔس‬, ٍَّٓ‫)كأ‬. As al- urhum puts it: “The repetition of such biliterals in straight order at the end of words is likely to point to them, just as the repetition of the letters (‫ )ا‬and (‫[ )ل‬at the beginning of words] is. Spotting the former postpositively is analogous to spotting the latter 1 (i.e. ‫ )ال‬prepositively.”

1.2.4. Manipulation of Bigrams and Trigrams (Combinatorics) al- urhum states the advantage the cryptanalyst gets from acquainting himself with these two types of words. He says: “Other means that assist in the cryptanalysis of letters include special insight 2 into the algorithms of cryptanalysing bigrams and trigrams.” A) Bigrams The cryptanalyst will have to know the general law that governs the number of possible bigrams within each of the various types of words when specific letters therein are sought out for cryptanalysis. This is essential to rule out any possibility of taking up the same bigram more than once, or inadvertently quitting one. “As for bigrams,” al- urhum reasons, “the way to elicit them is through establishing their total count for certain, so that you avoid the unnecessary job of working out 3 a bigram already spotted or leaving out one.” He then stes forth the general law of calculating bigrams ‫ ــــ‬the law of the permutations of (m) elements by taking up (2) elements at a time: 2 Pm = m ( m – 1) where (m) is the total number of elements or letters. As alurhum puts it: “The process involves multiplying the number of elements in the entity that you seek to know the count of bigrams 1

See p.156. See p.156. 3 See p.156. 2

130

contained in it by itself less 1. the product represents the aggregate 1 number of possible bigrams therein.” He proceeds to explain the algorithm of obtaining these permutation in tabular form, giving as an example the bigrams derived from the three-letter word (‫)َظش‬: Applying the above law we write: 2

P3 = 3 ( 3 - 1 ) = 3 x 2 = 6 which is the number of all bigrams that can possibly be derived therefrom. The table is arranged, according to al- urhum , by taking up each element (letter) a number of times that is equal to (m–1); i.e. twice, against which we write down the remaining elements: Reading direction The six resultant bigrams emerge by reading vertically:

Let us consider another example: the word ( ‫)ب ع خ س = تؼثش‬, where m=4. Using the same principle, we write: 2

P4 = 4 x 3 = 12 As in the previous example, the table is arranged taking each letter (m – 1) times; i.e. 3 times, against which the remaining letters are set down each time:

From these arrangements the twelve possible bigrams are derived, excluding those made up of the same letter repeated (which are 4 bigrams). Otherwise, the law would take the following formula: 1

See p.156.

131

1

P = m2 = 42 = 16 = 12 + 4 Next, al- urhum reckons the bigrams derivable from five-letter words: 2 P5 = 5 ( 5 – 1 ) = 5 x 4 = 20 B) Trigrams al- urhum demonstrates the possible trigrams that can be drawn from a number of letters, observing the same approach as with bigrams. He first states the law governing their number, and then expands on their sorting. However, he deviates here a little from the norm assumed with bigrams; he treats the possible trigrams including those made up of the same letter repeated (e.g. ‫سسس‬, ‫خدح‬, ‫ػؼغ‬, etc.). Although he gives no reason for this deviation, it is possibly built on the assumption that repetition, while unfeasible in bigrams, is more likely in trigrams. He considers the algorithm for establishing the count of trigrams. The process, he explains, “involves multiplying the aggregate number of components by itself twice; the product is the total number of 2 trigrams, whole and complete”. This may be construed as: N = m3. Using this formula in computing the trigrams inherent in the fourletter word (‫)خؼفش‬, we find: N = 43 = 64 This count is quite legitimate because of the likelihood of trigrams 3 composed of a single letter repeated. al- urhum elucidates the algorithm of extracting the trigrams pertaining in the four-letter name ( ‫)خؼفش‬. In his own words: “To sort them out, arrange the component letters in pairs so that each letter is placed respectively against all the letters in rotation. This engenders sixteen two-letter words. For the word ( ‫)خؼفش‬, a four-letter name, we multiply four by four to get sixteen, and this product by four again ‫ــــ‬that is sixty-four, which represents the whole number of trigrams possible. Thereupon we set down each of the component letters: ‫ج‬, ‫ع‬,

1

See p.158. See also Volume One of this series, p.54ff. See p.158. See also Volume One of this series, p.54ff. 3 Refer to ibn ad-Durayhim‟s tratise (Vol.3 of this series), p.88. 2

132

1

‫ ف‬and ‫ س‬in four combinations, against which we write the letters.” The combinations would take the following forms: ‫ج س‬ ‫ع س‬ ‫ف س‬ ‫س س‬

‫ج ف‬ ‫ع ف‬ ‫ف ف‬ ‫س ف‬

‫ج ع‬ ‫ع ع‬ ‫ف ع‬ ‫س ع‬

‫ج ج‬ ‫ع ج‬ ‫ف ج‬ ‫س ج‬

He goes on: “Then we make each of these sixteen words into four combinations, against each of which one letter of the [intended] word is added. The complete arrangement [of trigrams] becomes as 2 follows..”. The following table shows the resultant trigrams, divided into the four groups of combinations, with the respective letter against each: Group 1 (Against the letter ‫)ج‬ Group 2 (Against the letter ‫)ع‬ Group 3 (Against the letter ‫)ف‬ Group 4 (Against the letter ‫)س‬

1 2

‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬

‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬

‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬

‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬

‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬

See p.158. See p.160.

133

‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬

‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬

‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬

‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬

‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬

‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬ ‫ج‬ ‫ع‬ ‫ف‬ ‫س‬

‫ج‬ ‫ج‬ ‫ج‬ ‫ج‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ع‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫ف‬ ‫س‬ ‫س‬ ‫س‬ ‫س‬

1.2.5. Utilization of Bigrams and Trigrams in Cryptanalysis al- urhum turns now to address the technique of utilizing bigrams and trigrams in cryptanalysis. He says: “Now that you have had knowledge of the ways of working out bigrams and trigrams, we 1 say:…” In the following paragraphs we shall examine several cases of such utilization as related by al- urhum : 1) Algorithm (a) Calculating the number of bigrams and trigrams. (b) Dismissing as ineligible those that are found meaningless or not known to have been used by the Arabs. (c) Selecting the more convenient in terms of relevance to the general theme of the cipher being cryptanalysed. 2) Examples In explaining the above algorithm al- urhum invokes the following four examples:  “Consider, for example, the case when, after working out the best part of the alphabet, the letters: ‫خ‬, ‫ر‬, ‫ ص‬and ‫ ص‬remain 2 unknown.” In order to uncover a two-letter word out of these four letters, we reckon up the number of possible bigrams: 2

P4 = 4 x 3 = 12

bigrams

Sorting them out, as already mentioned, we get the following bigrams: ‫خ ر‬, ‫خ ص‬, ‫خ ص‬, ‫ر خ‬, ‫ر ص‬, ‫ر ص‬, ‫ص خ‬, ‫ص ر‬, ‫ص ص‬, ‫ص خ‬, ‫ ص ر‬and ‫ص ص‬. From these we pick only the meaningful ones such as: ‫خز‬, ‫خض‬, ‫خض‬,… and try to decide on the one that is most relevant to the theme in hand.  “Also bear in mind that we may manage to work out all the letters of the word but one. When this happens, you isolate those letters that you have already unfolded, and check the rest of the alphabet one by one until you get one or more 1 2

See p.160. See p.160.

134

useful words. Fix upon the most appropriate to the 1 theme.” al- urhum cites a case in point: the word ( ‫)يشْف‬, of which the first three letters have already been known, the last is still covert (x ‫)و س ْـ‬. Suppose the remaining unknown letters of the alphabet are: ‫ف‬, ‫ج‬, ‫ب‬, ‫ر‬, ‫ظ‬, ‫ ع‬and ‫ع‬. “When you match these letters [one by one] against the position of the last letter that is still undetermined, you are likely to hold the word to be no other than ( ‫ )يشْف‬or ( ‫)يشْح‬. Let the context determine the 2 intended one for good,” he says.  “If two consecutive letters of the [intended] word have yet to be determined, you eliminate those already known from the whole lot, and elicit the possible bigrams, used and unused alike, from the rest of the alphabet. All are then identified against the positions of the covert letters, and 3 they are sure to turn out well.” Note al- urhum ‟s keenness and dedication to accuracy in considering both the used and unused letters of the rest of the alphabet. The example he quotes on this case is a five-letter word, of which the first two letters are still close, the other three are ‫س‬, ‫ج‬, and ‫( ل‬the whole word is thus represented: ( ‫ س ج ل‬y x)). The remainder of the alphabet is found to be the five letters: ‫ص‬, ‫ع‬, ‫س‬, ‫ط‬ and ‫ف‬. Thus the possible bigrams are: 2

P5 = 5 x 4 = 20

bigrams

Upon checking these bigrams in turn with the first two letters, you will find on the spot that the bigram (‫ )ط ف‬is the fittest, and so you settle on the word (‫)سفشخم‬.  “If the two letters to be solved do not occur in succession, the algorithm is to extract the bigrams and slot them in the positions of the remaining letters, taking care not to drop the 4 unused ones. The target word is thus certain to show up.” 1

See p.162. See p.162. 3 See p.162. 4 See p.164. 2

135

This assertion by al- urhum not to exclude the unused bigrams is in fact another evidence of his meticulous precision. He sets forth an example illustrating this case ‫ـــــ‬a four-letter word, the second letter of which is (ٌ), the fourth (‫)س‬, with the first and third unrevealed ( ‫ س‬y ٌ x). Given that the remaining letters of the alphabet are: ‫ر‬, ‫ع‬, ‫ ص‬and ‫ت‬, you work out the bigrams derivable from these four letters: 2

P4 = 4 x 3 = 12 ‫تتت‬ ‫رعص‬

‫صصص‬ ‫رعت‬

‫ععع‬ ‫رصت‬

bigrams ‫ررر‬ ‫عصت‬

“Place the second letter [ٌ] of the word in between the letters of the bigram, so the fourth [‫ ]س‬comes last. Thereby you come away with three familiar words, to wit: ‫جُؼش‬, ‫ جُزس‬and ‫ػُحش‬, of which you single out the one you see the fittest for the position according to 1 context.” This is represented as follows: ‫ر ٌ ع س‬, ‫ر ٌ ص س‬, ‫ر ٌ ت س‬, ‫ع‬ ‫ٌ ر س‬, ‫ع ٌ ص س‬, ‫)عنتز ( ع ٌ ت س‬, ‫ص ٌ ر س‬, ‫ص ٌ ع س‬, ‫ص ٌ ت س‬, ‫ت ٌ ر س‬ ( ‫)تنذر‬, ‫)تنعز ( ت ٌ ع س‬, and ‫ ت ٌ ص س‬. It is worthwhile to note here that al- urhum drops any reference to repeating the same letter, and therefore leaving out four possibilities, i.e. ‫ر ٌ ر س‬, ‫ع ٌ ع س‬, ‫ص ٌ ص س‬, and ‫ ت ٌ ت س‬. He then indicates that “cryptanalysing trigrams is rendered in a 2 similar vein”.

1.2.6. The Importance of Ciphertext Length al- urhum concludes his treatise by stressing the significance of the length of the ciphertext in cryptanalysis. He gathers that cryptanalysis is all but impossible if the cipher is too short and executed using a simple substitution method of encipherment. The importance of this notion stems from the fact that it has not been established mathematically until late in the first half of the twentieth 1 2

See p.164. See p.164.

136

century. He says: “The cryptanalyst should understand, inter alia, that an underworded cipher, in which letters are not frequent enough, is not likely to enable him to exactly identify the intended message; he is liable to end up with more possible plaintexts than one, even with 1 something that might be quite the contrary to what is intended.” al- urhum gives an example thereof by enciphering the following hemistich that belongs to the brachycatalectic k mil meter: Consisting of only 11 letters, it is obviously scanty and less than the minimum length prescribed by such expert scholars of cryptology as al-Kind , the Author of the Two Essays, ibn Adl n, and ibn 2 Dunayn r. It follows that cryptanalysis may result in the intended message or something else that can be contrary in meaning to the encipherer‟s intent, such as: To demonstrate the above example: 1

2

3

4

5

6

7

8

9

10

11

CIPHERTEXT INTENDED PLAINTEXT RESULTANT PLAINTEXT (Possible Outcome)

“This is so because both are equal in the number of letters and words. The letter count in their respective words is also equal. Both choices, therefore, are equally feasible. Further, other worthy verses than these two may also issue forth. The fact remains that the sound identification is best attained by the frequency of letters being high enough, where all letters are well placed for their proper positions, and 3 where no letter can possibly take the place of another.”

1

See p.164. See Vol.4 of this series, pp.19-20. 3 See p.164. 2

137

In support of his argument, al- urhum puts forward a vibrant example ‫ـــــ‬a line of poetry he says enciphered in his days, whose total count of letters is (24), of which (11) are unrepeated. The line is: Three possible lines have been extracted. The following tables manifest the ciphertext, the cleartext, and the three lines achievable, with and without repetition of letters: I. Without Repetition Letters

Ciphertext Cleartext

Possible Possible Possible Outcome 1 Outcome 2 Outcome 3

1 2 3 4 5 6 7 8 9 10 11

138

II. With Repetition Letters

1

2

3

4

5

6

7

8

9

10

11

12

Ciphertext Cleartext Possible Outcome 1 Possible Outcome 2 Possible Outcome 3

139

13

14

15

16

17

18

19

20

21

22

23

24

The verses extracted are the following: 1) 2) 3) An unmistakably noticeable feature is that only two letters are common to all three verses: the fourth and the ninth, i.e. the letters (‫)ت‬ and (‫ )ب‬respectively. al- urhum finally points out to the letter (‫ )و‬going before (‫ )ل‬in the word ( ‫)حًم‬, maintaining that it is a necessity dictated by encipherment. He also indicates that it is possible to extract further verses owing to the limited number of symbols used in the cipher (11 symbols), others being mostly repetitions.

1.3. Originality of al- urhum To all appearances, al- urhum ‟s treatise does not end here. It looks as if interrupted in midstream without observing the conventional way early writers used to conclude their treatises (stating completion of the compilation, its date, the scribe‟s name, etc.). This vindicates the belief that this treatise is an excerpt from a larger work not included in the manuscript. There is a possibility that this excerpt has been specially extracted because it approaches a number of encipherment questions not tackled in other documents of its kind. Such originality is indeed evident in the treatise through the following manifestations: 1. His analysis of the idea of frequency reversal or evenness of distribution. 2. His meticulous precision in extracting the rhyme, linkage and relief letters from poetic ciphers. 3. His peculiar approach to calculating bigrams and trigrams, sorting out their frequencies of occurrence, and utilizing them in cryptanalysis. 4. His statement that scanty ciphers, with a number of letters short of a specified minimum, defy cryptanalysis if substitution

140

methods of encipherment are used, since one can have many corresponding cleartexts.

Chapter 2

al- urhum 's Edited Manuscripts

141

2.1. Description of the Manuscripts al- urhum ‟s two manuscripts are part of the same assemblage of cryptology. They come not consecutively, but separated by the treatise of ibn Wahab al-K tib. The first manuscript is entitled “From al- urhum ‟s Book”, and occupies three pages (i.e. 80/B - 81/B). The other manuscript, entitled “From al- urhum ‟s Treatise”, occupies some four sheets (i.e. 83/A - 86/B). Sample pages of both manuscripts follow.

142

A photocopy of the first sheet of al- urhum ‟s first manuscript (Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)

143

A photocopy of the last sheet of al- urhum ‟s first manuscript (Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)

144

A photocopy of the first sheet of al- urhum ‟s second manuscript (Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)

145

146

2.2. The Texts (Arabic Original and English Translation)

147

2.2.1. From al- urhum ‟s Book If you are given two or more lines of poetry in cipher to consider, you may find that the second line ends with two patterns identically akin to their counterparts at the end of the first. In that case one of the patterns is the rhyme letter (raw ), the other may be the relief (ridf) or linkage (wa l). If this is found to be the relief, it should be the first of the two patterns and may be any of the letters ‫ا‬, ٔ or ٘. The other is then the rhyme letter, which may be any letter of the alphabet without restriction. If, however, it is found to be the linkage, it should be the second and may be any of the letters: ‫ا‬, ٔ, ٘ [or ‫]ْـ‬. If you are to distinguish the rhyme letter from the relief and linkage letters, see which of the two patterns is less frequently used and make it the rhyme letter. This is typical of people‟s ordinary speech, not that other possibilities are inconceivable. If the first pattern is found less frequent, the other must be the linkage; if the second is the less frequent pattern, then the first must be the relief. Should two patterns [of letters] at the end of two verses be identical, with the preceding letter in both being different and anteceded by one and the same letter, this last is fixed to be the letter (‫ ـــــ)ا‬the so-called basal alif or ta's s.

148

If the verse ends in three repeated patterns, the first of which is the least frequent, then it is positively the rhyme letter, always followed by the linkage ( ‫ )ْـ‬and then by any of the three vowels: ‫ا‬, ٔ and ٘ immediately after, which is the exit or ur . If the second pattern is found to be the least frequent, it is unmistakably the rhyme letter; the first is relief, the third linkage. The first and the third may equally be ‫ا‬, ٔ or ٘; the third only may also be the letter ‫ْـ‬. If [each of] the two verses ends in four repeated patterns, then the first and the last may be any one of the vowels: ‫ا‬, ٔ or ٘; the second is the rhyme letter, and the third must be the letter ‫ ْـ‬beyond a shadow of doubt. Suppose you are to address a two-line cipher, of which the pattern at the end of one line is incompatible with that at the end of the other. In this case seek a match for the last pattern in the first verse in the last pattern but one or two in the other verse. Failing this, you decide the last of the one verse is the letter (‫)ا‬, and the last of the other verse is an undotted (ٖ) that is pronounced as (‫ )ا‬in spoken discourse, but assumes the shape of (ٖ) in writing. If, however, the last pattern of one verse is found to be the identical last pattern but one of the other verse, then the last pattern of this is decidedly the letter (٘), such as in:

150

In a single position the last pattern turns out to be the letter (ٔ); that is if the final word of a verse is [the proper name] ٔ‫ػًش‬. If it happens to be in agreement with the last pattern but two, then the first of these two is necessarily the letter (ٔ), the other [the functional] (‫[ )ا‬of differentiation denoting plurality], as in:

You should realize that by referring to the verses as the first and the last I do not mean the one that is written first in order, nor that written last; I mean what you intend to be first and last . For instance, if you are given in cipher the above line starting " ..ًٙ‫ "انشاج‬with the line that comes next to it, it follows that it is no longer the first. That is why I opt to say: „the one and the other‟ to suggest either of them.

2.2.2. From al- urhum ‟s Treatise He said: The encipherer may [deliberately] intend to make a generous use of the infrequent letters of a language, and to make a sparing use of the highly frequent letters. This would make cryptanalysis more strenuous, such as in the following verse:

in which the letters (‫ )ج‬and (‫ )ع‬are overused.

152

I have considered the letters in usage, and found they fall into the following five classes as far as their frequency is concerned, though they might be divided otherwise:

Class I (Letters of highest frequency): ‫ا‬, ‫ل‬, ‫و‬, ٌ, ‫ْـ‬, ٔ and ٘. Class II: ‫ب‬, ‫د‬, ‫س‬, ‫ف‬, ‫ ق‬and ‫ن‬. Class III: ‫ت‬, ‫ج‬, ‫ذ‬, ‫ ط‬and ‫ع‬. Class IV: ‫ص‬, ‫ ش‬and ‫ط‬. Class V (Letters of lowest frequency): ‫خ‬, ‫خ‬, ‫ر‬, ‫ص‬, ‫ع‬, ‫ ظ‬and ‫ؽ‬.

If you encounter a trigram starting with the letter (‫ )ا‬followed by (‫)ل‬, the third letter will most likely be (٘) or, less likely, (‫ )و‬or (‫)ْـ‬. Just as the repeated occurrence of the pattern (‫ )ال‬at front-position in words is indicative of the definite article, so is the repeated occurrence of certain biliterals at end-position in words [indicative of plurality, duality, femininity, etc.]; e.g. the letters (‫ )ْى‬in:

154

And the letters (‫ )ٔا‬in:

And the letters (ٍٚ) in:

Similar biliteral suffixes are: (ٌٔ) indicating sound masculine plurality, (ٌ‫ )ا‬and ( ٍٚ) indicating duality, (‫ )ات‬denoting sound feminine plurality (e.g. ‫)يسهًات طانحات‬, pronouns such as ( ‫ )ًْا‬and ( ٍَْ) (e.g. ‫ضَشَتًَٓا‬, ٍََُٓ‫)ضشَت‬, and so on and so forth. The repetition of such biliterals in straight order at the end of words is likely to point to them, just as the repetition of the letters (‫ )ا‬and (‫[ )ل‬at the beginning of words] is. Spotting the former postpositively is analogous to spotting the latter (i.e. ‫ )ال‬prepositively. Other means that assist in the cryptanalysis of letters include special insight into the algorithms of cryptanalysing bigrams and trigrams. As for bigrams, the way to elicit them is through establishing their total count for certain, so that you avoid the unnecessary job of working out a bigram already spotted or leaving out one. The process involves multiplying the number of elements in the entity that you seek to know the count of bigrams contained in it by itself less one. The product represents the aggregate number of possible bigrams therein. Now the permutations are obtained by taking up each element a number of times equal to the total number of elements minus one. Against it the remaining elements are placed.

156

For example, to make out the number of bigrams in the word (‫)َظش‬, a trigram, we multiply three by two to get six: we say that the number of bigrams obtainable from this word is six. The permutations are achieved by placing each component letter twice against the remaining letters in tabular form as follows:

As regards trigrams, the way to establish their total count before sorting them involves multiplying the aggregate number of components by itself twice; the product is the total number of trigrams, whole and complete. To sort them out, arrange the component letters in pairs so that each letter is placed respectively against all the letters in rotation. This engenders sixteen two-letter words. For the word ( ‫)خؼفش‬, a four-letter name, we multiply four by four to get sixteen, and this product by four yet again ‫ ـــــ‬that is sixtyfour, which represents the whole number of trigrams possible. Thereupon we set down each of the component letters: ‫ج‬, ‫ع‬, ‫ ف‬and ‫س‬ in four combinations, against which we write the letters as follows:

158

Then we make each of these sixteen words into four combinations, against each of which one letter of the [intended] word is added. The complete arrangement [of trigrams] becomes as follows:

Now that you have had knowledge of the ways of working out bigrams and trigrams, we say: If, in pursuing bigrams and trigrams, your objective is a two- or three-letter word only, you will have to dismiss those bigrams and trigrams that are found meaningless, and settle on the more convenient in terms of relevance to the general theme of the cipher being cryptanalysed. Consider, for example, the case when, after working out the best part of the alphabet, the letters: ‫خ‬, ‫ر‬, ‫ ص‬and ‫ ص‬remain unknown, and a two-letter word is to be disclosed. To that end we reckon up the number of possible bigrams derivable from these four letters; we achieve twelve bigrams, of which we dismiss the pointless ones as irrelevant, and select from the meaningful ‫خز‬, ّ‫ خض‬and ‫ خض‬the one that best serves the ultimate purpose.

160

Also bear in mind that we may manage to work out all the letters of the word but one. When this happens, you isolate those letters that you have already unfolded, and check the rest of the alphabet one by one until you get one or more useful words. Fix upon the most appropriate to the theme. Take, for example, the four-letter word ( ‫)يشْف‬, of which the first three letters have been uncovered. Suppose the remaining unknown letters of the alphabet are: ‫ف‬, ‫ج‬, ‫ب‬, ‫ر‬, ‫ظ‬, ‫ ع‬and ‫ ع‬. When you match these letters [one by one] against the position of the last letter that is still undetermined, you are likely to hold the word to be no other than ( ‫ )يشْف‬or ( ‫)يشْح‬. Let the context determine the intended one for good. If two consecutive letters of the [intended] word have yet to be determined, you eliminate those already known from the whole lot, and elicit the possible bigrams, used and unused alike, from the rest of the alphabet. All are then identified against the positions of the covert letters, and they are sure to turn out well, perhaps not without labour. Given a five-letter word, of which the first two are still close, and the remainder of the alphabet are five letters, i.e. ‫ص‬, ‫ع‬, ‫س‬, ‫ ط‬and ‫ف‬, we draw up the possible bigrams of these five ‫ ـــــ‬twenty bigrams. Upon checking these in turn with the first two letters, we will find on the spot that the bigram (‫ )ط ف‬is the fittest, and so we settle on the word (‫)سفشخم‬.

162

If the two letters to be solved do not occur in succession, the algorithm is to extract the bigrams and slot them in the positions of the remaining letters, taking care not to drop the unused ones. The target word is thus certain to show up. An example in point is a four-letter word, the second letter of which is (ٌ), the fourth (‫)س‬, with the first and third unrevealed. Given that the remaining letters of the alphabet are: ‫ر‬, ‫ع‬, ‫ ص‬and ‫ت‬, you work out the twelve bigrams derivable from these four letters. Place the second letter [ٌ] of the word in between the letters of the bigram, so the fourth [‫ ]س‬comes last. Thereby you come away with three familiar words, to wit: ‫جُؼش‬, ‫ جُزس‬and ‫ػُحش‬, of which you single out the one you see the fittest for the position according to context. Cryptanalysing trigrams is rendered in a similar vein. The cryptanalyst should understand, inter alia, that an underworded cipher, in which letters are not frequent enough, is not likely to enable him to exactly identify the intended message; he is liable to end up with more possible plaintexts than one, even with something that might be quite the contrary to what is intended. For example, the following hemistich: Can be enciphered thus: Cryptanalysis may produce the intended message or something else, perhaps contrary in meaning, such as: This is so because both are equal in the number of letters and words. The letter count in their respective words is also equal. Both choices, therefore, are equally feasible. Further, other worthy verses than these two may also issue forth. The fact remains that the sound identification is best attained by the frequency of letters being high enough, where all letters are well placed for their proper positions, and where no letter can possibly take the place of another.

164

In our time a line of poetry was ciphered in the following form:

The line is: 1

It has been cryptanalysed by one as: 2

and by another thus: 3

and yet as: 4

Note that the letter (‫ )و‬is seen to have gone before (‫ )ل‬in ( ‫ ـــــ )ٔحًم‬a necessity dedicated by encipherment and the state of letters. Still it [this last verse] lacks import. Also note that further alternatives can be developed, since the actual word count of the cipher verse is as small 5 as four ; it is made long only through the repetition of the word ًٗ‫سه‬. But for the repetition it would have been the only possible choice consequent upon cryptanalysis thereof.

1

So in the original Arabic manuscript; but that is simply not the case since the symbol corresponding to the letter (‫ )ل‬is ‫( سطذ‬appearing several times) not ‫ششف‬, which appears only once in the ciphertext. The word ‫سهى‬, therefore, may be a scribe‟s omission, and can possibly and correctly be ‫سمى‬, ‫ سأو‬or ‫سٓى‬. 2 Just so in the original; it should more correctly be ‫أنف‬. 3 Just so in the original; it should more correctly be ‫سؼذ‬. 4 Just so in the original; it should more correctly be ّ‫أن‬. 5 i.e. ‫َضنث‬, ًٗ‫سه‬, ٗ‫ فؼه‬and ‫سهى‬.

166

1

1

2

71 203 202

3

20 18

4 5

149

1

222 221

2

195

151

3

4

126

5

2

1 2 3

224 2 4 5 6

153

1

2 3

4

5

1

351 350 274 235 1 118

83 126

58

55

2

131 1 3

4 5

155

1

2

3

429 6

1

80 78 789

449 6 2

3

157

‫‪1‬‬

‫‪2‬‬

‫‪3‬‬

‫فغ‬

‫‪1‬‬ ‫‪2‬‬

‫‪3‬‬

‫‪159‬‬

1

2

3

1

2 3

161

1

2

1

85

163

2

1

2

1 2

165

1

9

8

7

10

1 2

3 4 5 6 7 8 9 10

167

168