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

v

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

vi

1.2.2. Requisites and tools for poetry cryptanalysis ................. 55

1.2.3. Prosody and rhyme ......................................................... 55

1.2.4. Insight into the knack of writing .................................... 56

1.2.5. The importance of metrical measures ............................ 59

1.2.6. Impediments to cryptanalysis ........................................ 59

1.2.7. Examples ........................................................................ 60

1.2.8. Annexes .......................................................................... 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

vii

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 Transliteration Examples

Short

Vowels

(fat a) a as u in cup.

( amma) u as o in rock,

and u in put.

(kasra) i as e in red,

and i in big.

Long

Vowels

As a in last.

(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).

.b as b in back ب

.t as t in tea ت

.as th in thin خ

.as g in logic ج

.(e.g. tim) ذ

.(e.g. lid) خ

.d as d in day د

.as th in then ر

.r as r in red س

.z as z in zoo ص

viii

.s as s in soon ط

.as sh in show ش

e.g. mi) ص r).

e.g. ir) ع r).

.(e.g. riq) ط

.(e.g. fir) ظ

e.g. Abb) ع s).

.(e.g. lib) ؽ

.f as f in few ف

'q (e.g. qur ق n).

.k as k in key ن

.l as l in led ل

.m as m in sum و

n as n in sun.

.h as h in hot ـ

w as w in wet (e.g. wahab, nawfal).

y 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.

ix

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 lil-

malik al-'A raf (A manual on cryptanalysis written for King al-A raf).

Volume Three deals with ibn ad-Durayhim's treatise Mift al-Kun z

f al-Marm z (Key to treasures on clarifying ciphers). Volume

Four covers ibn Dunayn r's book Maq id al-Fu l al-Mutar ima an

all at-Tar ama (Expositive Chapters on Cryptanalysis).

Volume Five (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 al-

urhum :

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.

x

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 at-

tadr 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

1

The First Treatise

ibn ab ab ’s Treatise

on Cryptanalysis

2

Chapter 1

Analytical Study of ibn ab ab 's Treatise on Cryptanalysis

4

5

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.

6

1.2. Study and Analysis of ibn ab ab ’sTreatise

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

of great advantage.” 1

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

to twenty-eight letters,” 2 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 See his treatise, p.24.

2 Ibid., p.26.

7

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

of the predominant majority of language scholars. 1 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".

8

beginning of the next. The difficulty, however, consists in the so-

called no-word-spacer encipherment, mentioned by ibn Adl n1 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

several places of our Series. 2

d) Letter frequency of occurrence: According to ibn ab ab , the

high-frequency letters, in order of precedence, are: ـ ,ع ,ب , , ,و ,ل ,ا,

) and . Note that he places the letters ت and () towards the end, in (ـ

contrast with the mainstream trend of relatively arranging these letters

as they appear in the word (ان), i.e. ـ ,و ,ل ,ا, , and . 3

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

of poetry. A line of poetry so characterized is called "mu arra ".4

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.

2 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.

9

(b) agreement not effecting ta r , as in:

in which the count of letters is also the same in either

hemistich. This kind of verse is called "muqaff ".1

(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 (ا) and (ل). For

example, a message ciphered using bird names, in which the letter (ا)

is represented by "sparrow" and the (ل) by "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 (ا) and (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: أ ,ي,

etc. Note here that ,سم ,دع ,خز .etc. ; and imperative verbs, e.g ,ػ ,يز

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 يفاػالت ,اسحفؼال, and the like.

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

10

(9) Making use of the beginning of the second hemistich, so far

made out, in determining the conjunctions () and (ف) if 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. فؼن //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

unresolved.” 1

(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. انز) requires 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.

11

(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

Dunayn r1. 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.

12

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

in his two practical examples1.

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 Bird Name Letter Bird Name

peacock Buzzard

pheasant Crow

hawk Raven

falcon Francolin

harrier Grouse

merlin Bobwhite

eagle Ringdove

saker Pigeon

vulture Duck

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

13

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:

14

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 يفاػه يفاػه يفاػه. If we start from the number

(4), i.e. leaving out the first syllable ( of al-haza (يفا foot, ar- ra az

meter emerges with its feet يسحفؼه يسحفؼه يسحفؼه. If, however, we start

from the number (6), i.e. skipping the second syllable ( of the (ػـ

foregoing haza foot, ar-ramal meter disengages itself: فاػالج 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.

15

Let us start with the second word ( from which emerges the ,(كشى

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 ( With the first syllable left out, the second alternative .(سا

(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.

16

17

Chapter 2

ibn ab ab ‟s Edited Treatise

18

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 words-

within square brackets [ ]; examples illustrating rules of

encipherment have been set off by round brackets (parentheses)

( ); book titles in italics; quoted material and Prophetic

traditions have appeared within quotation marks “ ” , while

floral brackets have been used to enclose Koranic verses.1

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

19

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 al-

mu 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”.

20

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

21

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

22

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

23

2.3. ibn ab ab ‟s Treatise

on Cryptanalysis

(Original Arabic Text and English Translation)

24

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.

26

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 word-

spacers 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 (ا) and

,( ب, , ,و) :are of highest frequency in usage; the next highest are (ل)

followed by (ت ,ـ ,ع, ), 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.

28

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, ( ) with

( ), or to have ( ) with ( ) for the feminine, in which case both

hemistichs agree in meter and differ in cipher form and the addition of

a letter.

30

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 (ا) and (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,

, , , , etc.

1 Note: To cryptologists, what counts is the graphical representation only. Thus, the

gemination in ( does not make a difference, while it does by the standards of (يذ

lexicographers.

32

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).

34

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 (خ ت ب ا …) until 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.

36

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.

38

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:

40

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.

42

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:

we write1:

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.

44

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:

46

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:

25

رسالة أبي الحسن بن طباطبا العلوي

1

792

79

27

1

247614154

1238254343349

5960

3

1290293342343

29

1

196

321712

1963

4196

5

1966

1967

196818

19681

31

1

197

812

1973

1974

1975

1976

197827

1978

1979

19710

11197

33

1

1972

1973

1974

5197

6197

35

1

1972

1973

1974

584

6198

37

1

1982

1983

1984

1985

198

39

1

1982

1983

1984

1985

198856

1987

1998

919986

1019986

41

1

199200

86872

13033073

199874

5

43

1

2200

3

304

45

1

2201

3201

4201

5201

620190

7201

8

9201

9010

20111

20112

2019013

20190

47

7474

1

202912

3

4

5

6

7203

48

49

The Second Treatise

A Treatise on Cryptanalysis of Poetry

by the Author of Adab a - u ar '

50

51

Chapter 1

Analytical Study of the Treatise on

Cryptanalysis of Poetry

by the Author of Adab a - u ar ' (The Art of Poets)

52

53

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,

and was one source of the other1.

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.

54

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

an element that is not part of the cryptogram…”1. 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

you think have I enciphered for you?‟ ”2. 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

communication with peers.” 3 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

same metric pattern” 4.

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.

2 See p.70.

3 See p.104.

4 See p.70.

55

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

discussed at great length in ibn Dunayn r's book. 1

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.

56

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 ا ( ) and ل (l).

2. Checking two-letter words (bigrams) such as: ذ ,ي ,لذ, etc.

3. Watching out for silent letters: letters written but not

pronounced (e.g. the terminal in the proper name ػش [ Amr],

and the functional ا of differentiation added to verbs denoting

plurality such as لانا).

4. Attending to voiced letters: letters pronounced but not written

(mainly the letter ا in such proper names as إتشى and 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.)

57

9. Marking the letters ت (t) and ـ (h) at end-positions (e.g. لايث,

.(فؼهح ,سحة

10. Scrutinizing doubled and geminated letters (e.g. سذ ,لهم).

11. Guessing probable words and using them as a vehicle for

uncovering other words.

12. Observing noun structures defined with (ال) and 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 (ال) And Their Different

Variations The author mentions a group of words defined with (ال), in which

the letters (ا) and (ل) are 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 Examples

… ,انهز ,انهف ,انهح ,انهة ,اهلل xا ل ل

… ,انهم لxا ل ل

(ء)انا ا xا ل (ء)انذا , (ء)انا , , …

…,انثا ,انؼاس ,انساق ,اناس ,انذاس y ا xا ل

...,أنثاب ,أنا ,إنحاذ ,إناو ,انشاش ,انا ,انثاب x ا xا ل

58

...,انؼماب ,انثاب ,انظاب ,انضشاب z ا y xا ل

...,انسائم ,انظاسو ,انضشاغى ,انالة ,انماة z w ا y xا ل

...,انحادخ ,انكاف ,انضا ,انشاي ,انمادو ,انضاسب ,انغائة z y ا xا ل

...,انحثا ,انحماطش ,انحؼاد ,انحماسب w v ا x y zا ل 1

…,انحؼاز ,انادم ,انمادم w v z ا y xا ل

...,انغاس ,انؼاس ,انؼحاو ,انغحاب ,انحاب v ا z y xا ل

...,انسحفاد ,انسحؼا ,انسحؼاس v اw z y x ا ل 2

...,األفضم ,األػظى ,األكثش ,األل z y xا ل ا

(ء)اإلػطا اy xا ل ا (ء)اإلغضا , ,...

(ء)األدػا اz y xا ل ا (ء)األحا , (ء)األثا , ,...

...,اخاو ,ايال y ا xا ل ا

...,األطاس ,األفؼال ,األػاو ,األحال ,األػال z ا y xا ل ا

...,األكاتش ,األطاغش ,األخاة ,األطاة ,األػاخى z y ا xا ل ا

...,األحادد ,األاتة ,األػاخة w z y ا xا ل ا

...,إرا ا xا

These are followed in the treatise by helpful observations towards

cryptanalysis. These are:

1. The letters of lower frequency of occurrence are: ظ ,ؽ ,ص ,ر ,خ ,خ,

.ش and ط ,ط

2. It is unlikely in poetry the occurrence of a geminate (doubled)

letter immediately after the letter (ا), such as: داب ,داتة.

3. No two consecutive neutral letters are likely to occur in Arabic

poetry except in a rhyme characterized by relief such as: انداد in

the following verse:

اناط نهت كخم انطشاد فانساتك انساتك يا انداد

4. There are a few long Arabic words that are devoid of the letters

.سسحذسخى ,فسكفكى .e.g ,(ل) and (ا)

1 This is true for words of this rhythmical measure having two initial affixing letters;

otherwise words of different beats, without the letters (و) and (ت), are also possible

such as انشخاة ,اندغشاف ,انؼثا ,انسشاف, 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), (ط) and

.etc ,انححذات ,انحشاء ,انكثشاء .are also conceivable possibilities, e.g ,(ت)

59

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

af ad-D n al- ill1, 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:

split ra az, manh k ra az, curtailed sar , or curtailed munsari . 2

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 d. AD 1349.

2 See p.110.

60

probably contain plenty of the letters () and ( as dependant (or (ـ

inseparable) pronouns, and also of the functional (ا) of

differentiation that appear in the written spelling of past verbs

denoting plurality, as in: لانا and فؼها. 1

- 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

unacceptable in Arabic poetry. 2

- 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 See p.96.

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

61

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.

62

63

Chapter 2

The Edited Treatise on Cryptanalysis

of Poetry

by the Author of Adab a - u ar '

(The Art of Poets)

64

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.

65

A photocopy of the first sheet of the Treatise on the Cryptanalysis of Poetry

(Document No. 5359, as-Sulaym niyya Ottoman Archives, Istanbul, Turkey)

66

A photocopy of the last sheet of the Treatise on the Cryptanalysis of Poetry

(Document No. 5359, as-Sulaym niyya Ottoman Archives, Istanbul, Turkey)

67

2.2. The Treatise

(Original Arabic Text and English Translation)

68

A Treatise on Cryptanalysis of Poetry

By the Author of

Adab a - u ar '

69

70

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.

72

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.

74

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 See also ibn Adl n's treatise, of which the 16

th 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. 2 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).

76

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 ا ( ) and ل (l) 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 ا's and ل's are then sought, and

the rest of the cipher is now apt to get easier to crack.

1 See p.55.

2 i.e. of which the letter preceding the rhyme letter is a neutral ا, or .

3 i.e. of which the letter (ا) is located prior to the rhyme letter but one.

78

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.

80

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 . Be equally heedful of the

extra ( ) added to the proper name (= 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.

82

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 in the

nominative, in the objective, and 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 ( ), a particle for

calling attention, so that together they form ( ), 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.

, , , ; , , , , , , , .

84

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. , , , ; , , 2); geminated

(e.g. , , , , , , , , ); 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.

86

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 (ال) is 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 ( ) [as a pronominal suffix] in such

words as: , and . 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 (و) in 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:

88

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.

90

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 See footnote No. 7, p.58.

2 See footnote No. 8, p.58.

92

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 ( ).

94

Bear in mind that the low-frequency letters that occur at end-

positions 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], , and the like.

1 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. 2 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 ( ).

96

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.

98

Poetical measures, as those developed by the poet Ab al-

At 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 ( ). If the foot

( ) undergoes qab , it becomes ( ). The effect of

al-qa phenomenon is not much of a problem as al-

kaff, 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.

100

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: and are distortions, the genuine

forms of which are: and .

- 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).

102

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 So in the Arabic original; it is in fact the first, as he states later in the treatise.

2

Mentioned by ibn Dunayn r with slight variation in wording, i.e. , ,

instead of , , respectively. See Vol.4 of this series, p.174. 3

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.

104

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.

106

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:

12

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 (ا) can be mistaken for (ل). That is why I have

already stated the conjunctions and their orders of frequency.

1 A word-spacer observed throughout the three cryptograms.

2 Not in the original.

3 Not in the original.

4 By al-Mutanabb . Its wording here is as follows:

108

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:

110

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-Raqq3

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

2 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. 3 d. AD 814.

112

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 ( ).

114

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.

116

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

Cacuminal Apical Orificial Uvular Letters

Guttural

(hamza)

Vocalic Labial Liquid Letters Gingival

Another verse consuming the Arabic letters: 2

1 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.2 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 ad-

Durayhim‟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.

71

1

2

3

4

73

1

2

3

4

75

1

2

1

1295300

5470722

77

1

2

3

1

2

3

79

81

1

23

45

1

1031042

3

42722

5

83

1

1

85

1

2

3

45

6

1

13632

3

744

5

6

87

12

3

45

6

7

1

2

3

4

5

676

7

89

1

2

3

1

1112

1121133

91

1

2

3

4

56

1

2

3

4

5

6

93

1

2

3

45

1

2

3

4

5

95

1

2

3

45

6

7

8

9

1

2

12743

4

5

6

7

82137

97182

97

1

2

34

1

2

39091

4

99

1

23

4

5

1

772

3

47177

5103212

101

1

2

3

4

5

6

7

1

62362

3

4333581

5

6

7124

3370

103

1

2

3

4

1

116248

18

62512

773

4

105

1

2

1

117

2

107

1

2

34

5

1

2

3286

4

5123

109

1

1

111

1

2

3

4

56

1

2101561486

4464512

3

1983164

5

6

3637

113

1

2

3

4

5

6

7

1

279

3

4

1272327

79

579

6

779

115

1

2

3

4

5

6

1

792

793

1204

5

8246

7199

1146

117

1

انحهمة

2

1

2

118

119

The Third Treatise

al- urhum 's Two Manuscripts

120

Chapter 1

Analytical Study of al- urhum ‟s Two Manuscripts

122

123

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

relief (ridf) if it precedes raw , or linkage (wa l) if it follows2. 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

those that occur as raw ;( and ,ا) 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

second is the less frequent pattern, then the first must be the relief.” 3

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.

124

where the letter (ب) is the rhyme letter, and the following (ا) the

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 (ل) is 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

the so-called basal alif or ta's ـــــ(ا) s.” 1 Example:

The two identical patterns in both verses are the terminal (ل) and

( in the (ذ) preceded by the letter ,(rhyme and linkage respectively) (ـ

first line and the letter (د) in the second (both are called the extraneous

letter or da l), then anteceded by the one basal (ta's s) letter (ا) in

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 ( ,ا :and then by any of the three vowels (ـ

and immediately after, which is the exit or ur .” 2

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 ( in (ـ

and . The last syllable can be represented: zyx, where x is the

1 See p.148.

2 See p.150.

125

least frequent of the three letters and therefore it is the rhyme letter

(the س here). The following y=ـ is 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

the letter ـ.” 1

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

.in between (ب)

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 ( beyond (ـ

a shadow of doubt.” 2 Example:

In each verse of the above, the repeated patterns are the last four

letters ( of which the first (relief ) and final (exit) are one and the ,(ايا

same letter (ا). The second (i.e. و) is 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 See p.150.

2 See p.150.

126

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 (ا) in spoken discourse,

but assumes the shape of () in writing.” 1

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 (و) without establishing it in writing. The (), in

contrast, materializes in (دي) because it is the first-person ().

8. “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] ػش.” 3

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] (ا) [of differentiation denoting plurality], such as in:

4”

1 See p.150.

2 See p.150.

3 See p.152.

4 See p.152.

127

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

normally of high frequency of occurrence (i.e. abundant letters). 1 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.98-

100; ibn Dunayn r (Vol.4), p.11 and p.70.

128

cites the following example of how the letters (ع) and (ج) are

overused:

He argues that this practice “makes cryptanalysis more

strenuous” 1, 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: ـ , ,و ,ل ,ا, and .

Class II includes the letters: ق ,ف ,س ,د ,ب and ن.

Class III includes the letters: ط ,ذ ,ج ,ت and ع.

Class IV includes the letters: ش ,ص and ط.

Class V includes the letters: ظ ,ع ,ص ,ر ,خ ,خ and ؽ. 2

It seems that this division of letters into five classes is unique to al-

urhum ; 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 al-

urhum the Author of the Two Essays, and ibn Adl n:

1 See p.152.

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

129

Letter Classes ibn Adl n Author of the

Two Essays

al- urhum

Class I

(Abundant

Letters)

ـ و ل ا

7

و ل ا

ـ

7

ـ و ل ا

7

Class II

(Common

Letters)

ب ت ف ع س

ج ذ ق ط د ن

11

ب ت ف ع س

ج ذ ق ط د ن

ص

12

ن ق ف س د ب

6

Class III

(Scarce Letters)

خ خ ص ط ؽ ظ

ر ص ش ع

10

ط ص خ ش خ ر

ع ظ ؽ

9

ع ط ذ ج ت

5

Class IV ط ش ص

3

Class V 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 (ا) which is by far the highest frequent letter.

Together they form the definite article. Therefore (ل) is spotted after

.at the beginning of words (ا)

In a three-letter word (trigram) beginning with (ا) plus (ل), the third

will most likely be one of the letters: (), (و) or ( ,أنى ,إن :such as in ,(ـ

. إن

Biliterals often occur suffixed to verbs, nouns, pronouns, and

particles. Examples of such biliteral suffixes are: ى (as in: حفظى,

,كاجث .e.g) ;(ت ,نهاخح ,جذسس .e.g) ;(اكحثا ,كحثا :as in) ا ;(سفى

130

;(ػها ,تحا ,ؼطا .e.g) ا ;(أدات .e.g) ات ;(لها .e.g) ا ;(ت ,حشخ

(e.g. ,ؼه ,دسس .(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 (ا) and (ل) [at the beginning of words] is.

Spotting the former postpositively is analogous to spotting the latter

(i.e. ال) prepositively.” 1

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

into the algorithms of cryptanalysing bigrams and trigrams.” 2

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

a bigram already spotted or leaving out one.” 3

He then stes forth the general law of calculating bigrams ــــ the law

of the permutations of (m) elements by taking up (2) elements at a

time:

P 2

= m ( m – 1) m

where (m) is the total number of elements or letters. As al-

urhum 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.

2 See p.156.

3 See p.156.

131

contained in it by itself less 1. the product represents the aggregate

number of possible bigrams therein.” 1 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:

P 2

= 3 ( 3 - 1 ) = 3 x 2 = 6 3

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:

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:

P 2

= 4 x 3 = 12 4

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.

Reading

direction

132

P = m2 = 4

2 = 16 = 12 + 4

1

Next, al- urhum reckons the bigrams derivable from five-letter

words:

P 2

= 5 ( 5 – 1 ) = 5 x 4 = 20 5

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. ػؼغ ,خدح ,سسس, 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

trigrams, whole and complete”. 2

This may be construed as: N = m3.

Using this formula in computing the trigrams inherent in the four-

letter word (خؼفش), we find:

N = 43 = 64

This count is quite legitimate because of the likelihood of trigrams

composed of a single letter repeated. 3

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 ( a four-letter name, we ,(خؼفش

multiply four by four to get sixteen, and this product by four again

that is sixty-four, which represents the whole number of trigramsــــ

possible. Thereupon we set down each of the component letters: ع ,ج,

1 See p.158. See also Volume One of this series, p.54ff.

2 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.

133

”.in four combinations, against which we write the letters س and ف 1

The combinations would take the following forms:

س ج ف ج ع ج ج ج

س عف ع ع ع ج ع

س فف ف ع ف ج ف

س سف س ع س ج س

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

follows..”. 2

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)

ج

ج

ج

ج

ج

ع

ف

س

ج

ج

ج

ج

ع

ع

ع

ع

ج

ع

ف

س

ج

ج

ج

ج

ف

ف

ف

ف

ج

ع

ف

س

ج

ج

ج

ج

س

س

س

س

ج

ع

ف

س

ج

ج

ج

ج

Group 2

(Against the

letter ع)

ج

ج

ج

ج

ج

ع

ف

س

ع

ع

ع

ع

ع

ع

ع

ع

ج

ع

ف

س

ع

ع

ع

ع

ف

ف

ف

ف

ج

ع

ف

س

ع

ع

ع

ع

س

س

س

س

ج

ع

ف

س

ع

ع

ع

ع

Group 3

(Against the

letter ف)

ج

ج

ج

ج

ج

ع

ف

س

ف

ف

ف

ف

ع

ع

ع

ع

ج

ع

ف

س

ف

ف

ف

ف

ف

ف

ف

ف

ج

ع

ف

س

ف

ف

ف

ف

س

س

س

س

ج

ع

ف

س

ف

ف

ف

ف

Group 4

(Against the

letter س)

ج

ج

ج

ج

ج

ع

ف

س

س

س

س

س

ع

ع

ع

ع

ج

ع

ف

س

س

س

س

س

ف

ف

ف

ف

ج

ع

ف

س

س

س

س

س

س

س

س

س

ج

ع

ف

س

س

س

س

س

1 See p.158.

2 See p.160.

134

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

say:…” 1 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: ص ,ر ,خ and ص remain

unknown.” 2 In order to uncover a two-letter word out of

these four letters, we reckon up the number of possible

bigrams:

P 2

= 4 x 3 = 12 bigrams 4

Sorting them out, as already mentioned, we get the

following bigrams: ص ر ,ص خ ,ر ص ,ر ص ,ر خ ,خ ص ,خ ص ,خ ر,

From these we pick only the .ص ص and ص ر ,ص خ ,ص ص

meaningful ones such as: خض ,خض ,خز,… 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 See p.160.

2 See p.160.

135

useful words. Fix upon the most appropriate to the

theme.”1 al- urhum cites a case in point: the word

of which the first three letters have already been ,(يشف)

known, the last is still covert (x و س ـ). Suppose the

remaining unknown letters of the alphabet are: ر ,ب ,ج ,ف,

When you match these letters [one by one]“ .ع and ع ,ظ

against the position of the last letter that is still

undetermined, you are likely to hold the word to be no

other than (يشف) or (يشح). Let the context determine the

intended one for good,” 2 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

they are sure to turn out well.” 3 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 ج ,س,

and ل (the whole word is thus represented: ( س ج ل y x)). The

remainder of the alphabet is found to be the five letters: ط ,س ,ع ,ص

and ف. Thus the possible bigrams are:

P 2

= 5 x 4 = 20 bigrams 5

Upon checking these bigrams in turn with the first two letters,

you will find on the spot that the bigram (ط ف) is 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

unused ones. The target word is thus certain to show up.” 4

1 See p.162.

2 See p.162.

3 See p.162.

4 See p.164.

136

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 ( س y x). Given that the remaining letters of

the alphabet are: ص ,ع ,ر and ت, you work out the bigrams derivable

from these four letters:

P 2

= 4 x 3 = 12 bigrams 4

ت ت تص ص ص ع ع ع ر ر ر

ر ع ص ر ع ت ر ص ت ع ص ت

“Place the second letter [] of the word in between the letters of the

bigram, so the fourth [س] comes last. Thereby you come away with

three familiar words, to wit: جزس ,جؼش and ػحش, of which you single

out the one you see the fittest for the position according to

context.” 1 This is represented as follows: ع ,ر ت س ,ر ص س ,ر ع س

) ع ت س ,ع ص س , ر س ت ر س ,ص ت س ,ص ع س ,ص ر س ,(عنتز

It is worthwhile to note here that . ت ص س and ,(تنعز) ت ع س ,(تنذر)

al- urhum drops any reference to repeating the same letter, and

therefore leaving out four possibilities, i.e. ص ص س ,ع ع س ,ر ر س,

and ت ت س .

He then indicates that “cryptanalysing trigrams is rendered in a

similar vein”. 2

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 See p.164.

2 See p.164.

137

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

something that might be quite the contrary to what is intended.” 1

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

Dunayn r. 2 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:

CIPHERTEXT 1 2 3 4 5 6 7 8 9 10 11

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

where no letter can possibly take the place of another.” 3

1 See p.164.

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

3 See p.164.

138

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

Outcome 1

Possible

Outcome 2

Possible

Outcome 3

1

2

3

4

5

6

7

8

9

10

11

139

II. With Repetition

Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Ciphertext

Cleartext

Possible

Outcome 1

Possible

Outcome 2

Possible

Outcome 3

140

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 (ب) respectively.

al- urhum finally points out to the letter (و) going before (ل) in the

word ( maintaining that it is a necessity dictated by ,(حم

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

141

methods of encipherment are used, since one can have many

corresponding cleartexts.

Chapter 2

al- urhum 's Edited Manuscripts

142

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.

143

A photocopy of the first sheet of al- urhum ‟s first manuscript

(Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)

144

A photocopy of the last sheet of al- urhum ‟s first manuscript

(Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)

145

A photocopy of the first sheet of al- urhum ‟s second manuscript

(Document No. 5359, as-Sulaym niyya Ottoman Archives, Turkey)

146

147

2.2. The Texts

(Arabic Original and English Translation)

148

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

(ا) ـــــ the so-called basal alif or ta's s.

150

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 ( and ,ا :and then by any of the three vowels (ـ

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 ـ beyond 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 (ا) in 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:

152

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] ػش. 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] (ا) [of

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 " ..انشاج " with 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 (ج) and (ع) are overused.

154

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): ـ , ,و ,ل ,ا, and .

Class II: ق ,ف ,س ,د ,ب and ن.

Class III: ط ,ذ ,ج ,ت and ع.

Class IV: ش ,ص and ط.

Class V (Letters of lowest frequency): ظ ,ع ,ص ,ر ,خ ,خ and ؽ.

If you encounter a trigram starting with the letter (ا) followed by

.(ـ) or (و) ,the third letter will most likely be () or, less likely ,(ل)

Just as the repeated occurrence of the pattern (ال) at 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 (ى) in:

156

And the letters (ا) in:

And the letters () in:

Similar biliteral suffixes are: () indicating sound masculine

plurality, (ا) and () indicating duality, (ات) denoting sound feminine

plurality (e.g. يسهات طانحات), pronouns such as ( ) and (ا ) (e.g.

,ضشتا and so on and so forth. The repetition of such biliterals ,(ضشت

in straight order at the end of words is likely to point to them, just as

the repetition of the letters (ا) and (ل) [at the beginning of words] is.

Spotting the former postpositively is analogous to spotting the latter

(i.e. ال) prepositively.

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.

158

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 ـــــ that is sixty-

four, which represents the whole number of trigrams possible.

Thereupon we set down each of the component letters: ف ,ع ,ج and س

in four combinations, against which we write the letters as follows:

160

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:

remain unknown, and a two-letter word is to be ص and ص ,ر ,خ

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 خض ,خز and خض the one that best serves the ultimate

purpose.

162

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 (يشف), of which

the first three letters have been uncovered. Suppose the remaining

unknown letters of the alphabet are: ع ,ظ ,ر ,ب ,ج ,ف and 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 (يشف) or (يشح). 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. ط ,س ,ع ,ص and ف, we

draw up the possible bigrams of these five ـــــ twenty bigrams. Upon

checking these in turn with the first two letters, we will find on the

spot that the bigram (ط ف) is the fittest, and so we settle on the word

.(سفشخم)

164

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: ص ,ع ,ر and 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 [س] comes last. Thereby you

come away with three familiar words, to wit: جزس ,جؼش and ػحش, 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.

166

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 (و) is seen to have gone before (ل) in (حم) a ـــــ

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

as four5; 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 (ل) is سطذ (appearing 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 سأو ,سمى or سى. 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. فؼه ,سه ,ضنث and سهى.

149

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