arabic origins of cryptology vol. 6

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Series on

Arabic Origins of Cryptology

Volume Six

Two Treatises on CryptanalysisThe Two Essays

The Treatise of ibn Wahab al-K tib

Series Editors

M. Mrayati, Ph.D.

Y. Meer Alam, Ph.D. M. H. at-Tayyan, Ph.D.

Published by

KFCRIS & KACST


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Acknowledgments

The editors of this series greatly appreciate the encouragement they

received from Dr. Yahya Mahmoud Ben Jonayd, Secretary General of

King Faisal Center for Research and Islamic Studies, to publish this

Series. We are also in the debt to Dr. Saleh Athel, the President of

King Abdulaziz City for Science and Technology (KACST), for

supporting the project of translating this series into English.

Many thanks go to Dr. Daham Ismail Alani, the Secretary General ofthe Scientific Council of KACST, for 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 series was realized with skill and

dedication by Mr. Ousama Rajab, to whom we express our deepest

appreciation.

Finally, we would like to mention our recognition to the many who

had previously contributed to the Arabic version of this series, and

particularly to Dr. Wathek Shaheed, Dr. Shaker al-Fahham, the lateProf. Rateb an-Naffakh and, last but not least, to Dr. Fouad Sezgin.


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Series on

Arabic Origins of Cryptology

Volume 6

Translated by

Said M. al-Asaad

Revised by

Mohammed I. al-Suwaiyel, Ph.D.

Ibrahim A. Kadi, Ph.D.

Marwan al-Bawab


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Contents

Transliterating Arabic words .......................................................vii

Preface ............................................................................................ ix

The First TreatiseThe Two Essays

Chapter 1: Analytical Study of the Two Essayson Cryptanalysis ....................................................... 3

1.1. Preliminary ............................................................................ 5

1.2. The First Essay on the Cryptanalysis of Straightforward

Ciphers (Simple Encipherment) ............................................ 6

1.2.1. Requisite Tools for the Cryptanalyst ............................. 7

1.2.2. Algorithms Not Based on Statistical Analysis ............... 8

1.2.3. Algorithms Based on Statistical Analysis ...................... 14

1.2.4. A Practical Example ....................................................... 161.2.5. Conclusions ..................................................................... 16

1.3. The Second Essay on the Cryptanalysis of Elaborate and

Demanding Ciphers (Advanced Cryptanalysis) .................... 17

Introduction ............................................................................ 17

1.3.1. Algorithms for Cryptanalysis ......................................... 17

1.3.2. Cryptanalysis of Simple-Substitution Ciphers Using Two

Cipherforms for the Letter () ....................................... 181.3.3. Cryptanalysis of Ciphers Rendered Using Forms of Close

Frequency ....................................................................... 19

1.3.4. Unanswering Ciphers ...................................................... 21

1.3.5. Annex .............................................................................. 24

1.4. Originality of the Author of the Two Essays ........................ 24

Chapter 2:The Edited Two Essays on Cryptanalysis ..............272.1. Editing Methodology............................................................ 282.2. Description of the Manuscript.............................................. 29


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2.3. The Texts (Arabic Original and English Translation) ........... 33

2.3.1. The First Essay ................................................................ 34

2.3.2. The Second Essay. ........................................................... 56

The Second TreatiseThe Treatise of ibn Wahab al-K tib

Chapter 1: Analytical Study of ibn Wahabs Treatise ............. 711.1. Preliminary ........................................................................... 73

1.2. Structure of the Treatise ....................................................... 73

Introduction: Motives for Using Secret Writing .................... 741.2.1. Letter Forms and Representations ................................... 74

1.2.2. Methods of Encipherment .............................................. 76

A) By Substitution (at-Tar ama) ................................... 76

B) By Concealment and Transposition (at-Ta miya) ..... 76

1.2.3. Algorithms of Cryptanalysis ...........................................80

- Form Count ....................................................................80

- Statistical Analysis (Frequency of Letters) ................... 80

- Combination of Letters ..................................................81

- Bigrams ..........................................................................81

- The Probable-Word Principle ........................................82

- Outlets of Letters ........................................................... 82- Word Length ..................................................................85

1.2.4. An Overview of Poetry Cryptanalysis ............................ 86

1.2.5. An Encipherment Method ................................................87

1.3. Originality of ibn Wahab al-K tib ..........................................87

Chapter 2:ibn Wahabs Edited Treatise ................................. 892.1. Description of the Manuscript.............................................. 902.2. ibn Wahabs Treatise

(Original Arabic Text and English Translation) .................. 93


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Transliterating Arabic words

For transliterating Arabic words (names, titles, etc.) we have adopted the

International System for the Transliteration of Arabic characters, devised by the

International Standards Organization (ISO). The system constitutes ISO

Recommendation R233 (December 1961). Given below is this system, with some

additional explanations found to be necessary.

Vowels:

Arabic characters Transliteration Examples

Short

Vowels

(fat a) a as u in cup.

( amma) uas o in rock,

and u in put.

(kasra) ias 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

charactersTransliteration 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. t as t in tea. as th in thin.

as g in logic. (e.g. tim). (e.g. lid). d as d in day. as th in then. r as r in red.


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

(e.g. lib).

f as f in few. q (e.g. qur' n). k as k in key. l as l in led. m as m in sum. n as n in sun. h as h in hot. 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.


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Preface

This is the sixth book ofThe Arabic Origins of Cryptologyseries,

which addresses the cryptological contributions of the Arabs, and

translates a number of treatises by Arab cryptologists. The first four

books are each dedicated to one treatise. Volume One was devoted to

the oldest treatise ever found on cryptanalysis, written by al-Kind , the

well-known Arab philosopher, about 1200 years ago. That volume isintroduced by a chapter studying the historical background of

cryptology as part of the Arab civilization. It studies the factors that

led to the early advances of Arab cryptology, highlighting important

aspects of the science in relation to other sciences. Volume Two

tackles ibn Adl n's treatise al-mu'allaf lil-malik al-'A raf (A manual

on cryptanalysis written for King al-A raf). Volume Three deals with

ibn ad-Durayhim's treatise Mift al-Kun z f al-Marm z (Key

to treasures on clarifying ciphers). Volume Four covers ibn Dunayn r's

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

(Expositive Chapters on Cryptanalysis).

Volume Five, unlike the previous four volumes, includes threetreatises on the cryptanalysis of poetry, i.e. those of ibn ab ab , the

Author ofThe Art of Poets, and al- urhum .

This volume (Volume Six) consists of the following two treatises:

1. A treatise incorporating the Two Essays on Cryptanalysis by an

author known only by these Essays that date back to the 4th

or 5th

century AH (10th

or 11th

AD); and

2. The treatise of ibn Wahab al-K tib, who is estimated to have

lived during the late 3rd

century AH (9th

AD) and the better part of the

4th

AH (10th

AD).

To be noted is that the first three volumes of this series are theEnglish 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.


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On the other hand, the second three volumes (i.e. Volumes Four,

Five and Six) are the English version of Book Two of our afore-stated

Arabic original, also published by the Arab Academy, Damascus,

1997.

More Arab treatises, dealing mainly with ancient calligraphs, are

currently in preparation in both Arabic and English.

* * *

Damascus, January 2007

Dr. M. Mrayati

Dr. Y. Meer Alam Dr. M. H. Tayyan


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The First Treatise

The Two Essays on Cryptanalysis


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Chapter 1

Analytical Study ofthe Two Essays

on Cryptanalysis


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1.1. Preliminary

The Two Essays constitute something of a compact treatise,

addressing simple encipherment that is easy to cryptanalyse, as the

author describes it, as well as demanding and highly elaborate

ciphers. The manuscript has the distinction of including cryptological

concepts of paramount importance, and also indications that the author

was a seasoned old hand at the art of cryptography, who experienced

encipherment and cryptanalysis through correspondence with

dignitaries and state officials. A chronological approximation showsthat the Two Essays must have been written prior to ibn Dunayn r

(AD 1187-1229), who makes reference to them in his bookExpositive

Chapters on Cryptanalysis.1

The likelihood is that they have been

written after ibn ab ab (d. AD 934), on the basis that their author

adopts for the termenciphermentthe term rendering or tar ama,

which is the one ibn ab ab uses in his Treatise on Cryptanalysis.

This is particularly sensible, given that the terms encipherment and

ciphers were the common terms in use before him. This leads to the

conclusion that the Two Essays are supposed to have been written

sometime in the 4th

and 5th

centuries of the Hegira (10th

and 11th

AD).On the other hand, the identity of the author is still unknown. Except

for a single indication by ibn Dunayn r to the Author of the Two

Essays,2

no reference whatsoever has been made to him in the sheer

bulk of authoritative sources consulted. ibn Dunayn rs refrainment

from explicitly stating the name of the Author of the Two Essays

could be attributed to one of the following two reasons:

1. Some prominent early figures are better known by their major

works than by their own names. This phenomenon is not

uncommon in the Arabic literature; for example Ab Al

al-F ris is widely known as the author of al-' , and Ab al-Baq ' al- Ukbur is dubbed the author of al-'I r b. If this

argument held good in our case, it would be an evidence of the

1See ibn Dunayn r (Volume Four of this Series), p.54 and p.176.

2See ibn Dunayn r, p.176.


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authors extensive knowledge in this science, and an expression

of the importance of the Two Essays.

2. The Author of the Two Essays was anonymous. Failing to

establish his name, ibn Dunayn r opted to identify him with his

Two Essays. Apart from that, he refers in his book to other

cryptological figures by name, such as al-Kind and ibn

ab ab .

Although there is not the slightest indication in the Two Essays as

to the motive for writing them, the odds are that they have been drawn

up at the instance of a then influential person, who seems to appreciatethe use of cryptography in the state affairs. This tone is demonstrated

towards the end of the First Essay, when the author cautions

professional experts in this invaluable science against downgrading

its worthy applications to unproductive ends, such as using it for fun

and betting on trifles that serve no purpose, instead of employing it in

pursuit of honourable objectives. This statement, in addition to the

ciphertext given in the First Essay as a practical example, reflects the

thriving activity of encipherment, and shows how far it was enjoying a

boost in circulation at the time of the Author.

1.2. The First Essay on the Cryptanalysis ofStraightforward Ciphers (SimpleEncipherment)

This essay opens right with the words: I tell you, may God

shepherd your steps3. By this the Author may be addressing himself

to every reader in the tradition of early Arab writers, not that the

discourse might be directed to the one for whom the Two Essays have

been written. This practice, if anything, is not unfamiliar; it was

observed before by al-Kind who addressed his treatise to Ab al-Abb s ibn al-Mu ta im,

4and by ibn Adl n later addressing his work

to the King al-'A raf.5

However, this possibility is rather discounted

3See p. 34.

4See al-Kind (Volume One of this series), p.118.

5See ibn Adl n (Volume Two of this series), p.29.


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by the fact that the formula of address used has nothing special, and

falls short of the big honorific openings that are particularly cut out for

personalities of high status.

1.2.1. Requisite Tools for the Cryptanalyst

The Author turns straight to discuss the tools necessary for the

cryptanalyst, and the attributes characteristic of him/her. These are:

1)Exercising the utmost degree of patience, and showing a real

sense of commitment.2)Quitting idleness and slackness.3)Poring over the cipher symbols from beginning to end, in the

interests of readjusting and learning by heart.

4)Applying the mind with wholehearted dedication. (This is aprinciple of special importance, probably unprecedented.)

5)Temporarily putting off elaborate ciphers to refresh the spiritbefore making an attempt again.

6)Familiarity with the algorithms typically utilized incryptanalysing simple ciphers. If cryptanalysis proves to be

impossible by the above, the following tools should be

observed:7)Acquaintance with the principles of elaborate encipherment that

is impervious to solution.

8)Cryptanalysis of insolvable ciphers that do not seem to respondexcept by sheer coincidence, i.e. through an inadvertent

omission of the encipherer. As the author puts it: possibly as

a result of an error on the part of the cipherer. A cryptologue

with cogent argument, sound intuition and genuine insight can

stand a chance of cracking it in consequence.6

This is a major

principle widely used in cryptanalysis; it is based on tracing

encipherment errors and turning them to good account towards

cryptanalysis. (To the best of our knowledge, this principle isalso unprecedented, and peculiar to the Author of the Two

Essays.)

9)The cipher length: The ciphertext should be ten lines at theminimum, because less than that is nothing if not wearing and

6See p. 34.


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literally exacting. Letters, if not used frequently enough, would

turn out futile.7

Determining the technique of processing or the algorithm of

cryptanalysis is dependent on the length of the cryptogram. Unless the

cryptogram exceeds ten lines (i.e. 400-500 letters), the statistical law

of letter frequency would no longer be applicable to it, and the

cryptogram is thus rendered quite difficult to handle by these

quantitative expedients. In fact this reflection goes to show the

Authors extensive grasp of the principles of encipherment in general,

and letter frequencies and their relative connection in particular. To be

noted is that al-Kind (d. AD 873) was the first to mention thisstatistical law. He says: It could happen sometimes that short

cryptograms are encountered, too short to contain all the symbols of

the alphabet, and where the order of letter frequency cannot be

applied. Indeed the order of letter frequency can normally be applied

in long texts, where the scarcity of letters in one part of the text is

compensated for by their abundance in another part. Consequently, if

the cryptogram was too short, then the correlation between the order

of letter frequency in it and in that of the language would no longer be

reliable, and thereupon you should use another, qualitative expedient

in cryptanalysing the letters.8

Later on, ibn Adl n (d. AD 1268) came to determine the

approximate minimum number of letters a ciphertext should include

for successful cryptanalysis. The length of the text to be

cryptanalysed, he argues, should be at least in the neighborhood of

ninety letters as a rule of thumb, because the letters thus would have

had three rotations. Yet the number of letters may be less than that in

certain cases.9

1.2.2. Algorithms Not Based on Statistical Analysis

There are a number of simple algorithms for cryptanalysis that aremore concerned with practice and experience than statistical analysis.

Of thesealgorithmstheAuthor of the Two Essays states the following:

7See p. 36.

8See al-Kind s treatise (Volume One of this series), pp.124-126.

9See ibn Adl ns treatise (Volume Two of this series), p.52.


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(1)Separation of letters with no spacers between words, such as: (plain) = (cipher)

(2)Transposition within each word, e.g. (plain) = (cipher)321 4321 1 2 3 1 2 3 4

The numbers indicate the relative positions of letters within

each word.

(3)Concealment by letters: operative and inoperative letters, i.e. byintroducing insignificant letters (nulls) in between the

ciphertext letters, e.g.

(plain) = (cipher)(4)Reversal of text with letters broken up, so that reading is

conducted from left to right:

(plain) (cipher)

123456789 1 2 3 4 5 6 7 8 9

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

Plain Cipher

=(6)Concealment of letters within words; only one letter of each

word (e.g. the first, second, third, fourth, or the last) is the

target letter. Example:

=

(7)Concealment within words, the starting point being the edge ofa page or the first letter of each line in it, so that these letters

together form a group of words making up the cryptogram.

Some later authors have taken a special interest in this kind ofwriting, and so compiled books on various fields such that

different information comes out pursuant to the way pages are

read: if a page is read widthways, a text in one field of science

emerges; if it is read lengthways ab initio, another field of

science develops; if read lengthways ab intra from a certain

point, a third field of science appears; and so on. A typical


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example on hand thereupon is a book entitled: Unw n a - araf

al-W f (The Quintessence of Distinction) by 'Ism l ibn Ab

Bakr al-Muqri' (d. AH 837/ AD 1434), covering the five

sciences of Islamic jurisprudence, history, syntax, prosody and

rhymes. Each page is divided into columns; reading it

widthways, irrespective of the columns, emanates

jurisprudence; the right-hand column concerns prosody; the

next columns are on history, syntax and rhymes respectively. A

sample page of the book is here quoted just for illustration.

(8)Concealment by changing especially the letters of the highestfrequency (i.e. , , , , , ), of which two, three, four, or fiveletters may be concealed. For instance, by concealing the two

letters: (= ) and (=3), the cleartext becomes in

cipher: 3 3 .

(9)Encipherment by arranging the letters of the alphabet in twoaligned arrays as follows:

and substituting reciprocally within the pairs ( and ), ( and

), ( and ), etc. For example:

(plain) = (cipher)


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(

(

(

(

)

( )

( )

)

(

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


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(10) Substituting some letters of the alphabet according to a setkey, such as that stated by the Author: Then consider the

key often used in our days, i.e. ( ). 10 Encipherment is done by substitution reciprocally only within

these pairs: ( and ), ( and ) ,( and ), ( and ), and( and ); all other letters of the alphabet remain unchanged:

Thus, the name is ciphered: .

(11) Encipherment utilizing the arithmetic of decimally-weightednumerical alphabet (ADWNA), giving the cryptogram the

appearance of a financial register (accounting sheet). The

Author invokes an example demonstrating a method for

expressing the tens, hundreds and thousands in order to

conceal the ADWNA numbers. He says: Encipherment may

be predicated on a special arithmetic [ADWNA]. You

arrange the numbers denoting units from one to nine using

whole [dinars]; under the tens you write fractions of quarters,

and under the hundreds write fractions of halves. Under the

thousand (standing for the letter ) you write fractions ofhalves and quarters.

11This can be represented as follows:

10See p. 38.

11See p. 38.


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Nine Eight Seven Six Five Four Three Two One

9 8 7 6 5 4 3 2 1

dinar dinar dinar dinar dinar dinar dinar dinar dinar

90 80 70 60 50 40 30 20 10

quarter quarter quarter quarter quarter quarter quarter quarter quarter

900 800 700 600 500 400 300 200 100

half half half half half half half half half

1000

quarter and half

Accordingly, the name , for instance, can be enciphered:

one three seven five two four four eight one

quarter quarters quarters quarters dinars dinars quarters dinars dinar

It is evident that ibn Dunayn r has taken this method from the TwoEssays, and included it in his Expositive Chapters on Cryptanalysis

anonymously of any ascription.12

12See ibn Dunayn r's book (Vol. 4 of this series), p.138.


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1.2.3. Algorithms Based on Statistical Analysis

In case the method of encipherment used turns out to be none of the

afore-mentioned or kindred ciphering methods, it is then supposed to

be simple encipherment. Cryptanalysis is conducted through the

following steps:

1. Counting up the cipher forms meticulously, taking special care of

the forms that are close in shape. Two closely similar forms may

be mistaken for one form, such as: or or the like; for inthat case cryptanalysis would become extremely taxing.

13Here

three cases can be distinguished:(a) If the count is found to be twenty-eight forms, you decide

that each letter of the alphabet has been assigned a single

form, with () deemed as two individual letters [not as adistinctive letter].

14

(b) If the count adds up to twenty-nine forms, then () isincluded as a stand-alone letter, too.

15

(c) If, however, it amounts to thirty forms, you conclude that

a space recurs between words.16

2. Sorting out the cipherforms: Then sort the forms out. The sorting

process involves taking up the first form, computing its frequencyof occurrence in the cipher, and affixing the frequency number to

it. Subsequent patterns are handled alike.17

3. Endorsement of cipherforms: Next, you mull the forms over, and

endorse them for good by marking them each with a point under

the number.18

4. Seek for a cipherform of higher frequency than all other forms,

making it the letter () in case the cryptogram is comprised oftwenty-nine letters.

19

13See p. 40.

14See p. 40.

15See p. 40.

16See p. 40.

17See p. 40.

18See p. 40.

19See p. 40.


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5. Recording the letters of the alphabet against their respective

cryptanalysed counterparts in tabular form, according to their

relative frequencies.

6. Hunting for an adjacent element that seems to recur often with the

most frequent letter, and approximates it in number, making it the

letter (). You can verify that by seeking for both forms togetherand consecutively to develop the definite article ().

7. If the cipher uses word-spacers [30 different cipherforms], you

are getting along well towards cryptanalysis, given the fact that

the spacer has a higher frequency than both () and (). It might be

extracted from within the cipher by sound intuition. If this provesdifficult, try to assume the last form of the cipher to be the space,

and estimate the context accordingly. Otherwise take up the first

form and check up on it, since it is possible to start a cipher with a

spacer as a method of further deception.20

8. Now that the space comes out right with both () and (), lookbetween two spaces for a light word such as: , , , or thelike, on the basis of what goes before and after, which you should

adopt and build upon.21

9. Taking advantage of any possible words deliberately kept plain in

the cryptogram, and using them as a vehicle for the intended goal.

10. Utilization of the probable word concept: In case the cipher

turns out to have been rendered without spaces, seek beside ( )a form which you can fairly guess as the letter ( ) and so read thename of God (). Now consider preceding and following formsalready known, and guess at such typical expressions as: , , , , , or the like as dictated by the context.

22

20See p. 42.

21See p. 42.

22See p. 42.


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1.2.4. A Practical Example

Having completed his discussion of the tools and algorithms of

cryptanalysis, the Author turns to give an illustrative cipher of topical

importance at the time. It is in fact a message describing the suffering

of harassed peasants in the Town of Peace, and their abandonment of

their farmlands as a result of the sharp increase in the number of

claims made on them for payment. It is worth noting that the original

version of the ciphertext is not without errors, additions and

omissions. However, these have all been redressed and set right in

light of the cleartext.

1.2.5. Conclusions

The Author concludes his First Essay by considering the benefits of

grasping this science, and regularly practising it to promote practical

experience. Serious cryptanalysts do not content themselves just with

the easy and straightforward, but show keen interest in pursuing the

opaque and the formidable. The Author strongly advises against

degrading this precious science, particularly on the part of those who

have attained the dizzy heights of knowledge in it, by using it for

unworthy intentions such as staking, entertainment, or fun in

company. Instead, he suggests, it should be employed in far more

serious purposes in activities that have to do with state affairs and

the like. This statement of the Author clearly indicates that

encipherment in his days was used for both objectives.

The Author stakes out his position on the issue of employing this

science for betting on solving ciphers, as this proves futile for two

reasons:

(a) that such ciphers are intended solely for sustained mentalexertion, which is impractical; and

(b) that they are unrealistic and not meant for live correspondence

between two minds or souls.


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1.3. The Second Essay on the Cryptanalysis

of Elaborate and Demanding Ciphers(Advanced Cryptanalysis)

This Second Essay incorporates advanced methods of

encipherment and algorithms of cryptanalysis, as opposed to the

contents of the First, which serves as an introduction to cryptanalysis.

This one may be equivalent to what is termed an advanced paper in

todays terminology, and can be divided into the following topics:

Introduction

It is a brief statement that lists types of advanced ciphers. These

are:

a) Ciphers responsive to cryptanalysis by deep insight and common

sense.

b) Ciphers that involve two or more types of encipherment, and are

therefore misleading to the cryptanalyst, giving him/her a false

impression of solution.

c) Ciphers hard to cryptanalyse, although seeminglystraightforward.

d) Ciphers that defy cryptanalysis, even by dedicated professionals

who might well, if at all, manage on mature reflection.

1.3.1. Algorithms for Cryptanalysis

According to the Author, elaborate ciphers may be cryptanalysed

along the following steps:

1. Attempting the tools and algorithms cited in the First Essay. The

Author says: If you are invited to solve a cipher that baffledother peoples endeavours, consider it first by all the weapons

I have already given you.23

23See p. 56.


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2. Verifying the cipherforms are properly sorted out: Make sure of

the sort-out and the number of cipherforms, for that is the

backbone of the whole process.24

3. Seeking for letters of high frequency of occurrence: Seek for

one of the pillars, namely the letters () and (). 25 4. Utilizing the ten principles earlier mentioned in the First Essay,

especially the last five. In the Authors own words: Work out the rest

by the algorithms already known to you. If [the cipher is] found still

unresponsive to ordinary techniques of treatment, you should realize

that the letter () probably assumes two cipherforms. 26 This suggestsa modification to the method of encipherment based on simplesubstitution.

1.3.2. Cryptanalysis of Simple-Substitution CiphersUsing Two Cipherforms for the Letter ()

Encipherment is here rendered by assigning two cipher symbols to

the most frequent Arabic letter (), rather than just one, as is typicallythe practice in simple substitution, particularly if the cryptogram

consists of thirty of them;

27

thereupon:a) Give up working on the letter () [for a while] and seek for theletter (); you will find more of it than all other forms. 28

b) Now spot its exact image next to it, add another unknown form

before it and guess at the word (), presuming the preceding letter tobe () by approximation, 29 denoting the utilization of the probableword (

), which was undoubtedly in common use in correspondence

at the time.

c) Look at the word closely and reflect on it; if you manage to

draw out the form of the letter () from this word, [ ], then trace its

other form with the adjoining () as they recur together in other

24See p. 56.

25See p. 56.

26See p. 56 and p. 58.

27See p. 58.

28See p. 58.

29See p. 58.


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positions, 30

namely make use of two-letter words (bigrams) of

higher frequency in general, and () in particular.d) With the forms of the letters , and coming out right, rack

your brains to resolve the rest.31

Otherwise, quit this algorithm altogether and use another approach;

the cipher could have been rendered by simple substitution but on a

different variation. The following are further possible approaches.

1.3.3. Cryptanalysis of Ciphers Rendered Using Forms

of Close Frequency

The count of cipher characters may turn out to be in excess of thirty

(the count of the alphabet and the space), and a statistical

(quantitative) analysis of the cipher text may give comparable

frequencies of the cipher forms. In this case the cryptologue can

decide for sure that the letters () and () are made to assume twocipher forms each, and that the cryptogram thus has its defects and

frailties blurred.32

Note that the main defect of encipherment by

simple substitution is the possibility for a cryptanalyst to arrive at the

letters of higher frequency in the language through statistical analysis.

It follows, the Author suggests, that cryptanalysis grows all the harderwhen high-frequency letters such as () and () are assigned more thanone cipher symbol.

Cryptanalysis of such ciphers is accomplished according to the

following steps:

1. Look for another technique; do not try to cryptanalyse the

pillars [=the letters () and ()] unless they emerge haphazardly uponreflection.

33

2. Seek for a form that is higher in frequency than all others, and

make it one of the abundant letters, i.e. , , , and . Take thepattern of the letter () if it has been assigned two forms. In case the ()assumes more forms than two, it certainly does not belong to the

30See p. 58.

31See p. 58.

32See p. 60.

33See p. 60.


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group of lucid letters, 34

i.e. the abundant letters or the letters of

highest frequency. Needless to say, this is an important indication of

the Authors deep understanding of the fine points of letters and their

frequency of occurrence. This idea can be elucidated by looking at the

table of frequency of the abundant (high-frequency) and common

(moderate-frequency) letters, as observed by al-Kind :35

High-Frequency Letters Moderate-Frequency LettersLetter Rank Percentage of Occurrence Letter Rank Percentage of Occurrence

1 16.36 8 4.22

2 11.91 9 3.57 3 8.72 10 3.32 4 7.44 11 3.27 5 7.14 12 3.05 6 6.87 13 3.05 7 6.02 14 2.50

15 2.48 16 1.71 17 1.55 18 1.25

Given that the letter () has two forms, the percentage of occurrencefor each would be 16.36/2 = 8.18%, which falls within the range of

abundant letters or lucid letters as the Author dubs them. If,

however, the () assumes three forms, the percentage becomes16.36/3 = 5.45%, which falls short of that of the last abundant letter

(i.e. = 6.02%), and therefore each of the forms representing the letter.) is effectively outside the range of these letters)

3. If a form is entertained to be the letter (), for example, match itup where you find it, and look if it blends in well with its

surroundings. Identify it with identical instances throughout the

cipher.4. If it comes out right, you have achieved the goal; if not, then

you have to retrace your steps straight from the beginning. Assume the

selfsame form to be the letter (), and manipulate it the way you have

34See p. 60.

35See Volume One of this series, p. 58.


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manipulated the (). You may this time fare well; otherwise, make itone or the other of the two forms representing the letter () and manageit as before until you are done with all the lucid letters.

36

1.3.4. Unanswering Ciphers

The Author of the Two Essays proceeds to advance a number of

issues and ideas of paramount importance on encipherment methods

and cryptanalysis algorithms. His argument is based on the following:

(1) There are some intricate ciphers that defy cryptanalysis by theafore-mentioned algorithms; they might be resolved quite by chance.

the Author says: If the cipher proves so refractory that employing all

these techniques of cryptanalysis is out of the question, you should

recognize that it is irretrievable except by sheer chance, since it is

hermetically sealed from all sides.37

(2) Other ciphers add nulls. The Author urges the cryptanalyst to

strain for tracing the nulls, now dropping one symbol, now including

another. On that you build, in the hope that it may respond.38

(3) Some ciphers are intended to be communicated specifically

between a sender and a recipient, and therefore they are impossible to

pierce by a third party.

(4) A wide knowledge of the algorithms of cryptanalysis and the

various techniques of cipher manipulation is bound to help in the

design of unattainable or inaccessible ciphers, through sealing up all

the gaps. He says: A retrievable cipher is typically positively

definable and restricted to specific limits, of which the clues to

cryptanalysis are often predictable. Stopping up these clues makes the

cipher impossible to solve, however great the toil is.39

This is a

general principle which is still effective even today: The encipherer

should assume the role of the cryptanalyst, trying to close the gaps in

his/her cipher and to offset the shortcomings therein, making it astightly and as closely knit as to grow unresponsive to solution.

36See p. 60.

37See p. 62.

38See p. 62.

39See p. 62.


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However, the belief of the existence of such an impregnable cipher

does not, in fact, hold good all the way. Mathematically speaking, all

ciphers are breakable somehow or other except the so-called one-time

pad cipher, proposed in 1917 by Gilbert Vernam, and proved

mathematically to be perfectly secure by Shannon in 1949.

(5) There are ciphers based on simple substitution, in which several

characters are used for each letter, thus increasing the count of

cipherforms to, perhaps, as many as a hundred. Consequently,

decipherment becomes a very complex and demanding task both to

the sending encipherer, should he need to read his cryptogram some

time later, and the receiving cryptologue, who has knowledge of theencipherment method used and also the key for decipherment. In fact

carrying the cipher complexity to excess would necessarily lead to

delays in deciphering the message a reality that can entail serious,

indeed sometimes disastrous, adverse consequences when the cipher

involves an urgent situation or a critical state of affairs that needs

prompt action, such as war.

This view of the Author of the Two Essays still holds true

nowadays. For all the sophistication and state-of-the-art electronics of

today, excessive complexity in the design of encryption algorithms

has its own drawbacks in implementation and decryption, even though

algorithms are known both to the sender and the recipient. Indeed anydelay may incur the forfeiture of precious opportunities, the loss of

which would cost dear. A case in point is the delay that occurred in

breaking a highly complex cipher transmitted to the U.S.S.Pueblo on

its maiden voyage to collect intelligence for the top-secret Operation

Clickbeetle. The incident ended in the ship being attacked and

captured by North Korean gunships on the high seas in January 1968

well before the completion of its first mission, showing how damaging

the intelligence loss is to national security.40

(6) Ciphering and cryptanalysis played an important role at the

time of the Author. It was practised on a large scale in many state

affairs among such personalities of high status as the king,

leaders, ministers, governors, etc., with each employing a scribe

40See Kahn, D. Kahn On Codes, New York: Macmillan, 1983, pp. 35, 181 & 188.

See also Lerner, Mitchell B. The Pueblo Incident: A Spy Ship and the Failure of

American Foreign Policy, University Press of Kansas, 2003.


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responsible for tasks concerned with cryptography and cryptanalysissomething similar to what is called today black chambers.

(7) The Second Essay concludes with an example of setting up a

cipher that is hard to retrieve and yet easy to read, given that the count

of the cipherforms is no more than 28. The method is based on

misleading the cryptanalyst into thinking that it is a simple-

substitution cipher, while it is really not. The letter () is here assignedthree symbols ( , , ) and the letter () three others ( , , ). Sucha practice is bound to complicate the statistical analysis on tha part of

the cryptanalyst. The four extra cipher symbols (i.e. , , , ) used

for () and () are compensated for by reducing the total count ofcipherforms to 28 through assuming a single symbol to at oncerepresent three letters having the same orthographic pattern such as

,) , ,) and ( ) and (, ), thereby making the count of cleartextletters and ciphertext symbols equal. As a result the seemingly easy

cryptanalysis would prove to be extremely difficult.

A noteworthy feature in the frequency of cipherforms so rendered

is the so-called spectrum flattening of the cipher symbols. A

comparison of the frequency of cipherforms to the original frequency

of letters shows a variation in the order of letters as well as bigrams in

terms of their frequency. The bigram () turns to assume nine (3x3)

possibleforms,namely: , , , , , , , and .The same applies to bigrams consisting of letters having the same

orthographic pattern, namely: , , . Such a variation in theorder of letters and bigrams results in considerable difficulty in

processing for statistical cryptanalysis.

It should be pointed out that ibn Dunayn r in his ExpositiveChapters on Cryptanalysis refers to this method of the Author,

disapproving of his use of a single form to denote orthographically

identical letters. This, ibn Dunayn r argues, is likely to confuse the

legitimate decipherer and create ambiguity in determining which of

the identical letters is meant.41

Although initially sound, ibn

Dunayn rs criticism would prove misplaced, given that the general

context and word order would all but certainly help the astute

legitimate decipherer to remove any possible ambiguity. This view is

particularly substantiated by the fact that the Arabic letters were

originally written undotted. It is not beyond the bounds of possibility,

41See ibn Dunayn rs book (Vol.4 of this series),p. 54 and p. 176.


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therefore, that this fact itself has prompted the Author of the Two

Essays to develop this method of encipherment.

1.3.5. Annex

The Two Essays, whole and complete, have been appended by a

practical follow-up that comes in useful in statistical cryptanalysis. It

covers the letters of the Arabic alphabet classified into three broad

categories as per their frequency of occurrence.

Order of letters Number Letters

Abundant(High Frequency)

7

Common(Medium Frequency)

12

Scarce(Low Frequency)

9

Total 28

By analogy, it is interesting to recall ibn Adl ns classification of

Arabic letters into these three categories.42

Apart from the slight

variation in the order of letters within each category, there is no other

difference between ibn Adl ns classification and that of the Author

of the Two Essays except for the letter (), which belongs under thescarce category according to the formers calculations, and under the

common category according to the latters. However, no significant

effect ensues, as the letter () often occupies a middle positionbetween the two categories.

1.4. Originality of the Author of the Two

Essays

The Author attains the furthest limits of distinction in his precision

of expression and profusion of information. He puts forward important

ground-breaking ideas, unprecedented in other cryptological

42See ibn Adl ns treatise (Vol. 2 of this series),p. 18 and p. 48.


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compilations so far explored. The Two Essays are in many ways

reminiscent of al-Kind s treatise as regards their originality. The

Authors contributions include:

1) The relative spectrum flattening in the frequency of the forms in

the ciphertext, through the utilization of several symbols to represent

one high-frequency letter. Note that the first use ever of this principle

in the West dates from the reign of King Henry IV of France (1589-

1610), that is at least four centuries later than the time of writing the

Two Essays.43

2) Advising against inordinate complexity in cipher construction,

as too much elaboration in encipherment can be dangerous, and mayincur the loss of irrecoverable opportunities owing to delayed

decryption.

3) Drawing attention to the importance of spotting potential errors,

inadvertently incurred by the encipherer, and using them profitably

toward cipher cryptanalysis. Note also that this principle has not been

conveyed by cryptographers in the West until quite recently.

4) Restricting the use of encipherment to serious matters related to

state affairs and military and diplomatic correspondence, cautioning

against using the art for unworthy purposes such as staking,

entertainment or the like.

5) Developing a method of encipherment that seems simple andeasy to solve on the face of it, but actually quite involved.

6) Thorough and perceptive knowledge of cryptanalysis by

statistical analysis of letters.7) A clear distinction between simple and complex ciphers.

8) Highlighting the cryptanalytical experience and expertise

required in cipher design, which contributes to sealing up the gaps, if

any, to ensure a tightly-knit cipher.

9) The Two Essays include many cryptological terms, some of

which are novel coinages; e.g. lucid letters, elaborate ciphers, ciphers

that do not answer (unanswering ciphers), closely-knit ciphers,

cipherforms, letter spotting, etc.

10) Stressing the psychological aspect in cryptanalysis. The Author

says: Then apply yourself to it wholeheartedly, undaunted and

unflinchingly determined to solve it, never letting go of hope. Set your

43See Treatise on Cryptography, A. Lange and E.A. Soudart; Laguna Hills, CA:

Aegean Park Press, 1981,pp. 4-5.


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mind at ease while exerting yourself all out for one day or so.

Otherwise, just relax and refresh your soul. Do not overtax your mind

in pursuit, since it is unlikely to pay in that mood.44

11) The Two Essays have become a source for other later authors

on cryptology to tap, such as ibn Dunayn r and probably ibn Adl n.

44See p. 34.


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Chapter 2

The Edited Two Essays

On Cryptanalysis


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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 theaddition -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'allifn 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 wehave 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 commonlyemployed 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.45

45Translator's explanatory additions are placed between pairs of hyphens: --.


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2.2. Description of the Manuscript

The manuscript of the Two Essays is part of the assemblage of

cryptology, which is estimated to date back to the sixth century of the

Hegira (12th

century AD).46

The Two Essays together occupy eleven

sheets, i.e. the sheets 108/B- 118/B, with the sheet no. 115/B

representing the end of the First Essay and the beginning of the

Second. The following two Exhibits are photocopies of the first sheet

of the First Essay, and the first sheet of the Second Essay (includingthe concluding lines of the First Essay).

46See Volume Two of this series, p. 28 for a full description of the assemblage and

its content. On the other hand, the identification number of the assemblage has

turned out to be 5300, not 5359 as previously stated; we do apologize for this

omission.


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


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


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2.3. The Texts(Arabic Original and English Translation)


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In the name of God

the Compassionate, the Merciful

Sufficient unto me is He

2.3.1. The First Essay

On the Cryptanalysis of

Straightforward Ciphers

[1. Requisite Tools for the Cryptanalyst]

I tell you, may God shepherd your steps, that the first things thecryptanalyst needs are: exercising the utmost degree of patience,

quitting idleness and slackness, scrutinizing the cipherforms from

beginning to end in the interests of readjusting and learning by heart.

Then apply yourself to them wholeheartedly, undaunted and

unflinchingly determined to solve the cipher, never letting go of hope.

Set your mind at ease while exerting your self all out for one day or

so. Otherwise, just relax and refresh your soul. Do not overtax your

mind in pursuit, since it is unlikely to pay in that mood. Reconsider it

later, keen to work it out according to the lights I have set for you and

your mind. If your attempt does not come to fruition, put it off again,

only to re-examine it yet again [later on]. If found anywayunresponsive, you should recognize it is one of the elaborate ciphers I

am to describe in the Second Essay. In this case the cipher is

calculated to be hermetically sealed and unlikely to yield to solution

except haphazardly, possibly as a result of an error on the part of the

cipherer. A cryptologue with cogent argument, sound intuition, and

genuine insight can stand a chance of cracking it in consequence.


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[2. Algorithms Not Based on Statistical Analysis]

The ciphertext should be ten lines at the minimum, because less

than that is nothing if not wearing and literally exacting. Letters, if not

used frequently enough, would turn out futile. First try the simple

algorithms, as the cipher might have been rendered by someone who

thinks that separating the letters of words would make them difficult

to read, such as:

Or by transposition within each word, writing each word in reverse:

=

Or through concealment by letters: operative and inoperative, e.g.

=

Or by inverting the text, with letters broken up:

=

Encipherment may also be accomplished by splitting the letters of

the ciphertext into two lines, and then taking one letter from the first

line, followed by the corresponding one from the other line

alternately, such as:

= {

Or by concealing the letters within words, so that only one letter ofeach word the first, second, third, fourth, or the last is the intended

letter. Example:


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Another method involves selecting for encipherment certain letters

e.g. two, three, four, or five- such as the letters , , , , , , and

leaving the rest intact.

Or by concealment within words, the starting point being the edge

of the page or the first letter of each line in it.

Or by systematically substituting for each letter another; thus

substituting for , for , etc. and vice versa after this fashion.

Then consider the key often used in our days, i.e. ( ).

Encipherment is done by substitution reciprocally only within the

pairs: ( and ), ( and ), ( and ), ( and ) ), and and ); all

other letters of the alphabet remain unaltered. Note that letters can be

written joined or detached. Cryptanalysis is thereby achieved using the

same rule.

Encipherment may be predicated on a special arithmetic

[ADWNA]. You arrange the numbers denoting units from one to nine

using whole [dinars]; under the tens you write fractions of quarters,

and under the hundreds write fractions of halves. Under the thousand

(standing for the letter ) you write fractions of halves and quarters,

and so on. Accordingly, the name , for instance, can be

enciphered thus:

one

dinar

eight

dinars

four

quarters

four

dinars

two

dinars

five

quarters

seven

quarters

three

quarters

one

quarter

Treat all kindred cases likewise, and investigate this category of

algorithms to its full potential.


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[3. Algorithms Based on Statistical Analysis]

You may get along perfectly well using the above algorithms. If so,

you have practically attained your objective; otherwise, you set about

counting the cipherforms meticulously, taking special care of the

forms that are close in shape. Two closely similar forms may be

mistaken for one form, such as: or or the like; for in that case

cryptanalysis would become extremely taxing.

If the count is found to be twenty-eight forms, you decide that each

letter of the alphabet has been assigned a single form, with () deemed

as two individual letters [not as a distinctive letter]. If the count adds

up to twenty-nine forms, then () is included as a distinctive letter,

too. If, however, it amounts to thirty forms, you conclude that a spacer

recurs between words.

Then sort the forms out. The sorting process involves taking up the

first form, computing its frequency of occurrence in the cipher, and

affixing the frequency number to it. Subsequent patterns are handled

alike.

Next, you mull the forms over, and endorse them for good by

marking them each with a point under the number. Seek for a

cipherform of higher frequency than all other forms, making it the

letter () in case the cryptogram is comprised of twenty-nine letters.


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Now write down the letters of the alphabet. Under the letter ( ) set

down the form held to be the letter ( ). Then hunt for an adjacent

element that seems to recur often with it, and approximates it in

number, making this cipher form stand for the letter () and affix it to

the letter (). You can seek for both forms together and consecutively

to develop the definite article () in one place.

If the cipher uses word-spacers [30 different cipher forms], you are

getting along well towards cryptanalysis, given the fact that the spacer

has a higher frequency than both () and (). It might be extracted from

within the cipher by sound intuition. If this proves difficult, try to

assume the last form of the cipher to be the space, and estimate the

context accordingly. Otherwise take up the first form and check up on

it, since it is possible to start a cipher with a spacer as a method of

further deception.

Now that the space comes out right with both () and (), lookbetween two spaces for a light word such as: , , , , , ,

,

, , , , , or the like, on the basis of what goes before and after,

which you should adopt and build upon. With such words laid clear,

cryptanalysing the rest would be plain sailing, particulary if you take

advantage of any possible words some encipherers deliberately leave

plain, and which you can use as a vehicle for the intended goal, God

willing.


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In case the cipher turns out to have been rendered without spaces,

seek beside ( ) a form which you can fairly guess as the letter ( )and so read the name of God (

). Now consider preceding and

following forms already known, and guess at such typical expressions

as: , , , , , or the like as dictated by the context. Indeed it is an agreed fact among encipherers

that once the letters () and () come out right, they are all but sure topoint to the rest, provided the cryptologue is endowed with patience. I

would call on you to bear with me while I give you an illustrative

example, so as to lend a helping hand to you and support to my own

argument, with the good assistance of God.

[4. Practical Example: Cryptanalysing a Ciphertext]47

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

47The cryptogram has suffered some errors, omissions and additions in the original

manuscript. These, however, have been set right in light of the plaintext that

follows shortly, and by making use of the cipherforms of the original as shown in

the scribes handwriting.


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For cryptanalysis, you set out to approach the cipher using all the

afore-mentioned simple methods. Or then you carefully compute its

component cipherforms in line with that I have already shown you.

Having found that their count adds up to thirty forms, you sort them

out, indicating the occurrence frequency of each cipher element apart

as follows48

:

Examing them closely in conformity with the rules I have

explained to you, you will find this form ( ) has higher frequencythan others; it recurs 64 times, and is therefore held to be the space.

You further support your belief sensibly by observing possible word

limits according to what I have previously stated.

Now you seek another form that occurs at the next higher

frequency than other letters. No other than () presents itself; it recurs30 times, and is consequently judged to be the letter ().

Then you look for a neighbouring and equally recurring form, to

find this () and to establish accordingly that it stands for theplaintext letter (). Set it down in place under the letters of thealphabet:

48The cipher elements in fact exceed 30 in number, as some of them are repeated. In

addition, they are not sorted out, nor are their frequencies indicated. However,

they will soon be stated properly under their respective letters of the alphabet

after cryptanalysis.


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Subsequently hunt for two spaces enclosing the letters ( ), plusanother letter yet unknown. At first glance you recognize this: ,

the unknown form being . Considering preceding forms so far

unfolded, you spot an (), an unknown letter, followed by () and ()respectively, thus: . You readily come to realize that this

unknown letter is (), and the first unknown is reasoned to be [theletter ], so that you read the statement:

. Your

discerning choice is fixed on the letter () in the word () ratherthan the letter ( ) (making ) because ( ) has already been workedout in the word (

). Thus you can now designate the letters

in their proper locations.In another location you come across two spacers with two forms in

between ( ), one of which is still covert. But owing to its highoccurrence frequency in the sort-out, you hold it to be the letter ().

In yet another location you find this: , of which two

letters are known and another unknown. Guided by the context, you

read it ( ).

Elsewhere you pick out this pattern: , followed by this:

, of which the letters () and ( ) have previously beendisclosed with the letter ( ) also uncovered already. On the spot it

comes home to you that it is the word ( ). So you designate theforms drawn.

49Then you observe these forms: , of

which the letters , , and have been made clear by now.Later you spot this: , which is known, and you read it:

.

This is followed by four known forms, namely , making

the word ( ).

49i.e. of the newly emerging letters: , , , and .


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You keep on in the same vein outright, reflecting on the

cipherforms and appropriately affixing them to their respective letters

of the alphabet, until they are exhausted. Thereupon you get the

following arrangement of the letters and their cipher counterparts50

:

Thereby you can read the plaintext, fully developed. The space is 51

:

52

53

54

50Note that the two letters and have not been used in the cipher.

51The space symbol could have been better placed at the end of the arrangement.

52So written in the original as well as in the ciphertext; it is typically written

.

53Just so written in the ciphertext, instead of.

54The square-bracketed statement has somehow been dropped from the original

here, and redressed from the ciphertext.


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2.3.2. The Second Essay

On the Cryptanalysis of

Elaborate and Demanding Ciphers

These include: [1] the difficult ciphers that are only responsive to

cryptanalysis by deep insight and common sense, [2] those [composite]

ciphers that mislead the cryptanalyst as to solution while in fact they

are still far from it, [3] ciphers that are hard to cryptanalyse although

they apparently seem straightforward, and [4] the ciphers that areinherently unresponsive to cryptanalysis even by dedicated

professionals who might well, if at all, manage on mature reflection.

[1. Algorithms for Cryptanalysing Elaborate Ciphers]

I have already considered the straightforward ciphers, and wearied

you with cryptanalysing the tough ones. I have also guided you to the

special snags and hitches thereof. Be sure to make that your standard

paradigm, and to take it as a basis of your knowledge and a prop to

your intellect. Never neglect or despise the art in the mistaken belief

that it is too easy for you to grasp, nor are you required to delve toofar into the depths of what remains unknown to you of this science.

Now that you got to grips with the better part of the foundations for

cryptanalysis, all that remains are bits and pieces not of vital

importance, and details too long to be discussed in a treatise the size

of this, but are bound to be acquired through abundant first-hand

involvement and enhanced by steady personal experience as time goes

by.

If you are invited to solve a cipher that baffled other peoples

endeavours, consider it first by all the weapons I have already given

you. Retreat into privacy to concentrate and work undisturbed in a

mood of peaceful mind. Make sure of the sort-out and the number ofcipherforms, for that is the backbone of the whole process. Seek for

one of the pillars, namely the letters () and (); extracting either ofthem would facilitate the cryptanalysis of the greater portion of the

enciphered message. Work out the rest by the algorithms already

known to you.


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[3. Cryptanalysis of Ciphers Rendered Using Forms of Close

Frequency]

Should you notice that the count of cipherforms exceeds thirty, and

that they are of close frequency, then you decide for sure that the letter

) also assumes two forms, and that the cryptogram thus has its)

defects and frailties blurred. So look for another technique; do not try

to cryptanalyse the pillars unless they emerge haphazardly upon

reflection. Instead, seek for a form that is higher in frequency than all

others, and make it one of the abundant letters, i.e. , , , and .

Take the pattern of the letter () if it has been assigned two forms. In

case the () assumes more forms than two, it certainly does not belong

to the group of lucid letters. Match it against other forms. The

matching is done such that if you entertain a given form to represent

the letter (), for example, you start right from where you find it and

reflect on it, guided by common sense and sound approximation. Keep

identifying the form, namely the assumed (), in its positions with

identical instances throughout the cipher. If it comes out right, you

have achieved the goal; if not, then you have to retrace your steps

straight from the beginning. Assume the selfsame form to be the letter

(), and manipulate it the way you have manipulated the (). You may

this time fare well; otherwise, make it one or the other of the two

forms representing the letter () and manage it as before. Carry on

patiently until you are done with all the lucid letters.


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[4. Unanswering Ciphers]

If the cipher proves so refractory that employing all these

techniques of cryptanalysis is out of the question, you should

recognize that it is irretrievable except by sheer chance, since it is

hermetically sealed from all sides. On the other hand, strain for tracing

the nulls, now dropping one symbol, now including another. On that

you build, in the hope that it may respond.

Furthermore, not every cipher communicated strictly and

exclusively between two persons is of necessity penetrable by a third

party. A retrievable cipher is typically positively definable and

restricted to specific limits, of which the clues to cryptanalysis areoften predictable. Stopping up these clues makes the cipher impossible

to solve, however great the toil is, particularly if more than one form

are assumed for each letter, thus increasing the number of cipherforms

to, perhaps, a hundred. Such ciphers, of course, would be hard to solve

even for those immediately concerned; cryptanalysis would take quite

a long precious time, and require serene frame of mind. Any delay in

cryptanalysing an intricately forged message of sensitive nature can

entail serious, if not disastrous consequences. Supposing the message

is conveyed to a sovereign by an army commander in wartime

demanding urgent military aid, defeat might be incurred in case of any

delay in fulfilling the need.

Let me now give you a typical example of a cipher the count of

whose forms does not go beyond twenty-eight letters55

.

55i.e. with () excluded.


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To set up a cipher that is the very devil to resolve and yet easy for

you to read, assume for the letter () the letters of a light name such as [, , ] and [ , , ], using them one by one. Do the samefor the letter (). On the other hand, assume a single form to at oncerepresent the letters , and , 56 and the same for and , [and alsofor and ]. The rest of the letters are each assigned one form, and ()is given a distinctive pattern, so that the letters of the alphabet are

represented as follows:

In this way, the letters are rendered thoroughly sealed and

impossible to break, because the encipherer represents the letter ( )once as (), another time as (), and a third time as (). And suchlikefor the letter (). If the letters () and () happen to occur together, youuse the set-up pattern

57that is unresponsive to solution, though

seemingly easy to solve, Deo volente.

End of the Two Essays. Praise belongs to God.

56Since they share the same orthographic pattern.

57i.e. the letters () and () are enciphered each by one of 3 forms; the outcome is 9possible bigrams to encipher ().


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[5. Annex]

Letters of high frequency in rank order of occurrence:

, , , , , ,

Letters of medium frequency in rank order of occurrence:

, , , , , , , , , , ,

Letters of low frequency in rank order of occurrence:

, , , , , , , , and .


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69

The Second Treatise

The Treatise of ibn Wahab al-Katib


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Chapter 1

Analytical Study of

ibn Wahabs Treatise


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1.1. Preliminary

ibn Wahabs treatise does not seem to fall in one single work.

Rather, it appears in the assamblage of cryptology under the title:

From the book: al-Bay n Wattaby n (Eloquence and Elucidation) by

Ab al- usayn 'Is q ibn 'Ibr h m ibn Sulaym n ibn Wahab al-

K tib. Upon further investigation, it turned out that the treatise,

whole and complete, is part of an edited book, also by ibn Wahab,

entitled: al-Burh n f Wu h al-Bay n (Demonstration of Eloquence

Aspects), printed twice: in Baghdad (1967) and in Cairo (1969).However, compared to the book, the assemblage version is found to

be broken and interrupted in two places: just prior to the manuscript

text, and right after it. Therefore, the treatise has been here completed

by making up the insufficiency from al-Burh n.

The Wahabs were household names in the writing profession. It

seems that this profession used to be passed down amongst them from

generation to generation. Moreover, some of them were concerned in

politics and high-powered government affairs, thus enjoying the best

of both worlds. They were known to have been favoured more by the

Abbasids than the Omayyads. To be noted is that the highly esteemedstatus of the Wahabs inspired great Abbasid poets, such as Ab

Tamm m, al-Bu tur and ibn ar-R m , to make panegyrics on

members of the family.

ibn Wahab, the author of this treatise, is estimated to have lived the

greater part of his life during the fourth century of the Hegira (10th

AD).

1.2. Structure of the Treatise

ibn Wahabs treatise can be divided into an introduction and five

sections as follows:

- Letter forms and representations

- Methods of encipherment

- Algorithms of cryptanalysis

- An overview of poetry cryptanalysis

- An encipherment method


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Introduction: Motives for Using Secret Writing

ibn Wahab starts by summing up the motives for utilizing secret

writing in general. He maintains that these are incorporated in the

need to keep certain information confidential for reasons of having

best interest properly safeguarded, so that such information can only

be disclosed to the initiated.

The author distinguishes between two states of such utilization, i.e.

the written state, for which encipherment is the appropriate means;

and the oral (spoken) state, for which signalling gesture is the suitable

medium.

1.2.1. Letter Forms and Representations

Given the constant change of writing styles everywhere according

to the changing conditions of people, the author establishes that the

letters of the Arabic alphabet in use are 29 in number. Hedifferentiates between the two terms of a letter and a letter image.

A letter, to him, is the uttered sound or contrastive sound unit the

so-called phoneme in todays terminology; while the letter image isits written form or grapheme. A grapheme represents any of the

letters of the Arabic alphabet. Indeed ibn Wahabs differentiation is

bound to resolve the mistaken belief, held by latter-day and modern

scholars, of considering () as one single stand-alone letter, makingthe count of letters thirty.

The fact remains that the Arabic alphabet consists of 29 letters, of

which 28 have fixed graphemes, with a distinctive articulation for

each. The 29th

letter, that is the alif, has no independent articulatory

pattern because it is ever neutral (quiescent) and never vocalized

(mobile). What appears to the laity as an alif pattern is in fact

nothing more than a prolonged hamza (). Since it is impossible forthe alif to be enunciated on its own, there was a need to use it alongwith another voiced letter, ideally the letter (), and thus () hasoriginated. Oddly enough, this pattern () has become an independent,free-standing symbol on printers, typewriters and computer

keyboards. It was not until the Arabic Standard ASMO 449 was


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far as meaning is concerned, between reading the Koranic verse

with a clear final () and an () slanted to ( ), or reading with a clear () and with the () slanted to ().

By extension, ibn Wahab addresses the letters that share the same

orthographical patterns, gathering that the 29-letter Arabic alphabet is

basically made up of 18 patterns, since the letters ( , , ) have thesame pattern in common, as do the letters ( , ) and ( , , .), etcThis typical feature has been put to good account by restricting

encipherment exclusively to these 18 letter-patterns, as we shall see in

the following paragraphs.

1.2.2. Methods of Encipherment

ibn Wahab distinguishes between two types of encipherment:

A) Encipherment by Substitution (at-Tar ama), i.e. by substituting

for each letter or its pattern another pattern.

B) Encipherment by Concealment and Transposition (at-Ta miya),

i.e. by concealing letters in names of species and genera, or by

changing their relative positions within the ciphertext

(transposition).

He then elaborates on two methods of the encipherment by

at-tar ama:

1. With each letter assuming the form of another, such as using

the form of the letter () to denote the letter (), and () toindicate ( ), etc. This is a type of encipherment using simplesubstitution observed by al-Kind and his successors, and

exemplified by the Qumm and Bis m encipherment.1

2. With letters assuming devised forms that do not pertain to

letter forms, such as: , ,

1The Qumm encipherment: i.e. employing the Qumm cipher alphabet in letter

substitution according to its key:

See Vol.3 of this series, p.10 ff and pp. 60-62. See also Vol.2, pp. 16-17 and pp.

42-44.


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As for the encipherment by at-ta miya, ibn Wahab identifies threemethods:

1. Encipherment by related conceptions what al-Kind calls theconceptual relationship and diffusion method, using generic or

species names to represent letters.1

2. Encipherment by transposition, through changing the order ofletters within a given cipher. This involves many approaches, of

which the author restricts himself to three, although he points to

a type of composite encipherment that utilizes transposition and

substitution together, making cryptanalysis more and more

difficult. However, ibn Wahab says, this method ofencipherment may be augmented either by letter substitution or

by pattern contrivance, thus intensifying obscurity.2 a

gesture of prime importance on the part of ibn Wahab.

3. Encipherment by letter addition and reduction, through the

inclusion of null letters, as has been stated earlier by al-Kind .3

ibn Wahab refers here to three different cases:

(a) Addition of insignificant nulls; for example: (clear)= (cipher), where a negligible null is added after eachletter. ibn Wahab indicates the possibility of incorporating

tar ama into nulls to obtain composite encipherment.(b) Reduction of letters through assigning common letter

combinations (such as the bigrams: , , , and thelike) single patterns in cipher, creating inconsistency between

the letter count of the ciphertext and that of the plaintext.

Given that such bigrams are normally extremely helpful in

the cryptanalysis process, ciphering them in this way is

bound to add to the difficulty of cryptanalysis, and to make

encipherment even more complicated. Indeed this is another

worthy gesture that is noted to ibn Wahabs credit.

(c) Reduction of letters by giving a single pattern to letters that

share the same orthographic image (e.g. , , ). This impliesthe adoption of the 18 images of the letters, not the 29 lettersproper, and also suggests non-observance of letter dotting.

1See Vol.1, p. 93 and p. 132; Vol.3, pp. 27-28 and p. 76; and Vol.4, p.34 and p.110.

2See p. 100.

3See Vol.1 of this series, p.92 and p.138.

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arabic origins of cryptology vol. 6

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