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Arab Contributions in Cryptography, Case Study: Ibn Dunaynir Effort

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Arab Contributions in Cryptography, Case Study: Ibn Dunaynir Effort

Bushra Mohamed Elamin Elnaim Hayder Abood S.Wsmi Al-Lami

Department of Computer Science & Information Department of Computer & Information Sattam bin Abdulaziz University Sattam bin Abdulaziz University Al Sulail, Kingdom of Saudi Arabia Al Sulail, Kingdom of Saudi Arabia [email protected] [email protected]

Abstract- Cryptography paved the way for the development of arguably humanity's greatest achievements yet,

Computers, the Internet and the digital world. Throughout history the need for secrecy has been important. Governments

and ordinary people have increasingly sought to secure the delivery of certain messages and important information in a

way that allows only the intended recipient access and comprehension. This need for secrecy brought about the invention

and the art of concealment, coding and code making. In return, the need for intelligence and information lead to the

development of code breaking techniques. These techniques primarily attack a particular weakness that a code or

concealment method may have, rendering the sought after information apparent and comprehensible to the assailant.

This paper presents Arab contributions in cryptography , it discuss Ibn Dunaynir cryptologist who was the first

described an arithmetical cipher, in which cleartext characters are converted into numbers and then some simple

arithmetic operations are performed on them.

I. INTRODUCTION

The Internet, comprised of millions of interconnected computers, allows nearly instantaneous communication and

transfer of information, around the world. People use e-mail to correspond with one another. The World Wide Web

is used for online business, data distribution, marketing, research, learning, and a myriad of other activities.

Cryptography allows people to carry over the confidence found in the physical world to the electronic world, thus

allowing people to do business electronically without worries of deceit and deception. Every day hundreds of

thousands of people interact electronically, whether it is through e-mail, e-commerce, ATM machines, or cellular

phones. The perpetual increase of information transmitted electronically has lead to an increased reliance on

cryptography [1]. Cryptography makes secure web sites and electronic safe transmissions possible. For a web site to

be secure all of the data transmitted between the computers where the data is kept and where it is received must be

encrypted. This allows people to do online banking, online trading, and make online purchases with their credit

cards, without worrying that any of their account information is being compromised. Cryptography is very important

to the continued growth of the Internet and electronic commerce.

Cryptography offers three core areas that protect data from attempt theft, theft or an unauthorized use of data and

possible fraud. Cryptography cover these essential area; authentication, integrity, and confidentiality. [2]

II. LITRUTURE REVIW

1. The Purpose of Cryptography

International Journal of Computer Science and Information Security (IJCSIS), Vol. 15, No. 1, January 2017

261 https://sites.google.com/site/ijcsis/ ISSN 1947-5500

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store

sensitive information or transmit it across insecure networks (like the Internet) so that it cannot be read by anyone

except the intended recipient [3]. While cryptography is the science of securing data, cryptanalysis is the science of

analyzing and breaking secure communication. Classical cryptanalysis involves an interesting combination of

analytical reasoning, application of mathematical tools, pattern finding, patience, determination, and luck.

Cryptology is the term referring to the broad study of secret writing, and encompasses both cryptography and

cryptanalysis. Cryptanalysts are also called attackers.

Cryptography can be strong or weak. Cryptographic strength is measured in the time and resources it would require

to recover the plaintext. The result of strong cryptography is cipher text that is very difficult to decipher without

possession of the appropriate decoding tool. How difficult? Given all of today’s computing power and available

time—even a billion computers doing a billion checks a second—it is not possible to decipher the result of strong

cryptography before the end of the universe.

Within the context of any application-to-application communication, there are some specific security requirements,

including [4]:

• Authentication: The process of proving one's identity. (The primary forms of host-to-host authentication on

the Internet today are name based or address-based, both of which are notoriously weak.)

• Privacy/confidentiality: Ensuring that no one can read the message except the intended receiver.

• Integrity: Assuring the receiver that the received message has not been altered in any way from the original.

• Non-repudiation: A mechanism to prove that the sender really sent this message.

2. TYPES OF CRYPTOGRAPHIC ALGORITHMS

There are several ways of classifying cryptographic algorithms that will be categorized based on the number of keys

that are employed for encryption and decryption, and further defined by their application and use. The three types of

algorithms are [5]:

• Secret Key Cryptography (SKC): Uses a single key for both encryption and decryption; also

called symmetric encryption. Primarily used for privacy and confidentiality.

• Public Key Cryptography (PKC): Uses one key for encryption and another for decryption; also

called asymmetric encryption. Primarily used for authentication, non-repudiation, and key exchange.

• Hash Functions: Uses a mathematical transformation to irreversibly "encrypt" information, providing a

digital fingerprint. Primarily used for message integrity.

3. The Drawbacks of Cryptography

There are many issues that affect the effective use of information [6]:



• A strongly encrypted, authentic, and digitally signed information can be difficult to access even for a

legitimate user at a crucial time of decision-making. The network or the computer system can be attacked

and rendered non-functional by an intruder.

• High availability, one of the fundamental aspects of information security, cannot be ensured through the

use of cryptography. Other methods are needed to guard against the threats such as denial of service or

complete breakdown of information system.

• Another fundamental need of information security of selective access control also cannot be realized

through the use of cryptography. Administrative controls and procedures are required to be exercised for

the same.

• Cryptography does not guard against the vulnerabilities and threats that emerge from the poor design of

systems, protocols, and procedures. These need to be fixed through proper design and setting up of a

defensive infrastructure.

• Cryptography comes at cost. The cost is in terms of time and money −

o Addition of cryptographic techniques in the information processing leads to delay.

o The use of public key cryptography requires setting up and maintenance of public key

infrastructure requiring the handsome financial budget.

• The security of cryptographic technique is based on the computational difficulty of mathematical

problems. Any breakthrough in solving such mathematical problems or increasing the computing power

can render a cryptographic technique vulnerable.

III. RELATED WORK

There are different studies which focus on the effort of Arab in cryptography:

In [7] research mentioned that recently discovered old manuscripts show that the origins of cryptology, and the Arab

contributions to it, are older and more extensive than previously thought. The word ‘cipher’ in European languages

comes from the Arabic word sifr. The 9th-century Arab scientist al-Kindī is the author of the oldest known book on

cryptology, antedating any other by more than 300 years. This paper highlights the specific contributions of some

Arab cryptologists based on newly discovered documents that include books of al-Kindī, ibn Adlān and ibn ad-

Duraihim. Factors behind the emergence and advancement of Arab cryptology were discussed.

In [8] study, discussed Cryptography and Steganography which were used in Maghreb and mentioned that several

ideas were introduced before 1600 (Arithmetical cryptography based on the factorization of integer and the calculus

“Hissab Al Jommal”, signature and the use of the ideas of cryptography to insure the security of transactions and



inheritance deeds). It gave an overview of some instances of cryptography which had found in Maghreb (from the

11th century to the 17th century.

In [9], this article argues that papermaking supported cryptanalysis's invention; that cryptology—meaning both

cryptography and cryptanalysis—could not be practiced before the sustained production of paper; and that Medieval

Arabic cryptology originated in tandem with algebra. Furthermore, this article posits that the regional Islamicate

postal service, or the barīd, was used to relay Medieval Arabic cryptograms and thereby shaped the substance of

cryptology. These conclusions stem from examining ninth century to fourteenth century Arabic cryptology as a

technology and relating Arabic cryptology to three other technological devices: papermaking in the Middle East,

algebra, and the barīd. Extant documents suggest that cryptology originated in ninth century Baghdad. This is

because no cryptanalytical writings are known to exist before this period, and cryptology requires both cryptography

and cryptanalysis. However, evidence of Medieval Arabic cryptology exists almost exclusively in practitioners'

treatises, not in cryptograms or the working papers of cryptanalysts.

IV. ARAB CYRPTOLOGISTICS

Cryptography has been practiced to conceal messages since antiquity by different civilizations, including the ancient

Egyptian, Chinese, Indian, Mesopotamian, Greek and Roman. But in none of them was there any cryptanalysis, only

cryptography existed [10]. Cryptology, the science of both making ciphers (cryptography) and breaking them

(Cryptanalysis), was born among the Arabs shortly after the rise of the Arab-Islamic Empire [11].

The most important cryptologists [12]:

• Al-KHALIL (718–786)

o Full name: Abu Abd al-Rahman al-Khalil ibn Ahmad ibn Amr ibn Tamman al Farahidi al-Zadi al

Yahmadi.

o His book: Kitab al Mu'amma (Book of Cryptographic Messages) is lost.

o Treats the method of probable word.

• Abu BAKR (?–?)

o Full name: Abu Bakr Ahmad ben Ali ben Whshiyya an-Nabati.

o His book: Kitab shauq al-mustaham fi ma'rifat rumuz al-aqlam from 855 (Book of the Frenzied

Devotee's Desire to Learn About the Riddles of Ancient Scripts) is also lost.

o Several cipher alphabets.

• Al-KINDI (801–873)



o Full name: Abu Yusuf Yaqub ibn Is-haq ibn as Sabbah ibn 'omran ibn Ismail Al-Kindi.

o Book: Risalah fi Istikhraj al Mu'amma (Treatise on Decrypting Cryptographic Messages), ca 850

AD, the oldest existent book on cryptology.

o Introduces frequency analysis—this makes Al-Kindi the prime father of mathematical statistics.

o Treats also transposition ciphers.

• Ibn ADLAN (1187–1268)

o Full name: Afif ad-Din ibn Adlan ibn Hammad ibn Ali al-Mousili an-Nahwi al-Mutarjim.

o Book: Al-Mu'allaf lil-Malik al-Ashraf (Written for King al-Ashraf)—rediscovered in 1987.

o Comprehensive instructions for cryptanalysis.

• Ibn DUNAINIR (1187–1229)

o Full name: Ibrahim ibn Mohammad ibn Dunainir.

o Book: Maqasid al-Fusul al-Mutarjamah an Hall at-Tarjamah (Comprehensive Instructions for

Solving Cryptograms)—rediscovered in 1987.

o Introduces algebraic ciphers (replace letters by numbers, transform them by arithmetic operations).

• Ibn AD-DURAIHIM (1312–1361)

o Full name: Taj ad-Din Ali ibn Muhammad ibn Abdul'aziz ibn ad-Duraihim.

o Book: Miftah al-Kunuz fi Idah al-Marmuz (Key to Uncovering Secret Writings)—rediscovered in

1987.

o Classification of ciphers, frequency analysis for many languages, Trithemius (Vigenère) table,

grille, arithmetic mod n.

• QALQASHANDI (1355–1418)

o Full name: Shihab al-Din abu l-Abbas Ahmad ben Ali ben Ahmad Abd Allah al-Qalqashandi.

o 14 volume encyclopedia Subh al-asha 1412.

o Contains a chapter on cryptology.



V. Discussion

In this paper we were going to discuss the effort of one of famous Arab cryptologist '' Ibn DUNAINIR (1187–1229)

'' and his effort:

1. Ibn Dunaynir's works[13]:

According to his biographies, ibn Dunaynir wrote primarily in the following two fields:

a) Poetry, in which he wrote two books, i.e. his own poetical collection (divan), and al-Kafi fi ilm al-qawafi

(Sufficiency in the science of rhymes), which is still missing.

b) Cryptology, the science in which he excelled and was particularly well-known. as- SafadI [a biographer and

historian, d. AH 764/AD 1363] has mentioned two books on cryptology by ibn Dunaynir, i.e.

The following methods were used by ibn Dunaynir:

1. Encipherment Using the Arithmetic of Decimally-Weighted Numerical Alphabet (ADWNA) Or " hisab al-

gummal" :

Important as it is, this method of encipherment has been overlooked by al-Kindi in his treatise on cryptanalysis,

despite his awareness of hisab al-gummal, and his reference to it elsewhere. The Author of the Two Essays,

however, does refer to it in his First Essay, and ibn Dunaynir seems to have quoted from him particularly the use of

the "quarter" and "half" fractions. "Hisab al-gummal" is an old method of encipherment, well-known to the Arabs at

an early stage of their civilization, and was practiced later in other languages such as Hebrew. ibn Dunaynir

addresses this method in its two divisions, the major and the minor, expanding on its significant applications by

developing highly relevant ways of ciphering that have subsequently been adopted by ibn ad-Durayhim. The

following table (Table 1) shows the letters of the numerical alphabet, with corresponding decimal numerical values

in ADWNA.

Table (1 &2): Numerical Values of Letters

9 8 7 6 5 4 3 2 1 X 1 ا ب ج د ھـ و ز ح ط 10 ي ك ل م ن س ع ف ص 100 ق ر ش ت ث خ ذ ض ظ 1000 غ

ا ب ج د ھـ و ز ح ط9 8 7 6 5 4 3 2 1 ي ك ل م ن س ع ف ص90 80 70 60 50 40 30 20 10 ق ر ش ت ث خ ذ ض ظ

900 800 700 600 500 400 300 200 100 غ 1000



Thus, the numerical cipher of the proper name زيد, for example, can be expressed: 7, 10, and 4; or (in words): seven,

ten, and four. Equally important is that this type of encipherment is simple substitution, with each letter substituted

by a single symbol throughout the cryptogram. Cryptanalysis is accomplished by utilizing the quantitative technique

stated earlier. According to ibn Dunaynir, the concept of composition in the area dependant decimal numerical

alphabet as a "composite" method of encipherment is predicated on making the cryptogram look like a peasant-

farming financial register. The measurement is done through adopting length units in common use at the time, such

as al- garib, alqafiz, and al-asir. The cryptogram is composed by representing the letters as land dimensions,

simulating an outward semblance of buying, selling, or otherwise similar bargains. This, ibn Dunaynir suggests,

tends to boost the concealment of the cipher and renders it even more difficult to cryptanalysis. He says: "If you fail

to do like we have told you as regards giving the cryptogram the semblance of a financial register of expenditure, an

episode about somebody, taking, buying or giving, you would incur a raw and unhappy [state of affairs], over and

above an unmistakable clue to exposing the intended encipherment. Otherwise, this course of action would be quaint

and pretty efficient [14].

2- Encipherment by Communication through Finger-Spelling, Using the Manual Alphabet and ADWNA:

In this type of encipherment ADWNA is instrumental in letter substitution; letters are replaced with numbers

communicated by bending the fingers in specific shapes so as to convey to a recipient the numerical values

corresponding to the respective letters. This kind of esoteric communication is particularly used by those specially

initiated, in the presence of another who is not meant to understand the discourse. Such a "manual alphabet" is an

already well-known Arab signaling method of communication. It can assume many different shapes (see figure 1).

ibn Dunaynir's method is based on representing the intended number by relative finger configurations. Thus he

represents the units and number ten, referring to other numbers by analogy. The following table (Table 3)

demonstrates the Arabic numerical alphabet, with the corresponding values in ADWNA of the individual letters, and

the finger configuration for each; the units being quoted from ibn Dunaynir, the rest from other sources.



Figure (1): Arab signaling method of communication

Table( 3): Finger spelling using ADWNA



3. Encipherment by ADWNA Using Further Numerical Processing:



Though simple substitution in substance, this method of ciphering, which is credited to ibn Dunaynir as its

originator, is extremely important in terms of its content and effect. Its importance stems especially from the fact

that it lends itself to a special numerical processing, through arithmetical operations governed by a set rule, that

makes it assume more complicated forms. This may be represented by the following model (Figure 2).

Figure (2) : Encipherment by Numerical Processing using ADWNA

Numerical processing involves making the representative numbers two, three, four, etc. times as great in value, thus

increasing the difficulty of cryptanalysis. For example, we encipher the phrase فيقي التوالله ول as follows: (Table 4)

Table (4): Enciphering the Phrase الله ولى التوفيق

Cleartext ق ي ف و ت ل ا ي ل و ه ل ل ا1 30 30 5 6 30 10 1 30 400 6 80 10 100 Numerical value in

ADWNA 2 60 60 10 12 60 20 2 60 800 12 160 20 200 Encipherment by

doubling the number (twofold)

Reconversion to ر ك قس يب ض س ب ك س يب ي س س بletters

4 120 120 20 24 120 40 4 120 1600 24 320 40 400 Encipherment by quadrupling the number (fourfold)

Reconversion to ت م شك كد غخ قك د م قك كد ك قك قك دletters

Fully awake to the significance of this method, ibn ad-Durayhim later takes up this method [15] from where ibn

Dunaynir left off, developing it and further expanding on it. He makes the numerical processing take other forms by

breaking up the number into a sum of two or more numbers of various choices, each corresponding to its respective

letter in ADWNA. For instance, enciphering the proper name محمد this way gives: (Table 5,6 &7)

Table (5,6 &7) Enciphering the Name محمد

Plaintext د م ح م40 8 40 4 Numerical value in ADWNA

(10+30) (6+2) (10+30) (3+1) Numerical processing of one choice

Corresponding letters اج لي بو لي



(20+20) (7+1) (20+20) (2+2) Numerical processing of another choice

Corresponding letters بب كك از كك

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

nowadays, this method forms, in principle, the basis of many algorithms in present-day cryptography.

4. Encipherment by Substituting For Letters the Days of the Week and Hours:

In this type of encipherment the cryptogram is "composed" on the seven days of the week, by coining seven words

that cover all the letters of the Arabic alphabet in such a way as to avoid the repetition of any of them. The words are

then associated with the days of the week one apiece, assigning to each letter of the cryptogram a specific hour of

the day. ibn Dunaynir elucidates this method by enciphering the phrase: الحمد as follows (with a slight change, as

most of the seven words in the original Arabic manuscript are illegible): ( Table 8)

Table (8): Enciphering the phrase الحمد

Thursday

Wednesday Tuesday

Monday

SundaySaturdayFriday Days of the week

Coined طاغيك نصفض خزعبل تثذق دور جحظه شمس words

=28 3 4+ 3+ 4+ 5+ 4+ 5+ Number of letters

الحمد = أ+ل+ح+م+د+ل+ل + ھـ

the second hour of Friday =أ

the last hour of Sunday = ل

the second hour of Wednesday=ح

the second hour of Thursday =م

the first hour of Tuesday = د



the last hour of Wednesday =ھـ

Ibn Dunaynir concludes by establishing that "the algorithm of cryptanalysing such ciphers is pursued through the

application of the quantitative expedients, namely by computing the order of letter occurrence frequencies. This type

of encipherment is most conveniently performed by way of a tale."[16]

Practical Examples:



In keeping with the common practice of most writers in this science, ibn Dunaynir works out practical examples to

illustrate his ideas.[17]

He therefore chooses two lines of verse, the first is of his own composition:

زاد الفؤاد تبلبلاً وولوعا قول العذول الا تكون سموعا

in which the letters و , ل , ا are found to be especially frequent. He restricts himself to disposing the letters of the

verse, attaching to each letter its symbol. The following table (Table 9) shows these letters arranged in descending

order according to their frequency of occurrence. Note that all symbols are chosen to be three-letter words ending

with the letter (ر), with the middle letter diacritically marked with the neutral "sukun".

Table (9): The first of ibn Dunaynir's two practical examples

Frequency Symbol Letter ا ظفر 9 ل سفر 8 و شعر 8 ع فجر 3 ب غمر 2 د سعر 2 ت بحر 2 م حجر 1 ن بدر 1 ز شھر 1 ف شقر 1 ق نذر 1 ذ شمر 1 س صفر 1 ك فھر 1 Space ن 7

In the other verse ibn Dunaynir expands on the algorithm of cryptanalysis, which is conducted according to the

following steps:

1. Calculating the number of letters that constitute the verse (34 in this example), to deduce its meter (al-basit in our

case).

2. Based on step 1, inferring that the rhyme is of the overlapping type.

3. Perceiving that the final letter of the verse is the same as that at the end of its first hemistich a phenomenon in

Arabic poetry called at-tasri.

4. Sorting out the letters according to their order of frequency, and thereupon eliciting the name of God الله , utilizing

the repetition of the letter ( ل). Three letters are thus determined, i.e. ل, ا and ھـ

5. Checking the next high-frequency letters (after ا and ل ), holding that they would probably be م and then ي

6. Experimenting with probable words, based on letters so far uncovered.

7. Composing a word-group that carries meaning and meter:



الله يعلم اني ...

8. Carrying on after this pattern, always building on what has already come out, and guessing yet unknown letters in

three- or four-letter words, until the following verse develops:

ة مني تحبكم ل جارح م وك رم بك ي مغ م ان الله يعل

Right from the outset, ibn Dunaynir lists the letters of the verse, together with their respective symbols. In the

following table (Table 10) these letters are re-arranged according to their descending order of frequency.

Table (10): The second of ibn Dunaynir's two practical examples

Frequency Symbol Letter م ملد 6 ل فھد 4 ا سعد 3 ي لبد 3 ك جلد 3 ھـ ورد 2 ن سھد 2 ر زند 2 ب بعد 2 ح مرد 2 ع عبد 1 غ عقد 1 و نجد 1

ج ھند 1 ت غرد 1

VI. Conclusion

Regardless of his drawing upon the works of his predecessors, ibn Dunaynir stands great amidst cryptological

figures. The features of his originality are manifested first and foremost in the following Contributions:

1. The utilization of numbers in substitution encipherment.

2. The employment of several numbers in ciphering each letter by substitution. This method as developed by ibn

Dunaynir (though tackled before him by the Author of the Two Essays, substituting several symbols for a single

letter) underscores his profound cryptographical knowledge, and is known today as the principle of "frequency



reversals". To be noted is that the earliest instances of using this method in Europe date from the reign of King

Henry IV of France, in his correspondence with the Landgrave of Hesse between 1602-1606 [18]. that is four

hundred years after ibn Dunaynir.

3. The demonstration of composite methods of encipherment such as the one implementing transposition and

substitution together [19], which has proved important in today’s block cipher algorithms such as the Data

Encryption Standard (DES) and the more recent Advanced Encryption Standard (AES), both are based on

the principle of encipherment using both methods simultaneously, but carrying it to a higher degree of

Sophistication by means of a binary number system.

4. The abundant use of encipherment by concealment, which he describes as composition on a background or

medium that disguises the actual intent, such as composing on a tale, dream, chessboard, financial register, planets,

etc.

5. The utilization of encipherment devices such as coloured beads, punched board and thread, folded paper, etc.

6. The use of encipherment by signaling, applying the arithmetic of decimally-weighted numerical alphabet

(ADWNA) and the finger-spelling method of communication between two individuals (manual alphabet).

It would finally be just as well to remark that most of ibn Dunayn r'scontributions listed above relate to prose

encipherment. Not that his contribution in poetry is any less worthy, but contributions there are common ground

among fellow authors of similar treatises; hence the difficulty defining clear-cut aspects of ibn Dunaynir's

originality. Suffice it to say that it is to his credit that he could exhaust the subject of encipherment and cryptanalysis

of both prose and poetry at such length that is unique to him among all those who have written on this art.

VII. REFERENCES

[1] RSA LABIROTRIES (2017), why is cryptography important, Available at: https://singapore.emc.com/emc-plus/rsa-labs/standards-initiatives/why-is-cryptography-important.htm, Accessed on 5/1/2017. [2] Industry News (2006), Importance Of Cryptography in Digital World, Available at: https://www.eukhost.com/blog/webhosting/importance-of-cryptography-in-degital-world/, Accessed on: 3/11/2016. [3] Network Associates (1999), An Introduction to Cryptography, Available at: ftp://ftp.pgpi.org/pub/pgp/6.5/docs/english/IntroToCrypto.pdf, Accessed on: 12/9/2016. [4] Gary C. Kessler (2010), An Overview of Cryptography, Available at: https://people.eecs.ku.edu/~saiedian/Teaching/Fa12/710/Lectures/Readings/02-crypto-an-overview.pdf, Accessed on 20/12/2016. [5] Gary C. Kessler (2017), An Overview of Cryptography, Available at: http://www.garykessler.net/library/crypto.html#types, Accessed on: 23/1/2017. [6] Tutorials point (2016), Cryptography Benefits & Drawbacks Available at: https://www.tutorialspoint.com/cryptography/benefits_and_drawbacks.htm, accessed on: 21/12/2016. [7] Ibrahim A. Al-Kadit (1992): ORIGINS OF CRYPTOLOGY: THE ARAB CONTRIBUTIONS, Cryptologia, 97-126. [8] Abdelmalek Azizi and Mostafa Azizi (2011), Instances of Arabic Cryptography in Morocco, Cryptologia, 47-57. [9] Kathryn A.Schwartz, (2014), From Text to Technological Context: Medieval Arabic Cryptology's Relation to Paper, Numbers, and the Post, Cryptologia, 133-146. [10] Kahn, David. 1967. The codebreakers: The story of secret writing. New York, Macmillan. [11] Ibrahim A. Al-Kadit (1992): ORIGINS OF CRYPTOLOGY: THE ARAB CONTRIBUTIONS, Cryptologia, 97-126. [12] Klaus Pommerening (2014), Monoalphabetic Substitutions, Available at: www.staff.unimainz.de/pommeren/Cryptology/Classic/1_Monoalph/EarlyHist.html, Accessed on 30/12/2016. [13] Al-Kadi,Ibrahim A.,(1992),Origin of Cryptology :The Arab Contributions ,Cryptologia,16(2) :pages :97-126.



[14] Mrayati, M., Alam, Y. Meer and at-Tayyan, M. H. Translated by al-Asaad, Said M.( 2005) Series on Arabic Origins of Cryptology, Volume Four: ibn Dunaynir's Book: Expositive Chapters on Cryptanalysis(Maqasid al-Fusul al-Mutargima an Hall at-Targama) page 116,King Faisal Center for Research and Islamic Studies and King Abdulaziz City for Science and Technology , Kingdom of Saudi Arabia. [15] Mrayati, M., Alam, Y. Meer and at-Tayyan, M. H. Translated by al-Asaad, Said M.( 2003) Series on Arabic Origins of Cryptology, Volume Three: ibn ad-Durayhim's Treatise on Cryptanalysispages24,25 and 68,King Faisal Center for Research and Islamic Studies and King Abdulaziz City for Science and Technology , Kingdom of Saudi Arabia. [16] Mrayati, M., Alam, Y. Meer and at-Tayyan, M. H. Translated by al-Asaad, Said M.( 2005) Series on Arabic Origins of Cryptology Volume Four: ibn Dunaynir's Book: Expositive Chapters on Cryptanalysis(Maqasid al-Fusul al-Mutargima an Hall at-Targama) page 128,King Faisal Center for Research and Islamic Studies and King Abdulaziz City for Science and Technology , Kingdom of Saudi Arabia. [17] Mrayati, M., Alam, Y. Meer and at-Tayyan, M. H. Translated by al-Asaad, Said M.( 2003) Series on Arabic Origins of Cryptology Volume Two: ibn Adlan's Treatise al-mu'allaf lil-malik al-'Asraf page 104, King Faisal Center for Research and Islamic Studies and King Abdulaziz City for Science and Technology , Kingdom of Saudi Arabia. [18] Lange, A. and Soudart, E. A( 1981), Treatise on Cryptography ,page 10 , Laguna Hills, CA: Aegean Park Press. [19] Mrayati, M., Alam, Y. Meer and at-Tayyan, M. H. Translated by al-Asaad, Said M.( 2005) Series on Arabic Origins of Cryptology Volume Four: ibn Dunaynir's Book: Expositive Chapters on Cryptanalysis (Maqasid al-Fusul al-Mutargima an Hall at-Targama) Chapters 13 and 14 ,King Faisal Center for Research and Islamic Studies and King Abdulaziz City for Science and Technology , Kingdom of Saudi Arabia.



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