by AH Al-Omari — ABJAD Arabic-Based Encryption. Ahmad H. Al-Omari. Computer Science Dept., Faculty of Science. Northern Border University, KSA.
7 pages
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(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 9, No. 10, 2018 164 | Page www.ijacsa.thesai.org ABJAD Arabic – Based Encryption Ahmad H. Al – Omari Computer Science Dept., Faculty of Science Northern Border University , KSA Abstract The researcher introduced an enhanced classical Arabic – based encryption technique that is essentially designed for Arab nations. The new algorithm uses the shared key technique where the Keyword system Modulus is employed to add randomness and confusion to the table of alphabets being used. The results proved that the technique is resistant to brute force and cryptanalysis attacks. The time needed to break the algorithm is huge and the possibilit ies of decrypting the cipher text using the language frequency and language characteristics are hard and unfeasible. The technique assumes the existence of a secure channel for the keyword exchange . Keywords Arabic – based cryptography; classical encryption ; Arabic language encryption; shared key; keyword I. I NTRODUCTION Cryptography is an Arab – born science unlike other sciences like mathematics and physics which were translated from their original languag e founders , developed and then enriched by western scientists [ 1 ] . David Khan , who is one of the greatest historians in cryptology, stated that cryptology was born in Arabic world [ 2 ] . This fact was confirmed in some Arabic cryptologic treatises in 1980 which were found Suleymanye library [ 3 ] in addition to the w ork of other scholars who wrote about cryptography and cryptanalysis in the Arab world [ 4 ] , [ 5 ] , [ 6 ] . Data protection mechanisms currently use two main algorithmic approaches, symmetric and asymmetric algorithms. Some examples are the AES and RSA algorithms that have proven their strength and practical use over many years. The development in th e field of quantum computing has brought a serious threat to the current state – of – the – art cryptology systems [ 7 ] . However, some cryptographic asymmetric systems such as RSA with a four – thousand – bit ke y are believed not to resist att acks by large quantum computers whereas cryptographic symmetric systems, such as AES – 256 bits, can resist attacks by large quantum computers. For instance, to break a single AES encryption, an exhaustive search would take steps requiring billions of years with state – of – the – art ultra – massive computing resources [ 8 ] [ 9 ] . Therefore, researchers have started to explore new encryption methods that are safe in classical computers as well as quantum computers. Some algorithms said to be post – quantum cryptography th at remain secure with the assumption that the attacker has a l arge quantum computing power [ 10 ] . A. Research Problem Recently, Arab communities encounter a real n eed for Arabic – Based cryptographic algorithm to be used as a second alternative technique in addition to the available encryption standards in the market. Thus, this research comes to bridge the gap that the Arab communities need. It is worth mentioning th at such encryption algorithm will be used solely in Arab language encryption intercommunication. B. Research Objectives and Limitations Arabic language is spoken by more than 350 million native speakers in 23 countries of the Arab world and is used by more th an 57 countries of the Islamic world. It is also one of the six official languages of the United Nations [ 11 ] [ 12 ] . This research grant supports th e design of Arabic – Based encryption technique that can be used by governments, institutions, public and private sectors or individuals . The research work aims to ac hieve the following objectives: 1) developing an Arabic – b ased encryption technique that is fast, cheap, secure and suitable for Arab communities 2) encouraging Arab researchers to employ modern technology in the service of Arabic language sciences 3) building cryptographic algorithms that use pure Arabic letters The project is restri cted to the follow ing criteria: 1) I t assumes the existence of secure Quantum Key Distribution (QKD) protocol like (BB84, SARG04, E91 or any other secure Key Distribution (KD) protocol) [ 9 ] . 2) I t is designed for Arabic alphan umeric data format. which is derived from the Arabic coding character set standard (ISO – 8859 – 6). 3) I t does not use the Unicode, ASCII, EBCDIC or any other data format or representation. 4) I t is targeted for the Arab language users . 5) T he non – Arabic character se ts are excluded in this phase of the project. 6) I t is limited to text message formats only . II. R ELATED W ORK In his paper, Ibrahim A. Al – Kadit proves that Arabs are the origins of cryptography. The researcher discussed the factors behind the Arab advancement in cryptology like translation, linguistic studies, administrative studies, public literacy and the advanced mathematics. The researcher briefly listed some of the famous Arab scientists who have contributed to cryptology as AL – Khalil , Jabir ibn Hayyan (Geber ) , Thoban al – Masry , Al – Kindi , Ibn Wahshiyya , Mohammad ibn Ahmad ibn Tabataba , This work is sponsored by the Deanship of Scientific Research at Northern Border University, Arar K.S.A .
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(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 9, No. 10, 2018 165 | Page www.ijacsa.thesai.org Adlan, Ibn Dunainair, Ibn ad – Durihimi, Ali ibn Mohammad ibn Aidamur al – Jaldki and Al – Qalqashandi . The researcher proved that the word encryption have developed from Arab s concealment of clear meaning of messages or simply encryption. The Arabic word sifr into European technical terms that mean enc ryption and which cipher [ 13 ] . Yahya Alqahtani, Prakash Kuppuswamy, Sikandhar Shah have proposed a modified version of the Vigenère cipher based on Arabic alphabets. The original Vigenère cipher is a method of encrypting alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword [ 14 ] . The modifi ed version of the Vigenère cipher works by adding a keyword repeatedly into the plaintext. The alphabets consist of 28 characters of Arabic letters , 1 blank character and 10 characters for the numbers . So the total number of the alphabets is 39 characters. The addition is carried out using the system modulo 39. That is to say, if the result is greater than 39, we subtract as many multiples of 39 as needed to bring us into the range (0 . . . 38). The above mentioned researchers claimed that they have a bette r secure algorithm than the original one using the Arabic alphabets and that their work is a milestone in Arabic language secure communication [ 15 ] . Haifaa Abdul – Zahra Atee has proposed a new cryptograp hic algorithm based on Arabic letters. The researcher demonstrated an encryption/ decryption example but she did not provide it with afterwards investigation regardding the strength of the algorithm and did not compare the results with any known classical algorithm [ 5 ] . Mohammed Abdullah Aysan and Prakash Kuppuswamy have adopted the Caesar cipher approach to Arabic lett ers after adding the 28 Arabic alphabet characters in addition to the 10 decimal numerals. Then they proposed generating two keys; the first key is based on a synthetic specific value for each Arabic letter from (0 38 ), whereas the second key is the lo garithmic value of the generated key (X), (log 3 (X)). The researchers have argued that their algorithm is simple, fast and has the advantage of using standard methods. Besides, it consumes less processing time and capacity [ 16 ] . On the other hand, Prakash Kuppuswamy, Yahya Alqahtani have proposed another symmetric encryption technique that is based on Arabic alphabets. Likewise, the initial key is randomly selected and its inverse is calculated. T hen another negative number is selected and its inverse is calculated again before generating the cipher text. The decryption is carried out using the reverse order process. The researchers have argued that their work presents more secure algorithms than b eing used by similar classical encryptions [ 4 ] . None of the related works can be adopted by Arab communities because they are either weak or not well designed. The proposed algorithm in th is work migh t be the outset after adding further enhancements and testing to the algorithm to be strong enough and attack resistance. III. T HE P ROPOSED S OLUTION In this work, we proposed an enhanced classical symmetric encryption algorithm that is based on an old encryptio n technique invented by al – “the Philosopher of the Arab world” [ 3 ] . The technique is similar to the Porta Cipher but with a modern renovation [ 17 ] . The proposed encryption technique is an enhanced version inspired by some techniques as Playfair, al – Kindy, Caeser and Porta ciphers [ 18 ] . Arabic encoding is similar to any other language alphabetic scripts. For instance, the Unicode standard is used for encoding a raw text not as a glyph list. The Unicode Standard specifies an algorithm for the presentation of the text with a bidirectional b ehavior i.e. Arabic and English [ 19 ] . In our project, we do not use the known standards as Unicode, ASCII or EBCDIC data representations but rather we use the Arabic alphanumeric data representation [ 20 ] . Arabic letters have many characteristics. For example, it has 28 characters, it has no upper or lower case characters, it views some of the two – character pairs as a single character and it is read an d written from right to left. Moreover, some shapes of Arabic Letters change depending on the context; some Arabic letters may have up to four shapes depending on the position of the letter in the word, its predecessor and its successor. Arabic Letters als o have an isolated shape, a connected shape, a left – connected sha pe and a right connected shape. TABLE I. F ORMS O F O RDER 0 Weight ABJAD Normal 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11 10 12 11 13 12 14 13 15 14 16 15 17 16 18 17 19 18 20 19 21 20 22 21 23 22 24 23 25 24 26 25 27 26 28 27
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(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 9, No. 10, 2018 166 | Page www.ijacsa.thesai.org Furthermore, Arabic has several diacritics (small vowels) that can be written above or beneath each letter. The use of diacritics is determined by the grammatical state of the word and eventually the meaning of the statement changes accordingly [ 19 ] [ 21 ] . However, in our research, we will not consider diacritics or language grammar. In addition to the normal order of Arabic alphabet (as used in diction [ 22 ] [ 23 ] . The two alphabetical orders are shown Table 1 Forms of order. Th e table 1 (forms of order) is read from right to left . T he first row (serial) shows the alphabet s order , the second row (weight) , represents a given numeric equivalent to each letter , the third row (ABJAD) represent the ABJAD order of the Arabic letters a nd the last row (normal) represents the normal alphabets order . A. The Solution Description The Arabic coding of character set (ISO – 8859 – 6) [ 24 ] is used to create a modified synthetic table composed of 75 characters that represent the standard alphabets, numbers and special characters. Table 2″Modified Arabic (ISO – 8859 – 6)” , represents a matrix M of (5×15) rows and columns. The matrix M (mi,j) contains 75 characters where mi,j represents the ith and jth character of the matrix (M). So (( 1 <= i <= 5 ) and ( 1 <=j< 1 5 )) , as defined in Equation (1). (1) The matrix M(mi,j) is the initial matrix and is reconstructed by distributing its content (characters) according to the keyword characters modulus value. The keywo rd is randomly chosen by the user. Besides, there are no restriction s on the length of the keyword yet it is recommended to be more than 10 characters. The Keyword is used as a shared key between the communicating parties. For the algorithm calculation pur poses, a copy of the keyword with non - redundant characters is used. Then the copied Keyword Length (KL) is calculated as defined in Equation 2. The Keyword Position (KP) in Equation 3 determines the insertion position in the table of alphabets. Nevertheles s, the insertion includes the Keyword with non - redundant characters followed by the rest of the non - contributing characters in the keyword from Table 2. Using the system modulus 75 adds randomness and confusion to the algorithm and hence will make it hard to brute - force attacks. The keyword insertion process is performed by filling the unique characters of the keyword followed b y the rest of Table 2 starting from position . Finally, at the end of the table reconstruction process, a new generated matrix (table) that is called the modified MM(mi,j) is created for the encryption purposes. (2) ( 3) To access the matrix (table), we need two indexes (r,c), the right index (r) and the top index (c) . The right index (Row) has the values (r1,r2,r3,r4,r5) and the top index (Column) has the values . While the ABJAD alphabets are use d to fill in the (r,c) pairs, the two indexes (r,c) are used to point to the matrix MM elements where MM(mi,j) elements are respectively determined by the value of (r,c) (i.e. i=r and j=c ). To determine which character of the ABJAD alphabets is the starti ng character to fill the (r,c) contents, the sum of the (keyword Weights system modulus 28) is used as defined in Equation 4. The resulting value points to the starting character to be inserted in r5. So the next character will be in r4,r3,r2,r1 ,c15,c14,c . (4) Using the keyword system modulus as in Equation (4) assures the randomness in choosing the starting character of the ABJAD alphabets. For each new plaintext character that is going to be encrypted, the ABJAD alphabets will be down - shifted for one character in a circular - round fashion (down - circular - shift). Using the down - circular - shift makes the algorithm more attack - resistant by adding randomness and confusion to the algorithm. The encryption process is performed in two steps. In the first step, the plain text is divided into distinct characters where each individual character is substituted with the corresponding pairs of characters from the row (ri) that is concatenated with column (cj) and which are b oth from MM(mi,j) table. The resulting text is a two - character text (S) as defined in Equation (5). (5) TABLE II. M ODIFIED A RABIC (ISO - 8859 - 6) 0 1 2 3 4 5 6 7 8 9 ! " # $ % & ' ( ) * + , - . / : ; < = > ? @ [ \ ] ^ _ ` { | } ~ In the second step, the resulting two – character pairs (S) are converted back to one character by substituting the corresponding letter from the original Table 2. The intersection of right index (r) and top index (c) determines the letter being substituted as defined in Equation 6. Likewise, the whole encryption pro cess is repeated for each plain text character in the same way until the end of the plain text message. (6) The decryption process works the same as the aforementioned encryption process but in reverse order. B. The Algorithm Steps The whole algorithm is clarified by steps, pseudo code and examples. A detailed explanation is shown with examples in the following section: The encryption algorithm consists of the following phases:
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(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 9, No. 10, 2018 167 | Page www.ijacsa.thesai.org 1) The initialization phase that consists of the following steps: a) Th e keyword sel ection: The keyword selection is the choice of the user and it is recommended t o meet the following properties . i. The Keyword characters should be selected from Table 2 . ii. The Keyword length is recommended to be not less than ten – character long and to contain a mixture of characters. iii. After algorithm calculations, the Keyword characters should be unique (i.e. each character appears only once, sans duplicates). b) The Keyword calculations : The calculations are performed as in Equations 3 and 4: i. The keyword Example: @ sp ii. The keyword summation modulus 7 5 is computed as in Equation 3. Example: KP = 298 mod 75=73, where the keyword starts iii. The keyword summation modulus 2 8 is computed as in Equation 4. Example: KP = 298 mod 28=23, where the ABJAD c) The table reconstruction : The table reconstruction is built as follows: i. The keyword inside the table starts from the position determined by computing the system modulus 75. 298 mod 75=73, where the keyword starts ii. F illing the tables from the rest of the non – contributing characters in the keyword is continued. d) The indexes reconstruction : In this step, the right (r) and top indexes (j) of the table are reconstructed as follows: i. The starting letter of the ABJAD alphabet s is determined to build the right and top indexes. 298 mod 28=23, where the ABJAD alphabets start ii. The ABJAD alphabets are written starting from the last r5 then backward until c1. 2) The encryption phase in which the encryption is performed in two rounds: a) Round – 1 , one to two characters substitution: Each single character from the plaintext is substituted with two – cipher characters from the first reconstructed table. b) Round – 2 , two to one character substitution: The resulted two – cipher characters are substitu ted with one cipher text character from the second reconstructed table. In the abovementioned example, the encryption of the i. In the first round, each plaintext character is substituted with two characters and the resulted text is ii. In the second round, the resulted text is substituted (encrypted) with one ciphertext and the resulted 3) The decryption phase in which the decryption is performed in two rounds: a) Round – 1, one to two ch aracters substitution back: Each single character from the cipher text is converted back to two characters from the first reconstructed table. b) Round – 2, two to one character substitution back: The resulted two – cipher characters are converted back to the ori ginal plain text characters from the second reconstructed table. converted back to its original plaintext characters in two rounds: i. Round – 1, in ach character is converted back to its two – characters equivalent from the second reconstructed table and the result is ii. Round – 2, in the ciphertext e ach two – character pairs was decrypted back to its original plaintext and the resu IV. D ISCUSSION AND A NALYSIS The research encryption algorithm is neither classical nor modern; it is better classified as a hybrid approach for it employs mathematics and is inspired by modern encryptions. The number of the alphabets in Arabic l anguage is more than in English. Thus, the use of 75 characters that are randomly distributed in the modified table MM(mi,j) makes the algorithm better in terms of the attack – resistance than many of the other known modern encryptions. The algorithm analysi s complies with the most common types of attacks like the cryptanalysis and the brute – force attacks. In the brute – force attack, the attacker tries every possible key until an intelligible translation of the ciphertext into plaintext is obtained [ 18 ] . The brute – force attack requires that three items should be known by the attacker: the encryption algorithms, the language of the plaintext and the number of the possible keys that could be generated [ 25 ] .
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(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 9, No. 10, 2018 168 | Page www.ijacsa.thesai.org In our work, to break the key, all the resulted alphabet diagraphs need to be obtained which means that you neeed to choose among the 75 characters minus the keyword length multiplied by the 28 possible c haracters from the ABJAD alphabets. The mathematical combinational formula ( n choose r ; C(n,r) ) is the best formula to describe our results. To make it clear , t his formula is used when the chosen characters do not need to be repeated and the order does not matter [ 26 ] . The formula is also called the Binomial Coeffici ent as defined in equation (7). Example: If we choose a keyword of n – character length, the number of possible generated diagraphs (combinations) to break a single letter is calculated according to the following formula: .. (7) Where D is the result, n is the set of characters to choose from, and r is the chosen character. Example: Suppose the keyword length n=15. = 63 840355228050 240 which is more than 63 quadrillion diagraphs. If we assume a supercomputer that is developed by China’s National University of Defense Technology [ 27 ] and is with 33.86 Peta – flops (33.86 quadrillion operations/second) that has been used to crack th e fifteen – character keyword, then this process will take approximately about years to break the keyword. Year s In the cryptanalysis attack, using the language characteristics to atta ck the ciphertext is unfeasible since the encryption algorithm passes through two rounds of encryptions that are previously explained. Hence t he attacker will not get benefits of language frequency and language characteristics since the relationship betwee n letters will disappear . F or example, the two and three letters that appear together different alphabets in each sub – process. This is also valid for the letters frequency analysi s since it is hard for the crypto analysts to get benefits of letters frequency because each letter will not be enc rypted to the same cipher – text. That is to say, it will be encrypted to a different cipher – text in each sub – process of the algorithm. The encryption proce ss guarantees randomness of the table distribution since the same character will be encrypted differently each time. Thus, hackers are not able to get benefit of having two or three combination letters that usually come together since each letter is encryp ted separately and independently. By nature, the encryption algorithm disseminates and hides the language characteristics and letters frequency. We performed some experiment measures to compare our algorithm speed with the well – known algorithms (AES and DE S). W e used the open source library Crypto++ for C++ programming language on a laptop core i5, 2.5 GHz CPU with operating Windows 7 operating system and w e used six different plaintext data size. The collected performance metrics are the encryption and the decryption time . The encryption speed chart in Table 3 shows that our algorithm speed outperforms the other two – encryption DES and AES algorithms. In the comparison chart (the encryption chart), our algorithm is faster than the DES and the AES in the encr yption process especially when the data size gets larger in size. TABLE III. T HE E NCRYPTION TIME Plaintext Size/KB DES AES Ours 15 3.8 5.07 2.08 30 7.5 17.09 4.2 45 8.5 19.96 5.7 60 8.8 22.91 6.1 75 9.33 29.99 7.4 90 10.7 38.15 8.3 Fig. 1. Encryption Speed . The Encryption and D ecryption speed are shown on Table 3, Table 4, Figure 1 and Figure 2. All the tables and figures show that our algorithm is faster than the DES and AES de cryptions especially wh en the data size grows in size. TABLE IV. T HE D ECRYPTION TIME Plaintext S ize/KB DES AES Ours 15 3.6 4.09 2.2 30 4.4 17.04 4.6 45 8.3 19.85 5.9 60 8.9 22.8 6.5 75 9.4 30.3 7.9 90 10.6 38.4 8.6 0 10 20 30 40 50 15 30 45 60 75 90 Time/Sec Data Size Encryption Speed DES AES Ours
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(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 9, No. 10, 2018 169 | Page www.ijacsa.thesai.org Fig. 2. Decryption Speed . The proof of concept used in this work aims to confirm that Arabic language can accommodate new technologies especially the encryption which is essentially an Arab – born science. The algorithm uses a shared – key classical encryption technique and gets benefi ts of mathematics and the spirit of modern encryptions, the fact that assures the flexibility and adaptability of Arabic language and encourages researchers from the Arab world to pay more attention to Arabic – based encryption techniques. The main contribut ion in this work is designing a new encryption algorithm that is based on the ABJAD – order Arabic alphabets and employ ing the Modified Arabic (ISO – 8859 – 6) to perform the encryption/decryption processes . T he new algorithm is resistant to the brute – force attacks and can relatively perform fast and secure encryption /decryption processes. V. C ONCLUSION A ND F UTURE W ORK Arabic language has special features that could be positively employed for the benefit of developing cryptographic algorithms specially designed to Arab nations. The research shows that Arabic language can be reactivated to generate more Arabic – based cryptographic techniques that could be us ed to serve the Arab community. The results of the research project prove that the presented algorithm is har d to break using brute – force attack; it needs a very long time to obtain the key or to decrypt the message. The Cryptanalysis attack is also very hard to be used since the letter frequency and language characteristics disappear. In the future, the cryptog raphic algorithm could be generalized to be used in any other language and will not be limited to Arabic language. The algorithm can also be expanded to include more characters, symbols from other languages, data types and file formats that could be flexib ly included. Moreover, other enhancements could be added to the algorithm like rounds of substitutions and permutations in addition to a keyword dynamic change in the encryption process. A CKNOWLEDGMENT The authors wish to acknowledge the approval and support of this research study by the grant No SCI – 2017 – 1 – 7 – F – 6891 from the Deanship of Scientific Research at Northern Border University, Arar K.S.A . R EFERENCES [1] Yahya Meer Alam, M. Hassan at – Tayyan Mohamme d Mrayati, al – Kindi’s Treatise on Cryptanalysis.: KFCRIS & KACST, 2003. [2] Monica Borda, Fundamentals in Information Theory and Coding.: Springer, 2011. [3] Ya – Tayyan. (et al) Mu Al – Kindi’s treatise on cryptanalysis. Riy adh: KFCRIS & KACST, c2003. 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