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International Journal of Computational Intelligence and Information Security, March 2012 Vol. 3, No. 3
Block Based Cryptographic Protocol Depending on G.C.D. for Secured Transmission
Tamisra Kundu1 , Sananda Bhattacharyya2 , Prof (Dr) Pranam Paul3 1 Student, M. Tech. (CSE), Narula Institute of Technology, Agarpara, West Bengal, INDIA tamisrakundu@gmail.com 2 Student, M. Tech. (CSE), Narula Institute of Technology, Agarpara, West Bengal, INDIA sanandabhattacharyya@gmail.com 3 HOD Computer Applic

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International Journal of Computational Intelligence and Information Security, March 2012 Vol. 3, No. 332
Block Based Cryptographic Protocol Depending on G.C.D. for SecuredTransmission
Tamisra Kundu
1
, Sananda Bhattacharyya
2
, Prof (Dr) Pranam Paul
3
1
Student, M. Tech. (CSE), Narula Institute of Technology, Agarpara, West Bengal, INDIAtamisrakundu@gmail.com
2
Student, M. Tech. (CSE), Narula Institute of Technology, Agarpara, West Bengal, INDIAsanandabhattacharyya@gmail.com
3
HOD Computer Application, Narula Institute of Technology, Agarpara, West Bengal,INDIApranam.paul@gmail.com
Abstract
With the growth of internet and network, the need for secure data transmission become more and moreessential and important, as security is a major concern in the internet world. Data likely to be kept hide from allpeople except from the authorized user cannot be sent in plain text. So the plain text should be codified by theprocess of encryption. Each type of data has its own features, therefore different techniques should be used toprotect confidential data from unauthorized access.Here a newly developed encryption technique, named Exponential of 2- XOR-Rail Fence is presented. Thetechnique can be implemented on any kind file as it is implemented in bit-level. The strength of the technique isanalyzed in this synopsis.Using this technique source bit stream is divided, XORed and Rail fenced to get the encrypted text. Thereverse process is applied on the encrypted text to get back the srcinal source bit stream.
Keywords:
Cryptography, Encryption, Decryption, Plain Text, Cipher Text, Network Security
1. Introduction
Cryptography is the science of writing messages in secret code and an ancient art; the first documented useof cryptography in writing dates back to circa 1900 B.C.The new forms of cryptography came soon after the widespread development of computer communications.In data and telecommunications, cryptography is necessary when communicating over any untrusted medium,which includes just about any network, particularly the Internet.Here I introduce a block based encryption technique named,
Exponential of 2- XOR-Rail Fence.
Forencryption a key has to be generated. Key length and bit stream is chosen at random. At first plain text isdecomposed into finite number of blocks having same size of random number. G.C.D. and two divisors arecalculated. Each distinct block is divided by divisors alternatively. New blocks are generated and XOR ed withthe random number. The Rail-Fence technique is applied on each distinct resultant block.In decryption process the encrypted text first divided into segments. Getting desirable information from key,reverse process of encryption has been applied on each segment.
International Journal of Computational Intelligence and Information Security, March 2012 Vol. 3, No. 333
2. Algorithm
In this section, encryption process is discussed in section 2.1.The section 2.2 and 2.3 discussed about thestructure of key and decryption respectively.
2.1 Encryption Process
Step 1: Source file is converted into binary form and the source binary bit stream S is generated.Step 2: A random number say R is generated by the user which is defined in the key.Step 3: The source bit stream S is decomposed into N number of distinct blocks where each block is of equallength of the random number R.Step 4: After decomposition of total source bit stream S, a block having n number of bits (0<n<R) is left asunchanged block, say UB, which kept unchanged during encryption process.Step 5: G.C.D. of total bit stream and number of bits containing in each block, say G, is calculated.Step 6: Now, two numbers represented in power of 2, are taken as divisors, where former one is immediatebefore G and the later one is immediate after G.Step 7: Two flags are taken. The odd flag (=0) represents the divisor less than G and the even flag (=1)represents the divisor greater than G. The flag bit of the starting divisor is defined in key.Step 8: Each distinct block of N is divided by the divisors alternatively starting from the divisor less than G.Step 9: After the division process is completed, new blocks representing each distinct block of N are formed byappending the remainder bits after the respective quotient bits.Step 10: Each new block is XORed with random number R.Step 11: The Rail fence technique is applied on each distinct resultant block.Step 12: Now, the unchanged block UB is appended at the beginning of the output of step 11.Hence theencrypted text is generated.
2.2 Key Structure
Table 2.2.1 shows the structure of the key
Table 2.2.1: Formation of Key
Segment DescriptionMaximum number of bits required(size)1Flag variable (to determine the 1
st
divisorsfor the blocks)12 Random Number mTotal Key size 1 + m
2.3 Decryption Process
Step 1: First n number of bits (calculated remainder of the division of the total stream length by random numberlength) are discarded from the encrypted text and stored in UB as unchanged block.Step 2: Rest of the encrypted text is decomposed into N number of distinct blocks, each block having length
International Journal of Computational Intelligence and Information Security, March 2012 Vol. 3, No. 334equal to R.Step 3: Now deciphering Rail fence technique is applied on each distinct block.Step 4: Each resultant block is XORed with random number R.Step 5: G.C.D. is calculated from total bits of encrypted text and random number R.Step 6: For each distinct block, respective flag is considered and the respective divisor is calculated. The bitsoccupied by the remainder of the division in encryption process are calculated and kept into a variablesay rem which is discarded from each block.Step 7: Rest of the bits of each distinct block are multiplied with the divisor. The remainder bits, rem are nowadded with the result of the multiplication.Step8: This consecutive decrypted distinct block are appended and lastly the content of the unchanged block UB is concatenated at the end of the decrypted text and in this way the srcinal plain text is recovered.
3. Example
To illustrate this algorithm an example has been shown. The algorithm can be operated on a binary stream Swhich acts as the plain text for the example.Let, S is
1101111001011010
3.1 Encryption Process
Let us start with the encryption process first. Random number, say R is taken from user.Let R is
1100
Decompose the binary stream S in finite blocks whose length is equal to R.So here distinct blocks areb1=1101;b2=1110;b3=0101;b4=1010Now we will calculate G.C.D.Here length of each block is 4 and length of the binary stream S is 16. So G.C.D will be 4.So two divisors will be2 (2^1) and 8 (2^3). Now two flags are taken, one is odd flag (=0) represents minimum divisor (i.e. 2) and theother one is the even flag (=1) represents the maximum divisor (i.e. 8). The blocks are divided by these divisorsalternatively.Now, showing the entire division process:-
b1 b2 b3 b4
Dividend=1101 Dividend=1110 Dividend=0101 Dividend=1010Divisor=2(10) Divisor=8(1000) Divisor=2(10) Divisor=8(1000)1101/10 1110/1000 0101/10 1010/1000Quotient=110 Quotient=1 Quotient=010 Quotient=1Remainder=1 Remainder=110 Remainder=1 Remainder=010
International Journal of Computational Intelligence and Information Security, March 2012 Vol. 3, No. 335For each block a new block is generated by appending the remainder with the quotient.Then the new blocks will be:-b1=1101;b2=1110;b3=0101;b4=1010Now, each block is XORed with the random number R we get new set of blocks.
b1 b2 b3 b4
(1101)XOR (1100) (1110) XOR (1100) (0101) XOR (1100) (1010) XOR (1100)=0001 =0010 =1001 =0110Now we will apply the rail-fence technique on the result of the XOR operation.We get:-b1=0001 b2=0100 b3=1001 b4=0110Concatenating all the blocks we get the final encrypted binary stream as :-
0001010010010110
3.2 Decryption Process
Now we will start the decryption process to recover the srcinal text. From the key structure we get thelength of each block (i.e.4).Now decomposing the encrypted stream we get distinct blocks say
c1=0001 c2=0100 c3=1001 c4=0110Now applying deciphering Rail fence technique on each block we get:c1=0001 c2=0010 c3=1001 c4=0110XORed random number R with c1, c2, c3 and c4 accordingly we get:-
c1 c2 c3 c4
(0001) XOR (1100) (0010) XOR (1100) (1001) XOR (1100) (0110) XOR (1100)=1101 =1110 =0101 =1010Now we calculate G.C.D. and the two divisors in same manner described in encryption process. From keystructure we get the flag bit for respective blocks and hence decide the divisor. The bits occupied by theremainder is calculated as-For, c1 dividend = (2^4), divisor = 2^1=2(10) so remainder will be (2^1) - 1=1 bit (1)c2 dividend= (2^4), divisor=2^3=8(1000) so remainder will be (2^3) - 1=3 bit(110)c3 dividend= (2^4), divisor=2^1=2(10) so remainder will be (2^1) - 1=1 bit(1)c4 dividend= (2^4), divisor=2^3=8(1000) so remainder will be (2^3) - 1=3 bit(010)

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