MODIFIED RECURSIVE MODULO 2 N AND KEY ROTATION TECHNIQUE (MRMKRT) Rajdeep Chakraborty* 1, Avishek Datta 2, J.K. Mandal 3

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1 ISSN IJESR/Feb 2015/ Vol-5/Issue-2/76-81 Rajdeep Chakraborty et. al./ International Journal of Engineering & Science Research MODIFIED RECURSIVE MODULO 2 N AND KEY ROTATION TECHNIQUE (MRMKRT) Rajdeep Chakraborty* 1, Avishek Datta 2, J.K. Mandal 3 1 Asst. Prof, Dept. of Computer Science and Engineering, Netaji Subhash Engineering College, Techno City, Kolkata, West Bengal, India. 2 Final Year Student, Dept. of Computer Science and Engineering, Netaji Subhash Engineering College, Techno City, Kolkata, West Bengal, India. 3 Prof, Dept. of Computer Science and Engineering, Netaji Subhash Engineering College, Techno City, Kolkata, ABSTRACT West Bengal, India. This research deals with a vital and important issue in computer world. This research has led to the working model of a new Cryptosystem based on Recursive Modulo Addition and Key Rotation Techniques. In today s world, protection of data in transit has become of prime importance. This algorithm is a Symmetric Cipher Cryptosystem with secure key exchange system. Currently, this model takes input from a file and gives the output to a file. This cryptosystem has its advantages and disadvantages. The main objective of this research is to bring to the world a new cryptosystem that can be used in to secure data in future using little computer and memory resources. Keywords: Cryptography, Data Protection, Modified Recursive Modulo 2 N and Key Rotation Technique, Microprocessor. 1. INTRODUCTION The use and importance of Computers in our lives can never be fully expressed in words, especially during our present time. It has become an important element in each type of industry and even in a developing country such as India. Nowadays each and every industry is heavily dependent on Computers and different Computer Systems. Computer is considered a time saving device and its progress helps in generating quicker, newer and accurate results; that too in a short time without the wastage of much resources. The increased amount of computers today has led to a continuous transaction of humungous amount of data around the globe. Due to this increasing dependence on computers for sharing data, it has become imperative to secure the data that is being shared or transferred between two systems. There are a lot of security measures adopted in a particular machine to secure the data on the machine. However, the need of similar protection, if not more, is important when the data is in transit from one station to another. This is where the use of Cryptography comes in. Cryptography is the practice and study of techniques for secure communication in the presence of third parties [1]. The aim of cryptography is to produce an algorithm to secure communication where any unwanted third party would not be able to read the transmission. 2. BRIEF DESCRIPTION In this research, a novel block cipher based on a microprocessor system has been proposed where the encryption and decryption is done through Modified Recursive Modulo 2 N and Key Rotation Technique (MRMKRT) [2]. The original message is considered as a stream of bits, which is then divided into blocks, each containing n bits, where n is any of 2, 4, 8, 16, 32, 64, 128, 256. The two adjacent blocks are then added where the modulus of addition is 2 N. The result replaces the second block, the first block remaining unchanged. The modulo addition has been implemented in a very simple manner where the MSB is discarded to get the result. After addition, one *Corresponding Author 76

2 bit left circular rotation to each block is applied. The next step involves a one bit left circular rotation of the entire stream. The technique is applied in a cascaded manner by varying the block size from 2 to 256. For this implementation the stream size of 256 bits has been taken but the scheme may be implemented for larger sizes also. The input stream, S, is first broken into a number of blocks, each containing n bits (n = 2 k : k = 1, 2, ) so that S = B 1 B 2 B 3...B m, where m = 512 / n. Starting from the MSB, the blocks are paired as (B 1 B 2 ), (B 3 B 4 ), and so on. The MRMKRT operation with modulo addition is then applied to each pair of blocks, the result replaces the second block keeping the first block intact. After addition one bit left circular addition is applied. The process is repeated, each time increasing the block size till n = 256. The proposed scheme has been implemented by using the reverse technique, i.e. modulo subtraction technique, for decryption. 3. ALGORITHM OF MRMKRT The algorithm of MRMKRT is based on bit level encryption scheme [3]. A plain-text is taken for encryption in the sender side and a cipher-text is taken for decryption from the receiver side. It is a bit level cipher. Hence, the encryption plaintext is first broken down into blocks of bits. Let B 1 = {a 0, a 1, a 2,...,a n-1 }, B 2 = {b 0, b 1, b 2,...,b n-1 },..., B m = {...}, so here each block is n-bits in size and the number of blocks is m then MRMKRT is performed which is again combined, C 1 C 2 C 3... C m, here block B 1 is converted to C 1 after MRMKRT encryption, B 2 into C 2, B 3 into C 3 and so on till B m becomes C m to form the cipher-text. During decryption, the cipher-text is broken down into blocks of bits. Let C 1 = {a 0, a 1, a 2,..., a n-1 ), C 2 = {b 0, b 1,...,b n-1 ),..., C m = {...}. Hence, here each block is n-bits in size and number of blocks are m. So, MRMKRT decryption is performed which is again combined B 1 B 2 B 3... B m. Block B 1 becomes C 1 after decryption and so on till block C m to form the plain-text. Figure 1 shows the basic flow of the algorithm. Fig 1: Algorithm for Modified Recursive Modulo 2 N and Key Rotation Technique 3.1 Rounds of MRMKRT Operation Figure 1 gives the block diagram for the algorithm of MRMKRT. The MRMKRT is defined with n-bit plaintext which is to be encrypted, k blocks with n/k bits per block. It has three main rounds/steps as follows: 1. Round 1: At first n-bit plain-text has been broken into k number of blocks and each block has n/k bits as given in Figure 1. Let the blocks be B 1, B 2, B 3,..., B k ; the following operations are performed starting from the most significant bits towards the least significant bits. 2. Round 2: In each pair of blocks, the first number of the pair, say Block B 1, is added to the second number, say Block B 2, where the modulus of addition is 2 N for the size N. Therefore, for 2-bit blocks, the size will be Round 3: One bit Left Circular Rotation is applied to each block. 4. Round 4: The whole n-bit text is left circular shifted/rotated by 1 bit position. Copyright 2013 Published by IJESR. All rights reserved 77

3 These rounds are repeated for a finite number of times and number of iterations will form a part of the session key (as discussed later) which is to be given by the user. During decryption, the reverse operation, i.e. modulo subtraction is performed instead of modulo addition starting from the LSB and decreasing the block size from maximum to 2. It also has three main rounds/steps as follows: 1. Round 1: At first whole n-bit cipher-text is right circular shifted/rotated by one position as shown in Figure Round 2: The n-bit cipher-text is broken into 256 bits. 3. Round 3: One bit Right Circular Rotation is applied to each block. 4. Round 4: The two adjacent blocks, say B 1 and B 2 are modulo subtracted instead of added. 3.2 Example As discussed in Section 3.1, MRMKRT encrypts n-bits of plain-text with k blocks with n/k bits per block. In this section, 32-bit plain-text is considered as an example of MRMKRT; the whole encryption and decryption is performed by the following four iterations: 1. Round 1 : In first round, 16 blocks are taken for encryption/decryption, therefore the block size is (32/16 =) 2 bits per block. 2. Round 2: In first round, 8 blocks are taken for encryption/decryption, therefore the block size is (32/8 =) 4 bits per block. 3. Round 3: In first round, 4 blocks are taken for encryption/decryption, therefore the block size is (32/4 =) 8 bits per block. 4. Round 4: In first round, 2 blocks are taken for encryption/decryption, therefore the block size is (32/2 =) 16 bits per block. Let us consider a stream of 32 bits, say S = The whole process of MRMKRT is described as follows: Round 1: Block Size = 2; Number of Blocks = B 9 B 10 B 11 B 12 B 13 B 14 B 15 B B 9 B 10 B 11 B 12 B 13 B 14 B 15 B B 9 B 10 B 11 B 12 B 13 B 14 B 15 B Step 4: Left Circular Rotation of entire Stream Intermediate Output (X)* *The Intermediate Output Stream X will be the input for the next round. Fig 2: Round 1 of MRMKRT Encryption Copyright 2013 Published by IJESR. All rights reserved 78

4 Round 2: Block Size = 4; Number of Blocks = Step 4: Left Circular Shift of the entire Stream Intermediate Output (X)* *The Intermediate Output Stream X will be the input for the next round. Round 3: Block Size = 8; Number of Blocks = 4 Fig 3: Round 2 of MRMKRT Encryption B 1 B 2 B 3 B B 1 B 2 B 3 B B 1 B 2 B 3 B Step 4: Left Circular Shift of the entire Stream Intermediate Output (X)* *The Intermediate Output Stream X will be the input for the next round. Round 4: Block Size = 16; Number of Blocks = 2 Fig 4: Round 3 of MRMKRT Encryption B 1 B B 1 B Step 4: Left Circular Shift of the entire Stream B 1 B Intermediate Output (X)* *This is the final result of the encryption operation since there cannot be any more division Fig 5: Round 4 of MRMKRT Encryption Copyright 2013 Published by IJESR. All rights reserved 79

5 4. KEY GENERATION The key is in the form of a 128 bit binary key which is formed from the number of times the data has been iterated to encrypt the certain data. Since this is a Symmetric Cipher Algorithm, only one key, i.e. Private Key is generated which is shared with the receiver of the data [4]. The data exchange can be made secure with other encryption algorithms like RSA or SHA-1 [5]. This would ensure the security of the data as well as the key which is very important for the decryption process. 5. TEST RESULTS Encryption Time of MRMKRT vs. Encryption Time of RSA (in seconds) Decryption Time of MRMKRT vs. Decryption Time of RSA (in seconds) Chi-Square Value of MRMKRT vs. Chi-Square Value of RSA [6] Copyright 2013 Published by IJESR. All rights reserved 80

6 REFERENCES [1] is the practice of techniques for secure communication in the presence of third parties. [2] Best RM. Software Piracy with Crypto-Microprocessors. [3] Elbirt AJ. An Instructor Level Distributed Processor for Symmetric Key Cryptography. [4] Delfs H, Knebl H. Symmetric Key Encryption. [5] Eastlake D, Jones P. US Secure Hash Algorithm. [6] Chi Square Test, from Wikipedia.org. Copyright 2013 Published by IJESR. All rights reserved 81