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Novel Data Encryption Algorithm IJCSI International Journal of Computer Science Issues, Vol. 8, Issue 4, No 2, July 2011 ISSN (Online): 1694-0814 www.IJCSI.org 561 Novel Data Encryption Algorithm Rajat Goel1, Ripu R Sinha2, O.P. Rishi3 1Central University of Rajasthan, Kishangarh, Rajasthan, India 2School of Computer and System Sciences, Jaipur national University Jaipur, Rajasthan, India-302025 3Central University of Rajasthan, Kishangarh, Rajasthan, India IDEA is an iterated block cipher algorithm based on Abstract the Fiestel network. It was designed by Xuejia Lai and James Massey in 1991. Feistel network or Fiestel We always strive to get better algorithms for securing cipher is a symmetric structure used in the construction of block ciphers. It was named after the data. A variety of such algorithms are being used in German cryptographer Horst Feistel. A Feistel cryptography. Manly block and stream ciphers are network is an iterated cipher with an internal function available and one of them is International Data called a r ound function. Iterated block ciphers are Encryption Algorithm (IDEA), which was regarded arguably as one of the best for encryption purposes. A constructed by repeatedly applying the round considerable time has elapsed since its advent and function. The number of rounds varies from algorithm to algorithm. The general setup of each this period has witnessed a wide development in round is almost the same. A key schedule is an process approaches and applications. The number of algorithm that, given the key, calculates the subkeys transactions and exchanges of data has increased for these rounds. A large number of block ciphers use exponentially. Consequently, better and novel attacks on data evolved. Researchers believe that the security the scheme, including the Data Encryption Standard of the algorithm needs to be improved keeping a (DES), IDEA etc. The advantage of Fiestel Cipher is that the operations of encryption and decryption are check on the time and space complexity. Within this very similar or even identical. This reduces the size of research work we are looking for a robust algorithm the code almost by half. The only change required is known as NDEA which can be applied for securing a reversal of the key schedule and inversion of their modern environment applications. values. Hence, the Feistel network model scores over substitution and transposition models as the round Keywords: Novel Data Encryption Algorithm function need not be invertible. A block cipher (NDEA), Data Encryption Standard (DES), encryption algorithm (E) takes plaintext M of a International Data Encryption Algorithm (IDEA), particular length and key K as an input, and outputs a Fiestel Structure corresponding ciphertext of the same length. The decryption algorithm (E−1) takes the cipher text as an input together with the key, and yields the original block of plaintext of the same length such that: 1. Introduction IJCSI International Journal of Computer Science Issues, Vol. 8, Issue 4, No 2, July 2011 ISSN (Online): 1694-0814 www.IJCSI.org 562 Lucifer was the first block cipher developed at IBM in the 1970s. The Data Encryption Standard (DES) appeared in 1976. Fig. 2 The last half round of IDEA 1.1 IDEA 1.1.1 Algorithm • Key size : 128 bits • Plaintext Block size : 64 bits Bruce Schneier [4] provided a f ourteen-step • Rounds: 8.5 algorithm of IDEA. Here are the fourteen steps of a complete round (multiply means multiplication It provides high level security not based on keeping modulo 216 + 1, and add means addition modulo 216): the algorithm a secret, but by keeping the key secret which makes it suitable for use in a wide range of 1. Multiply X1 and the first subkey K1. applications worldwide. It can be economically 2. Add X2 and the second subkey K2. implemented in electronic components (VLSI Chip). 3. Add X3 and the third subkey K3. 4. Multiply X4 and the fourth subkey K4. 5. Bitwise XOR the results of steps 1 and 3. 6. Bitwise XOR the results of steps 2 and 4. 7. Multiply the result of step 5 and the fifth subkey K5. 8. Add the results of steps 6 and 7. 9. Multiply the result of step 8 and the sixth subkey K6. 10. Add the results of steps 7 and 9. 11. Bitwise XOR the results of steps 1 and 9. 12. Bitwise XOR the results of steps 3 and 9. 13. Bitwise XOR the results of steps 2 and 10. 14. Bitwise XOR the results of steps 4 and 10. For every round except the final transformation, a swap occurs, and the input to the next round is: result Fig. 1 First 8 rounds of IDEA of step 11 k result of step 13 k result of step 12 k result of step 14, which becomes X1 k X2 k X3 k X4, Plaintext is divided into four 16-bit sub-blocks: X1, the input for the next round. After round 8, a ninth X2, X3 and X4 (see fig. 1) and identical operations “half round” final transformation occurs: are performed on the four parts in 8 rounds. The 128- bit key is split into eight 16-bit blocks, which become After the eighth round, there is a final output eight subkeys. The first six subkeys are used in round transformation: one, and the remaining two subkeys are used in round two, similarly each round uses six 16-bit sub-keys for (1) Multiply X and the first subkey. 8 rounds while the last half-round uses four, i.e. a 1 (2) Add X and the second subkey. total of 52 keys. First 6 keys are extracted directly 2 (3) Add X and the third subkey. from the main key. Further groups of keys are created 3 (4) Multiply X and the fourth subkey. by rotating the main key left by 25 bits. 4 Finally, the four sub-blocks are reattached to produce The mathematical operations involved in each of the the ciphertext. rounds are: 1.1.2 Decryption Bitwise Exclusive OR (denoted by ). Addition modulo 216 (denoted by ). Decryption algorithm is exactly the same. The Multiplication modulo 216+1 (denoted⊕ by ). ⊞ subkeys are reversed and slightly different. The decryption subkeys are either the additive or ⊙ After the eight rounds there is a half round (as multiplicative inverses of the encryption subkeys. illustrated in fig. 2): Table 1 shows the encryption subkeys and the corresponding decryption subkeys. IJCSI International Journal of Computer Science Issues, Vol. 8, Issue 4, No 2, July 2011 ISSN (Online): 1694-0814 www.IJCSI.org 563 Table 1: IDEA Encryption and Decryption Subkeys After an analysis of IDEA, some viable and feasible changes were made into it and so in this way NDEA Round Encryption Subkeys Decryption Subkeys came into being. (1) (1) (1) (9) - 1 (9) (9) K1 K2 K3 K1 –K2 –K3 2.1 Random Number and the Ordering of the 1st (1) (1) (1) (9) - 1 (8) (8) K4 K5 K6 K4 K5 K6 subkeys: (2) (2) (2) (8) - 1 (8) (8) K1 K2 K3 K1 –K3 –K2 2nd (2) (2) (2) (8) - 1 (7) (7) K4 K5 K6 K4 K5 K6 A random number is generated. The number of keys (3) (3) (3) (7) - 1 (7) (7) required in IDEA is 52, so it is ensured that random K1 K2 K3 K1 –K3 –K2 3rd (3) (3) (3) (7) - 1 (6) (6) K4 K5 K6 K4 K5 K6 number is in the range 1 to 52. The subkey of that (4) (4) (4) (6) - 1 (6) (6) number becomes the first subkey. System date-time K1 K2 K3 K1 –K3 –K2 4th (4) (4) (4) (6) - 1 (5) (5) may also be used to generate the random number as it K4 K5 K6 K4 K5 K6 will always be unique. It acts as a seed for the random (5) (5) (5) (5) - 1 (5) (5) K1 K2 K3 K1 –K3 –K2 function. In the original IDEA, as previously 5th (5) (5) (5) (5) - 1 5(4) (4) K4 K5 K6 K4 K5 K6 mentioned, the key schedule is static but it becomes (6) (6) (6) (4) - 1 (4) (4) dynamic in the NDEA. Hence, the security increases. K1 K2 K3 K1 –K3 –K2 6th (6) (6) (6) (4) - 1 (3) (3) The NDEA Encryption algorithm requires three K4 K5 K6 K4 K5 K6 inputs – Plaintext, Key and a r andom number as (7) (7) (7) (3) - 1 (3) (3) K1 K2 K3 K1 –K3 –K2 7th (7) (7) (7) (3) - 1 (2) (2) against only two in the Original IDEA. So even if an K4 K5 K6 K4 K5 K6 eavesdropper is able to lay his hands on the ciphertext (8) (8) (8) (2) - 1 (2) (2) K1 K2 K3 K1 –K3 –K2 and the key, he cannot obtain the plaintext. To make 8th (8) (8) (8) (2) - 1 (1) (1) K4 K5 K6 K4 K5 K6 it secure further, the random number can be encoded th 8.5 (9) (9) (1) - 1 (1) by a different encryption algorithm say RSA. This K1 K2 K1 –K2 (9) (9) (1) (1) - 1 will add the complexity of the RSA with that of the K3 K4 –K3 K4 IDEA and thus, make cryptanalysis attack even more difficult. S o at the receiving end, the decryption (1) th st Here, K4 denotes the 4 key of the 1 round process requires the following additional steps: The (1) - 1 (1) K4 denotes the multiplicative inverse of K4 key has to be first reshuffled back to the original form (1) (1) –K2 denotes the additive inverse of K2 using the random number and then fed into the decryption algorithm.
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