Abstract
In Advanced Encryption Standard (AES), the standard S-Box is conventionally generated by using a particular irreducible polynomial {11B} in GF(28) as the modulus and a particular additive constant polynomial {63} in GF(2), though it can be generated by many other polynomials. In this paper, it has been shown that it is possible to generate secured AES S-Boxes by using some other selected modulus and additive polynomials and also can be generated randomly, using a PRNG like BBS. A comparative study has been made on the randomness of corresponding AES ciphertexts generated, using these S-Boxes, by the NIST Test Suite coded for this paper. It has been found that besides using the standard one, other moduli and additive constants are also able to generate equally or better random ciphertexts; the same is true for random S-Boxes also. As these new types of S-Boxes are user-defined, hence unknown, they are able to prevent linear and differential cryptanalysis. Moreover, they act as additional key-inputs to AES, thus increasing the key-space.
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References
B.A. Foruzan, in Cryptography and network security, Spl. Indian Edn. (Tata McGraw-Hill, New Delhi, 2007)
W. Stallings, Cryptography and Network Security, 6th Impression (Pearson Prentice Hall, New Delhi, 2008)
D.R. Stinson, Cryptography—Theory and Practice. Department of Combinatorics and Optimization, University of Waterloo, Ontario, 2002
R. Church, Tables of irreducible polynomials for the first four prime moduli. Ann. Maths. 36(1), 198–209 (1935). 2nd Series. http://www.jstor.org/stable/1968675. Accessed 26 June 2012
J. Daemen, V. Rijmen, AES Proposal: Rijndael, Version 2 (1999). http://csrc.nist.gov/encrytion/aes. Accessed 15 May 2012
Federal Information Processing Standards Publication (FIPS), Announcing the Advanced Encryption Standard (AES) (2001). http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf. Accessed 15 May 2012
FIPS, PUB 197: the Official AES Standard, 2001-11-26. Retrieved (2010). http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf. Accessed 15 May 2010
National Institute of Standards and Technology (NIST), Technology Administration, U.S. Department of Commerce, A Statistical Test Suite for RNGs and PRNGs for cryptographic applications (2010). http://csrc.nist.gov/publications/nistpubs800/22rec1SP800-22red1.pdf. Accessed 12 Nov 2012
S.J. Kim, K. Umeno, A. Hasegawa, Corrections of the NIST Statistical Test Suite Communication Research Laboratory Inc., Tokyo 2004
K. Kazilauskas, J. Kazilauskas, Key-Dependent S-Box Generation in AES Block Cipher System Informatica (Institute of Maths and Informatics, Vilnius, 2009)
J.K.M.S.U. Zaman, R. Ghosh, A Review Study of NIST Statistical Test Suite: Development of an Indigenous Computer Package. Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, 2011
R. Hosseinkhani, et.al., Using cipher key to generate dynamic S-Box in AES cipher system. Int. J. Comput. Sci. Secur. 6, 19–28 (2012)
R. Paul, S. Saha, J.K.M.S.U. Zaman, S. Das, A. Chakrabarti, R. Ghosh, A simple 1-byte 1-clock RC4 hardware design and its implementation in FPGA coprocessor for secured Ethernet communication, Proceedings of National Workshop on Cryptology, VIT University and CRSI, Vellore, August 6–8, 2012
L. Jingmei et al., One AES S-box to increase complexity and its cryptanalysis. J. Syst. Eng. Electron. 18(2), 427–433 (2007)
S. Das, Generation of AES-like 8-bit random S-Box and comparative study on randomness of corresponding ciphertexts with other 8-bit AES S-Boxes. International Conference on Advanced Computing, N/w and Informatics (ICACNI-13), CIT, Raipur, India, June 2013, ISSN: 1867-5662
J. Cui, L. Huang, H. Zhong, C. Chang, W. Yang, An improved AES S-Box and its performance analysis. Int. J. Innov. Comput. Inf. Control 7(5(A)), ISSN: 1349-4198, May 2011
E.M. Mahmoud, A.A. Hafez, T.A. Elgarf, A. Zekry, Dynamic AES-128 with key-dependent S-Box. Int. J. Eng. Res. Appl. 3(1), 1662–1670 2013, ISSN: 2248-9622
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Das, S., Sadique Uz Zaman, J.K.M. & Ghosh, R. Study of Randomness in AES Ciphertexts Produced by Randomly Generated S-Boxes and S-Boxes with Various Modulus and Additive Constant Polynomials. J. Inst. Eng. India Ser. B 97, 193–208 (2016). https://doi.org/10.1007/s40031-014-0173-1
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DOI: https://doi.org/10.1007/s40031-014-0173-1