Evolutionary Design of Resilient Substitution Boxes: From Coding to Hardware Implementation
S-boxes constitute a cornerstone component in symmetric-key cryptographic algorithms, such as DES and AES encryption systems. In block ciphers, they are typically used to obscure the relationship between the plaintext and the ciphertext. Non-linear and non-correlated S-boxes are the most secure against linear and differential cryptanalysis. In this paper, we focus on a two-fold objective: first, we evolve regular an S-box with high non-linearity and low auto-correlation properties using evolutionary computation; then automatically generate evolvable hardware for the obtained S-box. Targeting the former, we use the Nash equilibrium-based multi-objective evolutionary algorithm to optimise regularity, non-linearity and auto- correlation, which constitute the three main desired properties in resilient S-boxes. Pursuing the latter, we exploit genetic programming to automatically generate the evolvable hardware designs of substitution boxes that minimise hardware space, encryption/decryption time and dissipated power, which form the three main hardware characteristics. We compare our results against existing and well-known designs, which were produced by using conventional methods as well as through evolution.
KeywordsNash Equilibrium Crossover Operator Hardware Implementation Block Cipher Evolutionary Design
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- 2.Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. In: Menezes, A.J., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 2–21. Springer, Heidelberg (1991)Google Scholar
- 4.Dorigo, M., Maniezzo, M.: Parallel Genetic Algorithms: Introduction and Overview of Current Research. In: Stender, J. (ed.) Parallel Genetic Algorithms, IOS Press, Amsterdam (1993)Google Scholar
- 6.Kwan, M.: Reducing the gate count of bitslice DES (2000), http://eprint.iacr.org/
- 7.Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)Google Scholar
- 8.Menezes, A.J., Van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton, USA (1996)Google Scholar
- 9.Millan, W., Burnett, L., Cater, G., Clark, J.A., Dawson, E.: Evolutionary Heuristics for Finding Cryptographically Strong S-Boxes. In: Varadharajan, V., Mu, Y. (eds.) Information and Communication Security. LNCS, vol. 1726, pp. 263–274. Springer, Heidelberg (1999)Google Scholar
- 11.National Institute of Standard and Technology, Data Encryption Standard, Federal Information Processing Standards 46 (November 1977)Google Scholar
- 14.Rhyne, V.T.: Fundamentals of digital systems design. Electrical Engineering Series. Prentice-Hall, Englewood Cliffs (1973)Google Scholar
- 15.Shanon, C.E.: Communication theory of secrecy systems. Bell Sys. Tech. J. 28(4), 656–715 (1949)Google Scholar