Abstract
This paper reports on an improvement of Matsui’s linear cryptanalysis that reduces the complexity of an attack with algorithm 2, by taking advantage of the Fast Fourier Transform. Using this improvement, the time complexity decreases from O(2k*2k) to O(k*2k), where k is the number of bits in the keyguess. This improvement is very generic and can be applied against a broad variety of ciphers including SPN and Feistel schemes. In certain (practically meaningful) contexts, it also involves a reduction of the attacks data complexity (which is usually the limiting factor in the linear cryptanalysis of block ciphers). For illustration, the method is applied against the AES candidate Serpent and the speed-up is given for exemplary attacks.
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References
Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)
Matsui, M.: The First Experimental Cryptanalysis of the Data Encryption Standard. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 1–11. Springer, Heidelberg (1994)
Chose, P., Joux, A., Mitton, M.: Fast Correlation Attacks: An Algorithmic Point of View. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 209–221. Springer, Heidelberg (2002)
Lu, Y., Meier, W., Vaudenay, S.: The Conditional Correlation Attack: A Practical Attack on Bluetooth Encryption. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 97–117. Springer, Heidelberg (2005)
Anderson, R., Biham, E., Knudsen, L.: Serpent: A Proposal for the Advanced Encryption Standard. In: The proceedings of the First Advanced Encryption Standard (AES) Conference, Ventura, CA (1998)
Biham, E., Dunkelman, O., Keller, N.: Linear Cryptanalysis of Reduced Round Serpent. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 16–27. Springer, Heidelberg (2002)
Biryukov, A., De Cannière, C., Quisquater, M.: On Multiple Linear Approximations. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 1–22. Springer, Heidelberg (2004)
Collard, B., Standaert, F.-X., Quisquater, J.-J.: Improved and Multiple Linear Cryptanalysis of Reduced Round Serpent. In: The proceedings of InsCrypt (to appear, 2007)
Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)
Davis, P.J.: Circulant Matrices, pp. 176–191. Wiley-Interscience, Chichester (1979)
Kaliski, B.S., Robshaw, M.J.B.: Linear Cryptanalysis using Multiple Approximations. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 26–39. Springer, Heidelberg (1994)
Lai, X., Massey, J.L.: A Proposal for a New Block Encryption Standard. In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 389–404. Springer, Heidelberg (1991)
Wheeler, D.J., Needham, R.M.: TEA, a Tiny Encryption Algorithm. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 363–366. Springer, Heidelberg (1995)
Kumar, S., Paar, C., Pelzl, J., Pfeiffer, G., Schimmler, M.: Breaking Ciphers with COPACOBANA - A Cost-Optimized Parallel Code Breaker. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, Springer, Heidelberg (2006)
Biham, E., Dunkelman, O., Keller, N.: Differential-linear Cryptanalysis of Serpent. In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 9–21. Springer, Heidelberg (2003)
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Collard, B., Standaert, F.X., Quisquater, JJ. (2007). Improving the Time Complexity of Matsui’s Linear Cryptanalysis. In: Nam, KH., Rhee, G. (eds) Information Security and Cryptology - ICISC 2007. ICISC 2007. Lecture Notes in Computer Science, vol 4817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76788-6_7
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DOI: https://doi.org/10.1007/978-3-540-76788-6_7
Publisher Name: Springer, Berlin, Heidelberg
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