Abstract
In this paper we present a theoretical framework to quantify the information brought by several linear approximations of a block-cipher without putting any restriction on these approximations. We quantify here the entropy of the key given the plaintext-ciphertext pairs statistics which is a much more accurate measure than the ones studied earlier. The techniques which are developed here apply to various ways of performing the linear attack and can also been used to measure the entropy of the key for other statistical attacks. Moreover, we present a realistic attack on the full DES with a time complexity of 248 for 241 pairs what is a big improvement comparing to Matsui’s algorithm 2 (251.9).
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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. LNS, vol. 839, pp. 1–11. Springer, Heidelberg (1994)
Tardy-Corfdir, A., Gilbert, H.: A Known Plaintext Attack of FEAL-4 and FEAL-6. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 172–181. Springer, Heidelberg (1992)
Matsui, M., Yamagishi, A.: A New Method for Known Plaintext Attack of FEAL Cipher. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 81–91. Springer, Heidelberg (1993)
Ohta, K., Aoki, K.: Linear Cryptanalysis of the Fast Data Encipherment Algorithm. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 12–16. Springer, Heidelberg (1994)
Tokita, T., Sorimachi, T., Matsui, M.: Linear Cryptanalysis of LOKI and s2DES. In: Safavi-Naini, R., Pieprzyk, J.P. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 293–303. Springer, Heidelberg (1995)
Murphy, S., Piper, F., Walker, M., Wild, P.: Likelihood Estimation for Block Cipher Keys. Technical report, Information Security Group, University of London, England (1995)
Vaudenay, S.: An Experiment on DES Statistical Cryptanalysis. In: CCS 1996, pp. 139–147. ACM, New York (1996)
Junod, P., Vaudenay, S.: Optimal key ranking procedures in a statistical cryptanalysis. In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 235–246. Springer, Heidelberg (2003)
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)
Biryukov, A., Cannière, C.D., 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: Pei, D., Yung, M., Lin, D., Wu, C. (eds.) Inscrypt 2007. LNCS, vol. 4990, pp. 51–65. Springer, Heidelberg (2008)
Collard, B., Standaert, F.X., Quisquater, J.J.: Experiments on the Multiple Linear Cryptanalysis of Reduced Round Serpent. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 382–397. Springer, Heidelberg (2008)
Hermelin, M., Cho, J.Y., Nyberg, K.: Multidimensional Linear Cryptanalysis of Reduced Round Serpent. In: Mu, Y., Susilo, W., Seberry, J. (eds.) ACISP 2008. LNCS, vol. 5107, pp. 203–215. Springer, Heidelberg (2008)
Junod, P.: On the Complexity of Matsui’s Attack. In: Vaudenay, S., Youssef, A.M. (eds.) SAC 2001. LNCS, vol. 2259, pp. 199–211. Springer, Heidelberg (2001)
Selçuk, A.: On Probability of Success in Linear and Differential Cryptanalysis. J. Cryptol. 21, 131–147 (2008)
Murphy, S.: The Independence of Linear Approximations in Symmetric Cryptology. IEEE Transactions on Information Theory 52, 5510–5518 (2006)
Cover, T., Thomas, J.: Information theory. Wiley series in communications. Wiley, Chichester (1991)
Collard, B., Standaert, F.X., Quisquater, J.J.: Improving the Time Complexity of Matsui’s Linear Cryptanalysis. In: Nam, K.-H., Rhee, G. (eds.) ICISC 2007. LNCS, vol. 4817, pp. 77–88. Springer, Heidelberg (2007)
Richardson, T., Urbanke, R.: Modern coding theory (2008)
Feller, W.: An introduction to probability theory and its applications, 3rd edn., vol. 1. John Wiley and Sons Inc, New York (1968)
Fourquet, R., Loidreau, P., Tavernier, C.: Finding Good Linear Approximations of Block Ciphers and its Application to Cryptanalysis of Reduced Round DES. In: WCC 2009, pp. 501–515 (2009)
Valembois, A.: Détection, Reconnaissance et Décodage des Codes Linéaires Binaires. PhD thesis, Université de Limoges (2000)
Biham, E., Dunkelman, O., Keller, N.: Linear Cryptanalysis of Reduced Round Serpent. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 219–238. Springer, Heidelberg (2002)
Hermelin, M., Cho, J.Y., Nyberg, K.: Multidimensional Extension of Matsui’s Algorithm 2. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 260–276. Springer, Heidelberg (2009)
Gérard, B., Tillich, J.-P.: On Linear Cryptanalysis with Many Linear Approximations (full version). Cryptology ePrint Archive, Report 2009/463 (2009), http://eprint.iacr.org/
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Gérard, B., Tillich, JP. (2009). On Linear Cryptanalysis with Many Linear Approximations. In: Parker, M.G. (eds) Cryptography and Coding. IMACC 2009. Lecture Notes in Computer Science, vol 5921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10868-6_8
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DOI: https://doi.org/10.1007/978-3-642-10868-6_8
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