Abstract
Differentials with low probability are used in improbable differential cryptanalysis to distinguish a cipher from a random permutation. Due to large diffusion, finding such differentials for actual ciphers remains a challenging task. At Indocrypt 2010, Tezcan proposed a method to derive improbable differential distinguishers from impossible differential ones. In this paper, we discuss the validity of the assumptions made in the computation of the improbable differential probabilities. In particular, we show based on experiments that such improbable differential cryptanalysis can fail. The validity of the improbable differential cryptanalyses on PRESENT and CLEFIA is discussed.
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References
Biham, E., Biryukov, A., Shamir, A.: Cryptanalysis of Skipjack Reduced to 31 Rounds Using Impossible Differentials. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 12–23. Springer, Heidelberg (1999)
Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 2–21. Springer, Heidelberg (1991)
Blondeau, C., Gérard, B.: Links Between Theoretical and Effective Differential Probabilities: Experiments on PRESENT. In: Ecrypt Workshop on Tools for Cryptanalysis (2010)
Blondeau, C., Gérard, B., Tillich, J.-P.: Accurate estimates of the data complexity and success probability for various cryptanalyses. Des. Codes Cryptography 59(1-3), 3–34 (2011)
Blondeau, C., Nyberg, K.: New Links Between Differential and Linear Cryptanalysis. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 388–404. Springer, Heidelberg (2013)
Bogdanov, A., Geng, H., Wang, M., Wen, L., Collard, B.: Zero-Correlation Linear Cryptanalysis with FFT and Improved Attacks on ISO Standards Camellia and CLEFIA. In: SAC (to appear, 2013)
Bogdanov, A.A., Knudsen, L.R., Leander, G., Paar, C., Poschmann, A., Robshaw, M., Seurin, Y., Vikkelsoe, C.: PRESENT: An Ultra-Lightweight Block Cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007)
Bogdanov, A., Rijmen, V.: Zero-Correlation Linear Cryptanalysis of Block Ciphers. IACR Cryptology ePrint Archive, 2011:123 (2011)
Borst, J., Knudsen, L.R., Rijmen, V.: Two Attacks on Reduced IDEA. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 1–13. Springer, Heidelberg (1997)
Cho, J.Y.: Linear Cryptanalysis of Reduced-Round PRESENT. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 302–317. Springer, Heidelberg (2010)
Daemen, J., Rijmen, V.: Probability distributions of correlation and differentials in block ciphers. J. Mathematical Cryptology 1(3), 221–242 (2007)
Knudsen, L.R.: Truncated and Higher Order Differentials. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 196–211. Springer, Heidelberg (1995)
Knudsen, L.R., Rijmen, V.: On the Decorrelated Fast Cipher (DFC) and Its Theory. In: Knudsen, L.R. (ed.) FSE 1999. LNCS, vol. 1636, pp. 81–94. Springer, Heidelberg (1999)
Lai, X., Massey, J.L., Murphy, S.: Markov Ciphers and Differentail Cryptanalysis. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 17–38. Springer, Heidelberg (1991)
Mala, H., Dakhilalian, M., Shakiba, M.: Cryptanalysis of Block Ciphers Using Almost-Impossible Differentials. IACR Cryptology ePrint Archive, 2010:485 (2010)
Mala, H., Dakhilalian, M., Shakiba, M.: Impossible Differential Attacks on 13-Round CLEFIA-128. J. Comput. Sci. Technol. 26(4), 744–750 (2011)
Matsui, M., Tokita, T.: Cryptanalysis of a Reduced Version of the Block Cipher E2 (1999)
Reichardt, B., Wagner, D.: Markov Truncated Differential Cryptanalysis of Skipjack. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 110–128. Springer, Heidelberg (2003)
Shirai, T., Shibutani, K., Akishita, T., Moriai, S., Iwata, T.: The 128-Bit Blockcipher CLEFIA (Extended Abstract). In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 181–195. Springer, Heidelberg (2007)
Tang, X., Sun, B., Li, R., Li, C.: Impossible differential cryptanalysis of 13-round CLEFIA-128. Journal of Systems and Software 84(7), 1191–1196 (2011)
Tezcan, C.: The Improbable Differential Attack: Cryptanalysis of Reduced Round CLEFIA. In: Gong, G., Gupta, K.C. (eds.) INDOCRYPT 2010. LNCS, vol. 6498, pp. 197–209. Springer, Heidelberg (2010)
Tezcan, C.: Improbable Differential Attack on PRESENT using Undisturbed Bits. In: International Conference on Applied and Computational Mathematics, Page Book of Abstracts, 2012, Ankara, Turkey, (October 3, 2012), http://cihangir.forgottenlance.com/papers/ICACM_Extended_Abstract.pdf
Tezcan, C.: Improbable differential attacks on PRESENT using undisturded bits. Journal of Computational and Applied Mathematics (in press, 2013)
Tsunoo, Y., Tsujihara, E., Shigeri, M., Saito, T., Suzaki, T., Kubo, H.: Impossible Differential Cryptanalysis of CLEFIA. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 398–411. Springer, Heidelberg (2008)
Yuan, Z., Li, X., Liu, H.: Impossible Differential-Linear Cryptanalysis of Full-Round CLEFIA-128. IACR Cryptology ePrint Archive, 2013:301 (2013)
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Blondeau, C. (2013). Improbable Differential from Impossible Differential: On the Validity of the Model. In: Paul, G., Vaudenay, S. (eds) Progress in Cryptology – INDOCRYPT 2013. INDOCRYPT 2013. Lecture Notes in Computer Science, vol 8250. Springer, Cham. https://doi.org/10.1007/978-3-319-03515-4_10
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DOI: https://doi.org/10.1007/978-3-319-03515-4_10
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