Abstract
We show that the so-called super S-box representation of AES – that provides a simplified view of two consecutive AES rounds – can be further simplified. In the untwisted representation of AES presented here, two consecutive AES rounds are viewed as the composition of a non-linear transformation S and an affine transformation R that respectively operate on the four 32-bit columns and on the four 32-bit rows of their 128-bit input. To illustrate that this representation can be helpful for analysing the resistance of AES-like ciphers or AES-based hash functions against some structural attacks, we present some improvements of the known-key distinguisher for the 7-round variant of AES presented by Knudsen and Rijmen at ASIACRYPT 2007. We first introduce a known-key distinguisher for the 8-round variant of AES which constructs a 264-tuple of (input,output) pairs satisfying a simple integral property. While this new 8-round known-key distinguisher is outperformed for 8 AES rounds by known-key differential distinguishers of time complexity 248 and 244 presented by Gilbert and Peyrin at FSE 2010 and Jean, Naya-Plasencia, and Peyrin at SAC 2013, we show that one can take advantage of its specific features to mount a known-key distinguisher for the 10-round AES with independent subkeys and the full AES-128. The obtained 10-round distinguisher has the same time complexity 264 as the 8-round distinguisher it is derived from, but the highlighted input-output correlation property is more intricate and therefore its impact on the security of the 10-round AES when used as a known key primitive, e.g. in a hash function construction, is questionable. The new known-key distinguishers do not affect at all the security of AES when used as a keyed primitive, for instance for encryption or message authentication purposes.
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References
Aumasson, J.-P., Meier, W.: Zero-sum distinguishers for reduced Keccak-f and for the core functions of Luffa and Hamsi, Comment on the NIST SHA-3 Hash Competition (2009)
Barkan, E., Biham, E.: In How Many Ways Can You Write Rijndael? In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 160–175. Springer, Heidelberg (2002)
Biryukov, A., De Cannière, C., Braeken, A., Preneel, B.: A Toolbox for Cryptanalysis: Linear and Affine Equivalence Algorithms. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 33–50. Springer, Heidelberg (2003)
Boura, C., Canteaut, A.: Zero-Sum Distinguishers for Iterated Permutations and Application to Keccak-f and Hamsi-256. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 1–17. Springer, Heidelberg (2011)
Boura, C., Canteaut, A., De Cannière, C.: Higher-Order Differential Properties of Keccak and Luffa. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 252–269. Springer, Heidelberg (2011)
Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004)
Daemen, J., Rijmen, V.: Understanding Two-Round Differentials in AES. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 78–94. Springer, Heidelberg (2006)
Davies, D.W., Murphy, S.: Pairs and Triplets of DES S-Boxes. Journal of Cryptology 8(1), 1–25 (1995)
Ferguson, N., Schroeppel, R., Whiting, D.L.: A Simple Algebraic Representation of Rijndael. In: Vaudenay, S., Youssef, A.M. (eds.) SAC 2001. LNCS, vol. 2259, pp. 103–111. Springer, Heidelberg (2001)
Fouque, P.-A., Jean, J., Peyrin, T.: Structural Evaluation of AES and Chosen-Key Distinguisher of 9-Round AES-128. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 183–203. Springer, Heidelberg (2013)
Gilbert, H., Peyrin, T.: Super-Sbox Cryptanalysis: Improved Attacks for AES-like permutations. IACR Cryptology ePrint Archive, 2009:531 (2009)
Gilbert, H., Peyrin, T.: Super-Sbox Cryptanalysis: Improved Attacks for AES-Like Permutations. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 365–383. Springer, Heidelberg (2010)
Iwamoto, M., Peyrin, T., Sasaki, Y.: Limited-Birthday Distinguishers for Hash Functions. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 504–523. Springer, Heidelberg (2013)
Jean, J., Naya-Plasencia, M., Peyrin, T.: Multiple Limited-Birthday Distinguishers and Applications
Jean, J., Naya-Plasencia, M., Peyrin, T.: Improved Rebound Attack on the Finalist Grøstl. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 110–126. Springer, Heidelberg (2012)
Jean, J., Naya-Plasencia, M., Schläffer, M.: Improved Analysis of ECHO-256. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 19–36. Springer, Heidelberg (2012)
Knudsen, L.R., Rijmen, V.: Known-Key Distinguishers for Some Block Ciphers. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 315–324. Springer, Heidelberg (2007)
Lamberger, M., Mendel, F., Rechberger, C., Rijmen, V., Schläffer, M.: Rebound Distinguishers: Results on the Full Whirlpool Compression Function. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 126–143. Springer, Heidelberg (2009)
Mendel, F., Rechberger, C., Schläffer, M., Thomsen, S.S.: Rebound Attacks on the Reduced Grøstl Hash Function. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 350–365. Springer, Heidelberg (2010)
Murphy, S., Robshaw, M.: Essential Algebraic Structure within the AES. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 1–16. Springer, Heidelberg (2002)
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Gilbert, H. (2014). A Simplified Representation of AES. In: Sarkar, P., Iwata, T. (eds) Advances in Cryptology – ASIACRYPT 2014. ASIACRYPT 2014. Lecture Notes in Computer Science, vol 8873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45611-8_11
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