On the security of rijndael-like structures against differential and linear cryptanalysis

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Abstract

Rijndael-like structure is a special case of SPN structure.The linear transformation of Rijndael-like structures consists of lineartransformations of two types, the one is byte permutation π and theother is linear transformation θ = (θ1, θ2, θ3, θ4), where each of θi separatelyoperates on each of the four columns of a state. Furthermore,π and θ have some interestingprop erties. In this paper, we present anew method for upper boundingthe maximum differential probabilityand the maximum linear hull probability for Rijndael-like structures. Byapplyingour method to Rijndael, we obtain that the maximum differentialprobability and the maximum linear hull probability for 4 rounds ofRijndael are bounded by 1.06 × 2−96.

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Park, S., Sung, S. H., Chee, S., Yoon, E. J., & Lim, J. (2002). On the security of rijndael-like structures against differential and linear cryptanalysis. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2501, pp. 176–191). Springer Verlag. https://doi.org/10.1007/3-540-36178-2_11

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