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A block cipher can be easily broken if its encryption functions can be seen as linear maps on a small vector space. Even more so, if its round functions can be seen as linear maps on a small vector space. We show that this cannot happen for the AES. More precisely, we prove that if the AES round transformations can be embedded into a linear cipher acting on a vector space, then this space is huge-dimensional and so this embedding is infeasible in practice. We present two elementary proofs. [ABSTRACT FROM AUTHOR]

Abstract: In this work an efficient algorithm to perform a block decomposition for large dense rectangular matrices with entries in is presented. Matrices are stored as column blocks of row major matrices in order to facilitate rows operation and matrix multiplications with blocks of columns. One of the major bottlenecks of matrix decomposition is the pivoting involving both rows and column exchanges. Since row swaps are cheap and column swaps are order of magnitude slower, the number of column swaps should be reduced as much as possible. Here an algorithm that completely avoids the column permutations is presented. An asymptotically fast algorithm is obtained by combining the four Russian algorithm and the recursion with the Strassen algorithm for matrix–matrix multiplication. Moreover optimal parameters for the tuning of the algorithm are theoretically estimated and then experimentally verified. A comparison with the state of the art public domain software SAGE shows that the proposed algorithm is generally faster. [Copyright &y& Elsevier]

Abstract: S-Boxes are important security components of block ciphers. We provide theoretical results on necessary or sufficient criteria for an (invertible) 4-bit S-Box to be weakly APN. Thanks to a classification of 4-bit invertible S-Boxes achieved independently by De Cannière and Leander–Poschmann, we can strengthen our results with a computer-aided proof. We also propose a class of 4-bit S-Boxes which are very strong from a security point of view. [Copyright &y& Elsevier]

BEAR, LION and LIONESS are block ciphers presented by Biham and Anderson (), inspired by the famous Luby-Rackoff constructions of block ciphers from other cryptographic primitives (). The ciphers proposed by Biham and Anderson are based on one stream cipher and one hash function. Good properties of the primitives may ensure good properties of the block cipher. In particular, Biham and Anderson are able to prove that their ciphers are immune to any efficient known-plaintext key-recovery attack that can use as input only one plaintext-ciphertext pair. Our contribution is showing that these ciphers are actually immune to any efficient known-plaintext key-recovery attack that can use as input any number of plaintext-ciphertext pairs. We are able to get this improvement by using slightly different hypotheses on the primitives. We also discuss the attack by Morin (). [ABSTRACT FROM AUTHOR]