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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]

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]