On Linear Approximation Tables and Ciphers secure against Linear Cryptanalysis

Linear cryptanalysis is an attack that derives a linear approximation between bits of the plaintext, ciphertext and key. This global approximation is constructed from the linear approximation tables of the nonlinear mappings used by the cipher, usually the S-boxes, as in the case of DES. In this paper we will describe the distribution of these tables for bijective mappings (permutations), concentrating on the expected value of the largest entry, and use our results to construct Feistel ciphers provably resistant to linear cryptanalysis.