UPPER BOUNDS OF MAXIMUM VALUES OF AVERAGE DIFFERENTIAL AND LINEAR CHARACTERISTIC PROBABILITIES OF FEISTEL CIPHER WITH ADDER MODULO 2 m

The paper discusses the Feistel cipher with a block size of n = 2m, where the addition \nof a round key and a part of an incoming massage in each round is carried out \nmodulo 2^m. In order to evaluate the security of such a cipher against differential and linear cryptanalyses, the new parameters of cipher s-boxes are introduced. The upper bounds of maximum average differential and linear probabilities of one round \nencryption transformation and the upper bounds of maximum average differential and \nlinear characteristics probabilities of the whole cipher are obtained. The practical \nsecurity of the cipher GOST (with independent and equiprobable random round keys) against differential and linear cryptanalysis is also evaluated. To the authors’ mind, the obtained results allow one to expand the basic statements concerning the practical security of Markov (Feistel and SPN) ciphers against conventionally differential and \nlinear attacks to a cipher of the type under study.