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

**A. ALEKSEYCHUK AND L. KOVALCHUK**

*Theory of Stochastic Processes*

*Vol. 12 (28), no. 1–2, 2006, pp. 20–32*

The paper discusses the Feistel cipher with a block size of $n=2m$, where the addition of a round key and a part of an incoming massage in each round is carried out modulo $2^m$. 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 encryption transformation and the upper bounds of maximum average differential and linear characteristics probabilities of the whole cipher are obtained. The practical security 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 linear attacks to a cipher of the type under study.

Full version