Some theoretical aspects of differential cryptanalysis of the iterated block ciphers with additive round key

A common method is formulated for differential cryptanalysis of any iterated block cipher with additive round key. For a $r$-round cipher, the method uses its $(r-1)$-round characteristic and an algorithm for solving the system of polynomial equations over a finite field describing for the $r$th round the dependencies of its known outputs on its input differences known with a nonzero probability and on its unknown inputs and round key elements. Before the method is stated necessary notions are introduced and basic propositions are given concerning the functions defined on finite abelian groups, iterated block ciphers, their round functions, additive round keys, differential characteristics, round system of equations over a finite field, and so on. All the notions and assertions are illustrated on DES.