CRYPTANALYSIS OF 2-CASCADE FINITE AUTOMATA GENERATOR WITH FUNCTIONAL KEY

A cryptographic generator under consideration is a serial connection G = A(1) . A(2) of two finite state machines (finite automata) A(1) = (F-2(n), F-2, g(1), f(1)) (it is autonomous) and A(2) = (F-2, F-2(n), F-2, g(2), f(2)). The key of the generator is the function f(1) and possibly the initial states x(1), y(1) of the automata A(1), A(2). The cryptanalysis problem for G is the following: given an output sequence gamma = z(1)z(2) . . . z(l), find the generator's key. Two algorithms for analysis of A(2) are presented, they allow to find a preimage u(1) . . . u(l) of gamma in general case and in the case when A(2) is the Moore automaton with the transition function g(2)(u, y) = inverted right perpendicularug(delta)(y) + ug(tau) (y) for some g : F-2(m) -> F-2(m) and delta, tau is an element of N. This preimage is an input to A(2) and an output from A(1). The values u(t) equal the values f(1)(x(t)) where x(t) is the state of A(1) at a time t, t = 1, 2, . . . l. If the initial state x(1) and a function class C-1 containing f(1) are known, then f(1) can be determined by its specifying in the class C-1.