On Implemented Graph-Based Generator of Cryptographically Strong Pseudorandom Sequences of Multivariate Nature

Classical Multivariate Cryptography is searching for the special families of functions F on the affine space Kn, where F is a quadratic or cubical polynomial map and K is a finite commutative ring with unity. Usually the map F is given in its standard form, which is the tuple C(F) of nonzero coefficients of F ordered in the lexicographical form. The owner of the publicly given map need the private key which is the piece of information T such that its knowledge allows to compute the reimage of F in a polynomial time O(nᾳ). We consider the Inverse Problem of multivariate Cryptography to find T for the given tuple C(F) of the multivariate map F. If α ≤ 2 then the solution of the Inverse Problem is harder than computation of the reimage of F which is NP-hard problem for general quadratic or cubic maps. We use Inverse Problem of the constructing C(F) for the cubic multivariate maps constructed in terms of well-known families of graphs of D(n,K) and A(n,K) which appear in the studies of Extremal Graph Theory and its applications. So piece of information T is a seed for cryptographically strong pseudorandom sequence C(F). We consider cases of K = Fq, K = Zq, q = 2 m and the case of Bollean ring B(m) of cardinality 2m.