On new key exchange multivariate protocols based on pseudorandom walks on incidence structures

A new key exchange protocol formulated in terms of multivariate cryptography and based on the elaboration of a common walk in the linguistic graph by correspondents is proposed. This algorithm is described in details in the case of a known family of graphs of large girth given by nonlinear equations over a finite field.Запропоновано новi протоколи обмiну ключами, що формулюються в термiнах алгебраїчної криптографiї вiд багатьох змiнних та базуються на створеннi кореспондентами спiльного блукання в лiнгвiстичному графi. Алгоритм детально описано у випадку вiдомої родини графiв великого обгорту, що задається нелiнiйними рiвняннями над скiнченним полем.Предложены новые протоколы обмена ключами, сформулированные в терминах алгебраической криптографии от многих переменных и основанные на создании корреспондентами общего блуждания в лингвистическом графе. Алгоритм детально описан в случае известной семьи графов большого захвата, заданной нелинейными уравнениями над конечным полем

On two windows multivariate cryptosystem depending on random parameters

The concept of multivariate bijective map of an affine space Kn over commutative Ring K was already used in Cryptography. We consider the idea of nonbijective multivariate polynomial map Fn of Kn into Kn represented as ''partially invertible decomposition'' F(1)nF(2)n…F(k)n, k=k(n), such that knowledge on the decomposition and given value u=F(v) allow to restore a special part v′ of reimage v. We combine an idea of ''oil and vinegar signatures cryptosystem'' with the idea of linguistic graph based map with partially invertible decomposition to introduce a new cryptosystem. The decomposition will be induced by pseudorandom walk on the linguistic graph and its special quotient (homomorphic image). We estimate the complexity of such general algorithm in case of special family of graphs with quotients, where both graphs form known families of Extremal Graph Theory. The map created by key holder (Alice) corresponds to pseudorandom sequence of ring elements. The postquantum version of the algorithm can be obtained simply by the usage of random strings instead of pseudorandom