Generation of high order primitive matrix elements for post-quantum key exchange protocol

Active work is performed to create quantum computers. Quantum computers can break existing public key cryptography. So they can break Diffie-Hellman key exchange protocol. Matrix algorithms of key exchange can be considered as the alternative to Diffie-Hellman key exchange protocol. The improved method of key-exchange protocol is offered in the article. The method deals with the original matrix one-way function and the generalized method of processing the corresponding high order matrix multiplicative finite commutative group. The general method of the insertion-enlarging method of building the primitive elements of the field is derived from elements of the matrix groups with different power. The article describes the results that give us the prospect of generating the high order multiplicative Abelian matrix groups and of creating key-exchange protocol, resistant to quantum computers attacks by means of this groups. Keywords— Matrix One-way Function, Abelian Finite Field, Asymmetric Cryptography, High order finite matrix Field, Primitive Matrix Element, quantum computers, post-quantum cryptography.