## Cryptology ePrint Archive: Report 2019/1295

A trip between creation and destruction of non-commutative public key exchange protocols

Borja Gómez

Abstract: Conventional asymmetric key exchange protocols rely on computing elements in commutative groups, where the employed trapdoor-permutation function is commutative, allowing Alice and Bob to compute the same element in $G$ as changing the orders of the variables or elements doesn't alter the output. The research found in this paper is focused on the analysis of key exchange protocols found in non-commutative cryptography, sometimes called group-based cryptography. Variations of these schemes made by the author are also included. Concretely, four schemes are presented using matrices over finite fields and permutation groups containing all the theory to break these schemes along with its pseudo-code and implementations in Mathematica.

Category / Keywords: non-commutative, public key cryptography, group based cryptography, group theory, algebraic combinatorics