A method for enhancing randomization in algebraic signature algorithms on non-commutative algebras

Abstract

The paradigm of algebraic signature schemes security of which is based on the computational difficulty of solving large systems of power equations is attractive for developing practical post-quantum signature algorithms. A significant drawback of the known algorithms of the mentioned type is the limited signature randomization, which creates preconditions for a decrease in security. A method for enhancing signature randomization is proposed and used for developing a digital signature algorithm that is free of the said drawback. The method is based on the use of three hidden commutative groups, such that in the general case the elements of one of them are non-commutative with the elements of the other two groups