Digital Signature Algorithms Based on Hidden Discrete Logarithm Problem

Abstract

The discrete logarithm problem in a hidden group, which is defined over finite non-commutative associative algebras, represents interest for constructing post-quantum public-key cryptoschemes. The currently known form of the hidden logarithm problem suits well for designing the public-key agreement protocols and public encryption algorithms, but not suits for designing the digital signature algorithms. In the present paper, there are introduced novel forms of defining the hidden discrete logarithm problem, on the base of which two digital signature algorithms are proposed. Two different four-dimensional finite non-commutative associative algebras have been used in the proposed signature algorithms. In one of the proposed algorithms, there are used globally non-invertible vectors that are invertible locally. A large set of the left-side and a large set of the right-side local units relates to some fixed globally non-invertible vector. Several different local units are used to define one of the proposed forms of the hidden logarithm problem.