Post-quantum electronic digital signature scheme based on the enhanced form of the hidden discrete logarithm problem

A digital signature scheme based on the computational difficulty of the hidden discrete logarithm problem defined in finite non-commutative associative algebras is proposed. The modified quaternion algebra and its properties are considered as the algebraic carrier of the introduced post-quantum digital signature scheme. Formulas describing the set of local units associated with a given non-invertible vector of a modified quaternion algebra are derived. \newpage A new form of the hidden discrete logarithm problem has been formulated and a digital signature scheme has been developed on its base.