Digital signature scheme with doubled verification equation

A novel design of the signature schemes based on the hidden discrete logarithm problem is proposed, which is characterized in using special criterion oriented to providing security to potential quantum attacks. The criterion consists in the requirement to ensure practical intractability of the task of constructing a periodic function with a period depending on the value of a discrete logarithm in a hidden cyclic group. A signature scheme satisfying the mentioned criterion is introduced. A 4-dimensional finite non-commutative associative algebra is considered as algebraic support. To implement the signature scheme, a commutative hidden group defined by generator system $<N,Q>$, where vectors $N$ and $Q$ have the same prime order, is exploited. For further development of the introduced method, an 8-dimensional algebra is proposed.