Signature schemes on algebras, satisfying enhanced criterion of post-quantum security

The paper introduces an enhanced criterion of the post-quantum security for designing post-quantum digital signature schemes based on the hidden discrete logarithm problem. The proposed criterion requires that it is computationally impossible to construct a periodic function containing a period whose length depends on the value of a discrete logarithm in a hidden cyclic group when using public parameters of the signature scheme. A practical post-quantum signature scheme which satisfies the criterion is proposed.