Alternative signature generation procedures in the digital signature schemes based on the hidden discrete logarithm problem

Public-key cryptographic algorithms and protocols based on computational difficulty of the factorization problem and on the discrete logarithm problem are widely used in information-telecommunication systems. Currently the problem of construction of the post-quantum algorithms and protocols, i.e. cryptoschemes that are secure to potential attacks using quantum computers, represents a challenge in the area of applied and theoretic cryptography. In the literature the postquantum signature schemes based on the hidden discrete logarithm problem that is formulated in the finite non-commutativeassociative algebras were proposed. A disadvantage of such signature schemes is comparatively large size of the private key. The goal of the study is to develop an alternative signature generation procedures that will allow to reduce significantly the size of the private key. To achieve the goal, it is using the elements of the public key to compute the fixation vector at the first step of the signature formation procedure. As a result, there are designed alternative signature generation procedures in two known signature schemes based on the computational difficulty of the hidden discrete logarithm problem. Application of the proposed procedures gives possibility to reduce the size of the private key. The practical significance of the study is reduction the size of the protected memory in the electronic devices used for computation of the digital signatures.