Open AccessA post-quantum digital signature scheme on groups with four-dimensional cyclicity
Author(s) -
Nikolay A. Moldovyan,
Dmitriy N. Moldovyan
Publication year - 2021
Publication title -
informacionno-upravlâûŝie sistemy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.202
H-Index - 6
eISSN - 2541-8610
pISSN - 1684-8853
DOI - 10.31799/1684-8853-2021-2-43-51
Subject(s) - discrete logarithm , public key cryptography , digital signature , signature (topology) , blind signature , mathematics , post quantum cryptography , discrete mathematics , commutative property , cryptography , key (lock) , finite field , computer science , algorithm , encryption , hash function , geometry , computer security , operating system
Development of practical post-quantum signature schemes is a current challenge in the applied cryptography. Recently, several different forms of the hidden discrete logarithm problem were proposed as primitive signature schemes resistant to quantum attacks. Purpose: Development of a new form of the hidden discrete logarithm problem set in finite commutative groups possessing multi-dimensional cyclicity, and a method for designing post-quantum signature schemes. Results: A new form of the hidden discrete logarithm problem is introduced as the base primitive of practical post-quantum digital signature algorithms. Two new four-dimensional finite commutative associative algebras have been proposed as algebraic support for the introduced computationally complex problem. A method for designing signature schemes on the base of the latter problem is developed. The method consists in using a doubled public key and two similar equations for the verification of the same signature. To generate a pair of public keys, two secret minimum generator systems and of two different finite groups G and G possessing two-dimensional cyclicity are selected at random. The first public key (Y, Z, U) is computed as follows: Y = Gy1Qy2a, Z = Gz1Qz2b, U = Gu1Qu2g, where the set of integers (y1, y2, a, z1, z2, b, u1, u2, g) is a private key. The second public key (Y¢, Z¢, U¢) is computed as follows: Y¢ = Hy1Vy2a, Z¢ = Hz1Vz2b, U¢ = Hu1Vu2g. Using the same parameters to calculate the corresponding elements belonging to different public keys makes it possible to calculate a single signature which satisfies two similar verification equations specified in different finite commutative associative algebras. Practical relevance: Due to a smaller size of the public key, private key and signature, as well as approximately equal performance as compared to the known analogues, the proposed digital signature scheme can be used in the development of post-quantum signature algorithms.