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Mathematics, Vol. 12, Pages 1970: A Method for Specifying Complete Signature Randomization and an Algebraic Algorithm Based on It
Mathematics doi: 10.3390/math12131970
Authors: Alexandr Moldovyan Dmitriy Moldovyan Nikolay Moldovyan Alyona Kurysheva
To eliminate the limitations of signature randomization in known algebraic algorithms with a hid den group, the security of which is based on the computational complexity of solving large systems of power equations, a method for ensuring complete randomization is proposed. Based on this method, a new algorithm of the indicated type was developed, using a four-dimensional finite non-commutative associative algebra as an algebraic basis. We obtained estimates of the security of algorithms to direct attacks as well as from attacks based on known signatures, which confirm the effectiveness of the proposed signature randomization method. Due to the relatively small size and signature of the public and private keys, the developed algorithm is of interest as a potential practical post-quantum digital signature scheme.
