Defining High-Dimensional Non-Commutative Algebras as Carriers for Post-Quantum Digital Signature Algorithms

In the development of generalized methods for defining finite non-commutative associative algebras of various dimensions for use as algebraic carriers of post-quantum two-key crypto schemes with a hidden group, new methods for defining the high-dimensional algebras are proposed. It is shown that one of the proposed methods allows defining high-dimensional algebras using a sparse basis vector multiplication table, which can significantly reduce the computational complexity of vector multiplication operations. This results in a substantial increase in the performance of digital signature algorithms that use non-commutative algebras as their carrier.