Post-Quantum Secure Digital Signature Scheme Based on Non-Commutative Matrix Algebra
Аннотация
This work investigated the post-quantum digital signature algorithm based on Finite Non-commutative Associative Algebras and also provides a brief analytical overview of certain post-quantum schemes. By defining algebraic operations using a Basis Vector Multiplication Table, we construct a 4-dimensional Finite Non-commutative Associative Algebras over a finite field and analyze its algebraic properties, including invertibility conditions, commutative subalgebras and multiplicative group structures. The Finite Non-commutative Associative Algebras structure enables efficient multiplication operations, which can be leveraged for high-performance digital signature generation and verification. The paper further presents a detailed classification of commutative subalgebras based on structural coefficients, along with their impact on security and computational complexity. The proposed signature scheme uses invertible matrices from Finite Non-commutative Associative Algebras and resists common algebraic attacks by incorporating non-commutative multiplication and hidden group structures. At the end of the paper, we also present an analysis of the Man-in-the-middle attack and discuss the results of the comparison of key sizes.