A new non-commutative key exchange protocol on combinatorial semigroup

Since the launch of the post-quantum cryptography standardization project by NIST, post-quantum cryptography has become a prominent research area. Non-commutative cryptography constructed using NP-complete problems is widely regarded resistant to quantum computing attacks, so it has become an important branch of post-quantum cryptography. Nonetheless, the existing non-commutative cryptographic protocol still exhibits certain shortcomings. In this paper, a non-commutative combinatorial semigroup with matrix power function is constructed from a modified medial semigroup by the method of semidirect product, and then a key exchange protocol is developed on it to provide a kind of novel non-commutative cryptographic protocol. Due to the non-commutativity of cryptographic platform, the proposed protocol could perform well in respect of antiquantum computing attack, which is superior to traditional cryptographic protocol. In addition, the security analysis shows that the protocol has significant advantages in resisting algebraic and brute force attacks, as well as aganist quantum cryptanalysis; the complexity analysis demonstrates that computation and storage complexities are of polynomial order, ensuring efficient operation even for large matrix sizes.