Post-Quantum Key Agreement Protocols Based on Modified Matrix-Power Functions over Singular Random Integer Matrix Semirings

TL;DR

This paper introduces two new post-quantum key agreement protocols based on modified matrix-power functions over singular integer matrix semirings, suitable for implementation on standard computers, enhancing security against quantum attacks.

Contribution

The paper presents novel post-quantum key agreement protocols utilizing generalized matrix power functions over singular matrix semirings, with proofs and complexity analysis.

Findings

Protocols are implementable on standard computers.

Security relies on NP-hard problem complexity.

Protocols resist quantum computational attacks.

Abstract

Post-quantum cryptography is essential for securing digital communications against threats posed by quantum computers. Re-searchers have focused on developing algorithms that can withstand attacks from both classical and quantum computers, thereby ensuring the security of data transmissions over public networks. A critical component of this security is the key agreement protocol, which allows two parties to establish a shared secret key over an insecure channel. This paper introduces two novel post-quantum key agreement protocols that can be easily implemented on standard computers using rectangular or rank-deficient matrices, exploiting the generalizations of the matrix power function, which is a generator of NP-hard problems. We provide basic concepts and proofs, pseudocodes, examples, and a discussion of complexity.