标题： 基于奇异随机整数矩阵半环上的修改矩阵幂函数的后量子密钥协商协议 显示英文标题

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

摘要： 后量子密码学对于抵御量子计算机带来的威胁，确保数字通信的安全至关重要。 研究人员专注于开发能够抵御经典和量子计算机攻击的算法，从而确保公共网络上数据传输的安全性。 这一安全性的关键组成部分是密钥协议，它允许双方在不安全的信道上建立共享的秘密密钥。 本文介绍了两种新颖的后量子密钥协议，这些协议可以使用矩形或秩亏矩阵在标准计算机上轻松实现，利用了矩阵幂函数的推广，该函数是NP难问题的生成器。 我们提供了基本概念和证明、伪代码、示例以及复杂度的讨论。 显示英文摘要

摘要： 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.