公钥加密算法与抗量子密码体制安全性的数学分析

Mathematical Analysis of Public Key Encryption Algorithm and Security of Anti Quantum Cryptography

摘要: 基于数学难解问题的公钥体制加密算法面临着计算机计算能力进步的挑战，如何优化现有公钥加密理论基础、从数学角度分析验证抗量子密码的安全性与实用性，进而推进密码学加密技术的进步，一直是密码学与计算机科学的主要攻坚方向。本文通过回顾大数分解、对数难解等数学难题分析公钥密码的数学基础，同时结合科研动态从数学理论出发验证抗量子公钥密码体制的可靠性。这对有效应对即将到来的量子计算对公钥密码体制的威胁具有现实意义。

Abstract: The public key system encryption algorithm based on the difficult problem of mathematics is faced with the challenge of the improving computing power of computers. How to keep the safety of mathematical problems and optimize the theoretical basis of the existing public key encryption, analyze and verify the reliability and practicability of quantum-resistant cryptography from the perspective of mathematics, and further advance encryption technology have been an important research direction in cryptography and computer science. By reviewing mathematical problems such as integer factorization and the difficulty of solving the discrete logarithm problem, and by following research trends, this paper analyzes the mathematical foundation of public key cryptography, and verifies the reliability of quantum-resistant cryptography. This is of practical significance to effectively cope with the threat of the forthcoming quantum computing to the public key cryptosystem.