标题： 基于格的后量子密码学同态加密 显示英文标题

标题： Homomorphic Encryption Based on Lattice Post-Quantum Cryptography

摘要： 随着量子计算技术的持续进步，能够抵抗量子攻击的后量子密码方法已成为一个关键的研究领域。 鉴于现有同态加密方法，如RSA、ElGamal和Paillier，可能受到量子计算攻击的威胁，本研究提出了一种基于格的后量子同态加密方案。 该方法利用格密码学来构建对量子威胁的抵抗力，同时支持实际的同态加密应用。 本研究提供了数学证明和计算示例，并对基于格的后量子同态加密方案进行了安全分析。 研究成果旨在为同态加密应用的开发者，如联邦学习系统，提供参考。 显示英文摘要

摘要： As quantum computing technology continues to advance, post-quantum cryptographic methods capable of resisting quantum attacks have emerged as a critical area of focus. Given the potential vulnerability of existing homomorphic encryption methods, such as RSA, ElGamal, and Paillier, to quantum computing attacks, this study proposes a lattice-based post-quantum homomorphic encryption scheme. The approach leverages lattice cryptography to build resilience against quantum threats while enabling practical homomorphic encryption applications. This research provides mathematical proofs and computational examples, alongside a security analysis of the lattice-based post-quantum homomorphic encryption scheme. The findings are intended to serve as a reference for developers of homomorphic encryption applications, such as federated learning systems.