密码学报（中英文）2025，Vol.12Issue(5)：1081-1105,25.DOI:10.13868/j.cnki.jcr.000814
格密码方案的多项式乘法多平台高效实现
Multi-Platform Efficient Implementation of Polynomial Multiplication for Lattice-Based Cryptographic Schemes
摘要
Abstract
Among the various post-quantum cryptographic approaches,lattice-based cryptographic schemes have emerged as a leading candidate due to their balanced performance in security and com-putational efficiency.As a fundamental yet time-intensive operation in lattice-based cryptographic schemes,polynomial multiplication plays a critical role in accelerating the overall performance of these schemes.This study first investigates and summarizes the key parameters of today's leading lattice-based cryptographic schemes and the polynomial multiplication methods employed.Subsequently,a multi-platform efficient implementation of polynomial multiplication is presented for lattice-based cryptographic schemes,supporting multiple NTT variants and a variety of parameter sets.The imple-mentation is tailored for diverse application scenarios across different platforms,including C language,AVX2,ARM Cortex-M4,and GPU optimizations.By leveraging the specific characteristics of each platform,this study incorporates innovative optimization techniques such as lazy reduction,parallel synchronized computation,optimized memory access patterns,and kernel fusion to enhance perfor-mance.Finally,the experimental evaluation compares the multi-platform efficient implementation with the C language optimized implementation and analyzes the advantages and disadvantages of different NTT variants under identical parameters,taking platform-specific characteristics into ac-count.The results show that,compared to the C language optimized implementation,the AVX2,ARM Cortex-M4,and GPU implementations achieve speedups of up to 29 times,7 times,and 8626 times,respectively.The efficiency and versatility of the multi-platform accelerated implementation are highly valuable for the practical deployment of post-quantum lattice-based cryptography in diverse applications,such as the Internet of Things and cloud computing environments.关键词
后量子密码/格密码/多项式乘法/数论变换/多平台高效实现Key words
post-quantum cryptography/lattice-based cryptography/polynomial multiplication/number theoretic transform/multi-platform efficient implementation分类
信息技术与安全科学引用本文复制引用
张宏,沈诗羽,赵运磊..格密码方案的多项式乘法多平台高效实现[J].密码学报（中英文）,2025,12(5):1081-1105,25.基金项目
国家重点研发计划(2022YFB2701601) （2022YFB2701601）
密码科学技术全国重点实验室面上课题(MMKFKT202227) （MMKFKT202227）
上海市科委技术标准基金(21DZ2200500) （21DZ2200500）
上海市协同创新基金(XTCX-KJ-2023-54) （XTCX-KJ-2023-54）
上海市科委区块链关键技术攻关专项基金(23511100300)National Key Research and Development Program of China(2022YFB2701601) （23511100300）
General Project of State Key Laboratory of Cryptography(MMKFKT202227) （MMKFKT202227）
Technical Standard Project of Shanghai Scientific and Technological Committee(21DZ2200500) （21DZ2200500）
Shanghai Collaborative Innovation Fund(XTCX-KJ-2023-54) （XTCX-KJ-2023-54）
Special Fund for Key Technologies in Blockchain of Shanghai Scientific and Technological Committee(23511100300) （23511100300）
