河南理工大学学报（自然科学版）2025，Vol.44Issue(2)：138-144,7.DOI:10.16186/j.cnki.1673-9787.2023100040
矩阵NTRU密码体制参数研究
Study on the parameters of the matrix NTRU cryptosystem
摘要
Abstract
With the rapid development of quantum computers,post-quantum cryptography has emerged as a prominent area of research in cryptography.Objectives In order to avoid the decryption failure in matrix NTRU as NTRU,the Matrix NTRU algorithm was optimized.Methods Based on the method of constraining the parameter space in congruent cryptographic algorithms,a method for optimal selection of the parameter space of matrix NTRU cryptographic regimes was proposed.This method redefined the parameter space and accurately improved the choice of parameters,allowing control of the operation of matrix elements within a specific range.By compressing the original parameter space,decryption failures caused by modulo opera-tions going out of bounds were avoided.Results It was theoretically proved that the improved matrix NTRU algorithm avoided encryption and decryption failures.In order to test the performance of the improved ma-trix NTRU,a theoretical analysis was first carried out.The improved matrix NTRU and NTRU cipher algo-rithms were compared and analyzed in terms of key and plaintext security,key length,ciphertext exten-sion,encryption and decryption speed.By choosing a suitable value of d,the message and key security of the improved matrix NTRU algorithm was several times greater than the message and key security of the NTRU algorithm.The public and private key lengths and ciphertext extensions are the same as in the NTRU scheme.The improved matrix NTRU algorithm is n times faster than the NTRU algorithm for encryp-tion and decryption.Finally,the efficiency of the improved matrix NTRU was further verified by experi-ments,and the encryption and decryption speeds were consistent with the theoretical analysis.Conclusions The result indicated that the matrix NTRU algorithm,optimized with adjusted parameters,possessed char-acteristics such as accurate encryption and decryption,as well as high efficiency.关键词
矩阵NTRU/解密失败/矩阵环/后量子密码Key words
matrix NTRU/decryption failure/matrix ring/post-quantum cipher分类
计算机与自动化引用本文复制引用
李子臣,吴庆豪,宋佳烁,彭海朋..矩阵NTRU密码体制参数研究[J].河南理工大学学报（自然科学版）,2025,44(2):138-144,7.基金项目
国家自然科学基金资助项目(61370188) （61370188）
北京市教委科研计划项目(KM202010015009,KM202110015004,KM202310015002) （KM202010015009,KM202110015004,KM202310015002）
北京印刷学院博士启动金资助项目(27170120003/020,27170122006) （27170120003/020,27170122006）
北京印刷学院科研创新团队项目(Eb202101) （Eb202101）
北京印刷学院校内学科建设项目(21090121021) （21090121021）
北京印刷学院重点教改项目(22150121033/009) （22150121033/009）
北京印刷学院科研基础研究一般项目(Ec202201) （Ec202201）
北京市高等教育学会课题资助项目(MS2022093) （MS2022093）
