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工程科学与技术:2020,52(5):186-193
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NTRU型多密钥全同态加密方案的优化
(1.武警工程大学 密码工程学院,陕西 西安 710086;2.网络和信息安全武警部队重点实验室,陕西 西安 710086)
Optimization of NTRU-type Multi-key Fully Homomorphic Encryption Scheme
(1.School of Cryptographic Eng., Eng. Univ. of PAP, Xi’an 710086, China;2.Key Lab. of Network and Info. Security of PAP, Xi’an 710086, China)
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投稿时间:2019-12-16    修订日期:2020-08-11
中文摘要: 现有的NTRU型多密钥全同态加密方案多是基于2的幂次分圆多项式环构造的,全同态计算过程使用了复杂的密钥交换操作,这类方案容易遭受子域攻击,且同态运算效率较低,对此本文提出了一个安全性更好、效率更高的NTRU型多密钥全同态加密方案。首先,将现有方案底层的分圆多项式环扩展应用到素数次分圆多项式环上,给出了基于素数次分圆多项式环的NTRU型多密钥全同态加密的基础方案模型(B-MKFHE方案),该方案模型可以抵御更多的子域攻击。其次,在B-MKFHE方案模型的基础上,通过扩展密文多项式维度,优化了NTRU型多密钥同态运算结构,使得同态运算过程不再需要复杂耗时的密钥交换操作。最后,根据优化的多密钥同态运算结构,结合模交换技术,构造了无需密钥交换的层级的NTRU型多密钥全同态加密方案(M-MKFHE方案)。分析结果表明,本文提出的M-MKFHE方案能有效抵御子域攻击,满足IND-CPA安全。与B-MKFHE方案相比,M-MKFHE方案具有更小的存储开销和计算开销,同态运算过程中产生的噪声值较小,运算效率较高,且支持更深层次的同态运算。
Abstract:The previous NTRU-type multi-key fully homomorphic encryption (MKFHE) schemes were constructed over power-of-2 cyclotomic polynomial rings, and the complicated key-switching operations were used in the schemes to complete the fully homomorphic computation. They were suffered from the subfield attacks and had low evaluating efficiency. In this paper, an NTRU-type MKFHE scheme with better security and higher efficiency was proposed. Firstly, the prime cyclotomic polynomial ring was applied to the previous NTRU-type MKFHE schemes, and a NTRU-type MKFHE basic scheme model (B-MKFHE) that could resist more subfield attacks was presented. Secondly, based on the B-MKFHE model, the NTRU-type multi-key homomorphic evaluating structure was optimized by extending the dimension of ciphertext polynomial, so that the complicated and time-consuming key-switching operations were eliminated when running the homomorphic operations. Finally, combined the optimized multi-key homomorphic evaluating structure and modulus-switching technology, a leveled NTRU-type MKFHE scheme (M-MKFHE) without key-switching operations was constructed. The result showed that the proposed M-MKFHE scheme could resist the subfield attacks well and was proved to be IND-CPA security. Compared with the B-MKFHE, the memory (bit-size) and evaluating costs of the M-MKFHE are reduced, and the error magnitude is decreased in the homomorphic evaluating process. In all, the M-MKFHE scheme has higher evaluating efficiency and supports deeper homomorphic evaluations.
文章编号:201901197     中图分类号:TP391    文献标志码:
基金项目:国家重点研发计划项目(2017YFB0802000);国家自然科学基金项目(U1636114);国家密码发展基金项目(MMJJ20170112);陕西省自然科学基金项目(2020JQ-492)
作者简介:车小亮(1987-),男,博士生.研究方向:信息安全;密码学.E-mail:xawjchexl@126.com
引用文本:
车小亮,周潭平,李宁波,周昊楠,刘龙飞,杨晓元.NTRU型多密钥全同态加密方案的优化[J].工程科学与技术,2020,52(5):186-193.
CHE Xiaoliang,ZHOU Tanping,LI Ningbo,ZHOU Haonan,LIU Longfei,YANG Xiaoyuan.Optimization of NTRU-type Multi-key Fully Homomorphic Encryption Scheme[J].Advanced Engineering Sciences,2020,52(5):186-193.