环LWE上高效的多密钥全同态加密方案  

Efficient multi-key fully homomorphic encryption scheme from RLWE

作　　者：车小亮 周昊楠[2] 杨晓元 周潭平[1,2] 刘龙飞[1] 李宁波 CHE Xiaoliang;ZHOU Haonan;YANG Xiaoyuan;ZHOU Tanping;LIU Longfei;LI Ningbo(College of Cryptographic Engineering,Engineering University of PAP,Xi’an 710086,China;Key Laboratory of Network and Information Security of the PAP,Xi’an 710086,China)

机构地区：[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

出　　处：《西安电子科技大学学报》2021年第1期87-95,共9页Journal of Xidian University

基　　金：国家重点研发计划(2017YFB0802000);国家自然科学基金(U1636114);国家密码发展基金(MMJJ20170112);陕西省自然科学基金(2020JQ-492)。

摘　　要：基于RLWE问题的BGV型多密钥全同态加密方案具有较大的密文量和密钥量,且生成计算密钥的过程复杂,致使同态运算效率较低。针对该问题,提出了一种密钥量小、计算密钥生成效率高的BGV型多密钥全同态加密方案。首先,通过改进密文的扩展形式,优化了计算密钥的生成算法,提高了计算密钥的生成效率;其次,利用低位比特丢弃技术,减小了计算密钥生成算法中的计算冗余,降低了计算开销;最后,根据优化的算法,结合模交换技术和密钥交换技术,构造了一种高效的层级BGV型多密钥全同态加密方案。相比于现有的层级BGV型多密钥全同态加密方案,新方案在满足IND-CPA安全的条件下,简化了计算密钥生成过程,降低了存储和计算开销,且同态运算过程中产生的噪声值较小,运算效率较高。The ring-LWE-based BGV-type multi-key fully homomorphic encryption(MKFHE)scheme has a large size of ciphertexts and keys,and the generation process of evaluation key is complicated,which results in a low homomorphic evaluating efficiency.To improve these problems,a BGV-type MKFHE scheme with a small-size key and a high efficiency of evaluation of key generation is proposed.First,by modifying the expansion of the ciphertext,the algorithm for generation of the evaluation key is optimized and the efficiency of the algorithm is improved.Second,the low bit discarding technique is used in the generation algorithm,which reduces the calculated redundancy and decreases the calculated complexity.Finally,by applying modulus-switching and key-switching techniques to the optimized algorithm,an efficient leveled BGV-type MKFHE scheme with IND-CPA security is proposed.Compared with the previous leveled BGV-type MKFHE schemes,the proposed scheme can simplify the process of generation of the evaluation key and decrease memory(bit-size)and calculation costs.Moreover,the proposed scheme has a higher efficiency and a less noise magnitude.

关 键 词：多密钥全同态加密 密文扩展算法 计算密钥 密钥交换 混合同态乘法 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]