基于素数幂次阶分圆多项式环的多密钥全同态方案

doi:10.3969/j.issn.1671-1122.2020.05.010

信息网络安全 ›› 2020, Vol. 20 ›› Issue (5): 83-87.doi: 10.3969/j.issn.1671-1122.2020.05.010

基于素数幂次阶分圆多项式环的多密钥全同态方案

周昊楠¹^,²^,^*(), 李宁波¹^,², 车小亮¹^,², 杨晓元¹^,²

^1. 网络和信息安全武警部队重点实验室,西安 710086
^2. 武警工程大学密码工程学院,西安 710086

收稿日期:2019-10-15 出版日期:2020-05-10 发布日期:2020-06-05
通讯作者: 周昊楠 E-mail:1957028@qq.com
作者简介:周昊楠（1992—）,男,黑龙江,硕士研究生,主要研究方向为信息安全、全同态加密;|李宁波（1992—）,男,河南,博士,主要研究方向为信息安全、全同态加密|车小亮（1987—）,男,安徽,博士,主要研究方向为信息安全、全同态加密|杨晓元（1959—）,男,湖南,教授,硕士,主要研究方向为信息安全、密码学
基金资助:
国家重点研发计划(2017YFB0802000);国家密码发展基金(MMJJ20170112)

Multi-key Fully Homomorphic Encryption Scheme over Prime Power Cyclotomic Rings

ZHOU Haonan¹^,²^,^*(), LI Ningbo¹^,², CHE Xiaoliang¹^,², YANG Xiaoyuan¹^,²

^1. College of Cryptographic Engineering, Engineering University of PAP, Xi’an 710086, China
^2. Network and Information Security Key Laboratory of PAP, Xi’an 710086, China

Received:2019-10-15 Online:2020-05-10 Published:2020-06-05
Contact: Haonan ZHOU E-mail:1957028@qq.com

摘要/Abstract

摘要：

传统的全同态加密方案允许对单个用户的密文进行任意计算,计算结果解密后能够得到与明文计算相一致的结果。多密钥全同态加密方案允许云服务器对多个用户的密文进行任意计算,更适用云计算的应用场景。基于公钥加密方案NTRU的多密钥全同态加密方案被称为NTRU型多密钥全同态加密方案,具有密钥和密文尺寸短、运算速度快和潜在的抗量子攻击等特性。但是,现有的NTRU型多密钥全同态加密方案存在可选的环结构少、使用的环结构容易受到子域攻击等问题。文章以NTRU型多密钥全同态加密方案LTV12为研究对象,将该方案中的2的幂次阶分圆多项式环替换为素数幂次阶分圆多项式环,密钥生成算法采用正则嵌入下的高斯分布,优化了LTV12方案,增加了可选环结构的数量,并使其免受子域攻击的危害,对其实用性和安全性具有推动意义。

关键词: 多密钥, 全同态加密, 素数幂次阶分圆多项式环, 正则嵌入

Abstract:

The traditional fully homomorphic encryption scheme allows arbitrary evaluations on the ciphertext from a single user.After decryption, a result consistent with the plaintext evaluations can be obtained.The multi-key fully homomorphic encryption schemes allow the cloud server to perform arbitrary evaluations on ciphertexts from multiple parties, which is more suitable for cloud computing application. The multi-key fully homomorphic encryption schemes based on NTRU have the characteristics of short keys, small ciphertext sizes, high operation speed and potential resistant from quantum attacks. However, the existing NTRU multi-key fully homomorphic encryption schemes have the problems that they have rare optional ring structures, and the ring structure is vulnerable to subfield attacks. In this paper, the power of 2 cyclotomic ring in the multi-key homomorphic scheme LTV12 was changed into the prime power cyclotomic ring. The key generation algorithm uses the Gaussian distribution over canonical embedding. Therefore, the number of optional ring structures increased and the scheme is not vulnerable to subfield attacks anymore, which has a driving significance for the practicability and security of the scheme, which has a driving significance for the practicability and security of the scheme.

Key words: multi-key, fully homomorphic encryption, prime power cyclotomic rings, canonical embedding

中图分类号:

TP309

周昊楠, 李宁波, 车小亮, 杨晓元. 基于素数幂次阶分圆多项式环的多密钥全同态方案[J]. 信息网络安全, 2020, 20(5): 83-87.

ZHOU Haonan, LI Ningbo, CHE Xiaoliang, YANG Xiaoyuan. Multi-key Fully Homomorphic Encryption Scheme over Prime Power Cyclotomic Rings[J]. Netinfo Security, 2020, 20(5): 83-87.

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基于素数幂次阶分圆多项式环的多密钥全同态方案

Multi-key Fully Homomorphic Encryption Scheme over Prime Power Cyclotomic Rings

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