基于ELWE的多密钥全同态加密方案  

Multi‑key homomorphic encryption scheme based on ELWE

作　　者：祁正华 何菲菲 何校漫 QI Zhenghua;HE Feifei;HE Xiaoman(School of Computer Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学计算机学院,江苏南京210023

出　　处：《南京邮电大学学报(自然科学版)》2025年第1期90-98,共9页Journal of Nanjing University of Posts and Telecommunications:Natural Science Edition

基　　金：国家自然科学基金(61972209);安徽省高等学校科研计划重大项目(2022AH040148)资助项目。

摘　　要：格上基于容错学习(LWE)的多密钥全同态加密方案在密钥生成阶段通常直接选取随机矩阵和秘密向量,攻击者容易获得足够多低范数秘密向量或低范数的误差向量,从而获得秘密向量,使得公钥加密的安全性受到削弱。规避LWE(ELWE)是非标准LWE的一种变体,指即使敌手额外获得了短高斯前像,加密方案仍可以避免归零攻击。首先基于ELWE构造了一个选择明文安全的单密钥全同态加密方案;其次利用线性组合算法提出了一种密文扩展算法,将单密钥方案扩展为多密钥加密方案。方案的扩展扩大了应用空间,且构造的多密钥方案与其他方案的对比表明,所提方案将解密噪声从8(8m^(4)+m)mkδ降低为2(2m+1)mkδ,具有更强的实用性。The multi⁃key fully homomorphic encryption scheme from based on learning with errors(LWE)on lattice usually selects random matrixes and secret vectors directly in the key generation stage,so that the attacker can easily obtain enough low⁃norm secret vectors or low⁃norm error vectors to obtain the secret vector,which makesand the security of public key encryption is weakened.Evasive LWE(ELWE)is a non⁃standard variant of the LWE assumption where the distinguisher additionally receives short Gaussian pre⁃images while avoiding zeroizing attacks.Firstly,a single key homomorphic encryption scheme with selective plaintext security is constructed from based on ELWE.Secondly,a ciphertext ex⁃tension algorithm is proposed by using the linear combination algorithm to extend the single⁃key scheme to a multi⁃key encryption scheme.Finally,the expansion of the scheme expands the application space of the scheme,and the comparison between the proposed multi⁃key scheme constructed in this paper and others schemes shows that the this scheme reduces the decryption noise from 8(8m^(4)+m)mkδto 2(2m+1)mkδ,and has stronger practicability.

关 键 词：多密钥全同态加密 规避容错学习 格 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]