摘要：

针对整数上全同态加密方案公钥尺寸偏大且效率较低的问题,将Coron的公钥压缩技术以二次的形式运用到加密算法中,提出一个可以将公钥尺寸降低到O～(λ3.5)的部分同态加密方案。同时该方案一次可以加密n bit明文。分析结果表明,相比于DGHV方案,该方案具有更短 的公钥尺寸且加密效率更高,更适用于云计算的实际应用。

关键词: 全同态加密, 公钥尺寸, 近似最大公约数问题, 稀疏子集和问题, 安全性

Abstract:

Aiming at the problem that the efficiency of the integer Fully Homomorphic Encryption(FHE) scheme is low and the public key is long,Coron’s public key compression technique is used to encryption algorithm with a quadratic form,a partial homomorphic encryption scheme with the property of reducing public key size to O～(λ3.5) is proposed.This scheme can encrypt n bit plaintext once.Compared with DGHV scheme,the proposed scheme has lower public key size and higher encryption efficiency,which is more suitable for the practical application of cloud computing.

Key words: Fully Homomorphic Encryption(FHE), public key size, approximate Greatest Common Divisor(GCD) problem, sparse subset sum problem, security

中图分类号: 

• TP301.9