一种短密钥高效全同态加密方案

Highly efficient fully homomorphic encryption scheme with shorter public keys

针对Van Dijk等人在2010年欧密会上提出的基于整数的全同态加密方案进行了研究,此方案的主要优势在于概念上的简单性,将原来的基于理想格的同态加密体制替换为一个非常简单的整数描述的同态加密体制,但是它的公钥尺寸为O(λ^(10)),并且每次只能加密1 bit。在原始DGHV同态加密的基础上,通过改变整数的选取方式和模数,提出了一种一次可以加密k bit的同态加密方案,且公钥的尺寸降低至O(λ~7)。最后给出了安全性证明和效率分析,方案与原始方案基于相同的困难问题,且加/解密效率有所提高。

Van Dijk et al. discribed a fully homomorphic encryption scheme over the integers at Eurocrypt 2010. The main appeal of this scheme is its conceptual simplicity. The original scheme which based on ideal lattices is replaced by a very simple homomorphic encryption scheme described by the integers. This simplicity comes at the expense of a publiekey size in （λ10） and only encrypts 1 bit at a time. On the basis of the original DGHV homomorphism encryption scheme ,this paper proposed a scheme by changing intenger selection mode and modulus. It could encrypt k bits at a time, and reduced the public key size to （λ10）. Then, it gave the security certificates and efficiency analysis. The scheme is based on the same difficult problems as DGHV, and has a better performance in efficience.