近似理想格上的全同态加密方案

Fully Homomorphic Encryption from Approximate Ideal Lattices

构造高效、安全的全同态加密方案目前仍然是一个公开问题.通过扩展近似GCD到近似理想格的方法,首先构造一个基于整数上部分近似理想格问题(PAILP)的有点同态加密方案,并使用Gentry的引导技术将其转换到全同态加密方案.归约有点同态加密方案的安全性到求解部分近似理想格问题;其次,构造基于PAILP的批全同态加密方案和基于近似理想格(AILP)的全同态加密方案;最后,实现基于PAILP/AILP的全同态加密方案,并通过计算实验,其结果表明,所提方案比已有方案性能更好.

Constructing efficient and secured fully homomorphic encryption is still an open problem. By generalizing approximate GCD to approximate ideal lattice, a somewhat homomorphic encryption scheme is first presented based on partial approximate ideal lattice problem （PAILP） over the integers. The scheme is then converted it into a fully homomorphic encryption scheme （FHE） by applying Gentry＇s bootstrappable techniques. Next, the security of the somewhat homomorphic encryption scheme is reduced to solving a partial approximate ideal lattice problem. Furthermore, a PAILP-based batch FHE and an AILP-based FHE are constructed. Finally, the PAILP/AILP-based FHE is implemented, and the performance of the proposed scheme is demonstrated to be better than that of previous schemes by computational experimental.