支持多比特加密的全同态加密体制设计

现有全同态加密体制普遍存在密文尺寸较大和采用单比特加密所导致的效率较低问题.在Gentry等人提出的全同态加密体制(简称GS W13体制)的基础上,通过修改其展开方式,利用近似特征向量技术,提出了一种新的全同态加密体制.在随机喻示模型下,将新体制的安全性归约到判定性容错学习问题(decisional lear-ning with errors,DLWE)的难解性,给出了其正确性和安全性的证明.又在不改变系统参数的条件下,采用多比特加密,对新体制进行优化.与GSW13体制相比,新体制的密文尺寸减小61.47％,加密运算量减少68.97％.新体制不仅减小密文扩张,而且减少同态运算计算次数,从而提高了体制效率.

Design of fully homomorphic encryption scheme supporting multi-bit encryption

The existing full homomorphic encryption schemes are faced with challenges like large ciphertext sizes or low efficiency in calculation due to single-bit encryption. Based on the fully homomorphic encryption scheme proposed by Gentry et al. (GSW13 scheme), this paper proposed a full homomorphic encryption scheme by modifying its expansion method and using the idea of approximate eigenvector. It reduced the security of the new scheme to the complexity of the decisional LWE problem under the random oracle model, and gave the proof of its correctness and security. It used the multi-bit encryption to optimize the new scheme without changing the scheme parameters. Compared with the GSW13 scheme, the ciphertext size of the proposed scheme is reduced by 61.47%, and the number of encryption operations is minimized by 68.97%. The proposed scheme not only further reduces the ciphertext size, but also greatly reduces the number of homomorphic operations, thus further improving the scheme efficiency.