一种小数精确加法同态方案的研究OA

In previous work,Cheon et al.proposed a method for constructing approximate arithmetic homomorphic encryption schemes(CKKS).Nevertheless,the approximate nature of these computa-tions sometimes fails to meet the requirements for precise calculations.In response to this limitation,this paper presents a rational number encoding method in the complex plane,combined with complex canonical embedding techniques,to construct a fractional exact addition homomorphic scheme based on RLWE.The scheme can perform precise encryption,decryption,and homomorphic operations with predetermined accuracy.Both theoretical analysis and experimental validation demonstrate that the proposed scheme can correctly perform encryption,decryption,and homomorphic addition while en-suring semantic security.With appropriately chosen parameters,the proposed scheme achieves smaller polynomial norms compared to CKKS,allowing for higher precision inputs and supporting more rounds of homomorphic additions.Finally,experiments show that the proposed scheme incurs no efficiency loss compared to the CKKS scheme under the same precision requirements.