ckks方案优化最好的_优化的基于错误学习问题的CKKS方案

Abstract： Focused on the issue that the CKKS(Cheon-Kim-Kim-Song) homomorphic encryption scheme based on the Learning With Errors (LWE) problem has large ciphertext, complicated calculation of key generation and low homomorphic calculation efficiency in the ciphertext calculation, an optimized scheme of LWE type CKKS was proposed through the method of bit discarding and homomorphic calculation of key reorganization. Firstly, The size of the ciphertext in the homomorphic multiplication process was reduced by discarding part of the low-order bits of the ciphertext vector and the tensor product of the two ciphertext vectors in the homomorphic multiplication. Secondly, The method of bit discarding was used to reorganize and optimize the homomorphic calculation key, which removed the irrelevant extension items in powersof2 during the key switching procedure and reduced the scale of the calculation key and the noise increase in the process of homomorphic multiplication. On the basis of ensuring the security of the original scheme, the dimension of the calculation key is reduced from (N+1)2[lb ql]×(N+1) to (N+1)2[lb ql-δ']×(N+1) , and the computational complexity of homomorphic multiplication is reduced from (N+1)3[lb ql] to (N+1)3[lb ql-δ'] . The analysis shows that this proposed optimization method reduces the computational complexity of the homomorphic calculation and calculation key generation process, reduces the storage overhead, and improves the efficiency of the homomorphic multiplication operation to a certain extent.