Research On Multi-key Fully Homomorphic Encryption Based On LW

The concept of fully homomorphic encryption(FHE)has become the "holy grail" in modern cryptography since it was first proposed.It allows arbitrary computation on the encrypted data,and the decryption of the resulting ciphertext is the same as the result that performed on the corresponding plaintext.Since FHE can strictly control the security of data during the process of evaluation.Therefore,it is significant to research FHE to promote the development and application of emerging technologies with the background of big data and cloud computing.Recently,the research of FHE keeps deepening and advancing,especially the construction of FHE scheme based on the Learning with Errors(LWE)problem is already the trend in this field.However,it only supports the evaluation of ciphertexts that are encrypted under the same secret key,which seriously reduces its practicality.Thus,proposing multi-key fully homomorphic encryption(MKFHE)for the evaluation of ciphertexts encrypted under different keys can effectively improve the applicability of FHE.Nevertheless,traditional MKFHE schemes still suffer from the problems of complexity and security.Hence,it is meaningful to propose an efficient and secure MKFHE scheme,which is one of the main research works in this paper.Besides,the multiple directions of LWE-based FHE,especially the heterogeneity of vector-type and matrix-type leads to a blocking in the evaluation.To address the compatibility problem for FHE schemes,we also study the cross-structural transformation of FHE ciphertexts.The main works are as follows.1.We propose a dynamic multi-key fully homomorphic encryption scheme.The ciphertext extension algorithm is solely based on the standard LWE assumption.Meanshile.it can correctly extend the single/multi-key ciphertext of GSW encryption to an extra secret key.In addition,we first implemented the ciphertext extension algorithm using secure multi-party computation,which breaks the traditional MKFHE ciphertext extension method.2.We present a conversion algorithm for fresh ciphertexts of different structure based on FHEW bootstrapping.We implement the conversion algorithm according to the principle of serial adder based on Ring-GSW encryption algorithm and bootstrapping technique in FHEW.Thus,supporting the evaluation can be performed on fresh cross-structure ciphertexts that encrypted under different FHE schemes and secret keys.Meanwhile,we perform a detailed analysis of the correctness of the algorithms.