Multi-key fully homomorphic encryption scheme based on NTRU bootstrapping

Multi-key fully homomorphic encryption (MK-FHE) technology supports homomorphic operations on ciphertexts encrypted with different keys, and can be directly applied to real-world multi-user data fusion computing scenarios, such as multi-party collaborative computing and federated learning. At present, mainstream multi-key fully homomorphic encryption mainly uses bootstrapping technology to achieve multi-key homomorphic computing of LWE (learning with errors) encrypted ciphertexts. The time efficiency and storage overhead of expanding single-key ciphertexts to multi-key ciphertexts are closely related to the bootstrapping technology, which usually requires a large number of homomorphic evaluation keys and complex operations. Therefore, designing a multi-key fully homomorphic encryption scheme in combination with a better bootstrapping technology to improve computational efficiency and reduce storage overhead had become a key research issue. Based on the NTRU (number theory research unit) bootstrapping technology, an efficient multi-key fully homomorphic encryption scheme for LWE ciphertexts was designed. Compared with other schemes, the proposed scheme exhibited higher computational efficiency in the ciphertext expansion process. In addition, the correctness of the proposed scheme was elaborated and analyzed in detail. The proposed scheme was compared with the existing mainstream multi-key fully homomorphic encryption scheme in theory. The results show that the proposed scheme has better computational efficiency. Finally, the potential application of the scheme in cross-departmental supervision scenarios of multi-industry and multi-source data sales data was explored, which helped the tax department to realize tax verification under the premise of protecting data privacy, and helped promote the digital transformation and healthy development of various industries.