Homomorphic encryption allows computations to be performed directly on encrypted data, with the decrypted results matching those obtained from computations on the plaintext data, providing strong protection for user data privacy. While existing homomorphic encryption schemes support Single Instruction Multiple Data (SIMD) operations to enhance the efficiency of ciphertext computation, the complexity of ciphertext structure still results in high computational costs in encrypted matrix operations. This has become one of the major bottlenecks hindering the widespread application of homomorphic encryption.

Recently, the Automatic Reasoning and Cognitive Research Center at our institute has made significant progress in the field of homomorphically encrypted matrix computation. The results, titled “Homomorphic Matrix Operations Under Bicyclic Encoding”, were published in the journal IEEE Transactions on Information Forensics and Security. The researchers proposed a bicyclic encoding method for matrices and designed a series of homomorphic encrypted matrix multiplication algorithms under this encoding. These algorithms not only outperform existing methods in theory, but experimental results demonstrate an almost 40X speedup compared to the SOTA algorithms, significantly advancing the development of homomorphic encryption technologies in the field of data privacy protection.

This work was supported by the National Key R&D Program, the Western Young Scholars Program of Chinese Academy of Sciences, and the Chongqing Natural Science Foundation.