Verifiable computation scheme of batch matrix multiplication based on triple perturbation and linear combination

Abstract

With the development of cloud computing and internet of things technology, verifiable computing has been widely used as a new computing technology. While verifiable computing brings convenience to users, there are also security challenges: data privacy, verifiability of results, and efficiency. At present, the sparse matrix multiplication encryption method is used to protect the privacy of data in the matrix multiplication verifiable calculation scheme. After analyzing the sparse matrix encryption algorithm, it is found that there are two challenges. The one is that the row or column common factor leaks the row or column data of the original matrix. The other is that the zero element leaks the statistic information of the zero element of the original matrix. Meanwhile,the existing scheme is also not ideal for the verification efficiency of cloud server computing results.Aiming at the challenge of data privacy protection, the designed batch matrix multiplication verifiable computation scheme uses triple perturbation encryption algorithm to achieve stronger privacy protection without increasing the computational complexity of encryption and decryption. Specifically, a special upper or lower triangular sparse matrix is constructed to add double perturbation (multiplicative perturbation and additive perturbation) to protect row or column data, and a special additive sparse matrix is constructed to add a single perturbation (additive perturbation) to protect zero element information. Aiming at the challenge of verification efficiency of cloud server computing results, the scheme uses matrix linear combination technology to realize batch verification of calculation results. The verification efficiency is increased by about 50 times and increases with the increase of the number of matrices. Performance analysis shows that this scheme does not increase the client encryption and decryption overhead and improves the efficiency of result verification.

Keywords

• triple perturbation
• linear combination
• enhanced privacy
• improved efficiency
• verifiable computation