MAT-FHE: arbitrary dimension matrix multiplication scheme for floating point over fully homomorphic encryption

MAT-FHE: arbitrary dimension matrix multiplication scheme for floating point over fully homomorphic encryption

연구 분야: Cryptography

학회: Cybersecurity

Matrix operation is one of the most basic and practical operations in statistical analysis and machine learning. The secure matrix operation over homomorphic encryption technology can protect the confidentiality of input data. However, it has not come up with an optimal solution for modern machine learning frameworks, partially due to a lack of efficient matrix computation mechanisms. In this paper, a universal secure matrix multiplication scheme MAT-FHE for any dimension matrix over fully homomorphic encryption technology is designed to realize non-square matrix multiplication, such as \(A_{m\times l}\times B_{l\times n}\). The matrix is filled into a hypercube structure and encrypted into a single ciphertext. The number of ciphertext multiplications with the highest computational overhead is reduced through operations such as rotating by rows and columns, ciphertext addition, and multiplication of ciphertext and plaintext. After analysis, it is secure under the CPA model, composable, and supports floating matrix continuous multiplication. The CKKS algorithm of the Microsoft SEAL library is used to implement the matrix multiplication of floating point numbers in any dimension. Shared the computing overhead with SIMD technology and improved the implementation speed. In this paper, the operation time of 16-dimensional matrix multiplication is 4.2253s, which is about 1.5 times faster than the existing best square matrix multiplication scheme. The experimental results show that this method is superior to the existing secure matrix multiplication scheme and can be applied to various secure computing outsourcing and machine learning scenarios.