Matrix computation over homomorphic plaintext-ciphertext and its application

Abstract

Those homomorphic encryption schemes supporting single instruction multiple data (SIMD) operations effectively enhance the amortized efficiency of ciphertext computations, yet the structure of ciphertexts leads to high complexity in matrix operations.In many applications, employing plaintext-ciphertext matrix operations can achieve privacy-preserving computing.Based on this, a plaintext-ciphertext matrix multiplication scheme for matrices of arbitrary dimension was proposed.The resulting ciphertext was computed through steps such as encoding the plaintext matrix, transforming the dimensions of the encrypted matrix, etc.Compared to the best-known encrypted matrix multiplication algorithm for square matrices proposed by Jiang et al., the proposed scheme supported matrix multiplication of arbitrary dimension, and consecutive matrix multiplications.Both theoretical analysis and experimental results show that the proposed scheme requires less rotations on ciphertexts and hence features higher efficiency.When applied to a privacy-preserving Bayesian classifier, the proposed scheme can complete classification tasks with higher security parameters and reduced running time.

Keywords

• homomorphic encryption;matrix computation;machine learning;Bayesian classifier