Privacy-Preserving Verifiable Matrix Multiplication With Reduced Critical Dimension for Intelligent Connected Vehicles

In intelligent connected vehicle applications, tasks, such as path planning and health management involve numerous matrix operations, particularly matrix multiplication. Due to limited resources, these tasks are often outsourced to the edge server. However, outsourcing these tasks involving matrix multiplication might incur potential risks, such as returning incorrect results to expedite processing or even exposing sensitive data during the computation. Privacy-preserving verifiable matrix multiplication schemes address these concerns. However, it is meaningful in practice only if the verification and decoding time is lower than that of local computation. In this article, we propose a privacy-preserving verifiable matrix multiplication for intelligent connected vehicles that further reduces the verification and decoding time. To achieve this, we first reduce the length of the ciphertext of linearly homomorphic encryption (LHE) when encrypting a group of messages. Subsequently, we construct our verifiable matrix multiplication scheme based on the improved LHE. It has a lower critical dimension than the state-of-the-art scheme with a similar security level, since the shorter ciphertext and the simpler LHE algorithm. Performance analysis and experimental results demonstrate that the critical dimensions of our improved scheme are reduced by 23.3%, while the communication cost is reduced by 68.3%, making it particularly suitable for intelligent connected vehicle applications.