An Efficient SM9 Aggregate Signature Scheme for IoV Based on FPGA

With the rapid development of the Internet of Vehicles (IoV), the demand for secure and efficient signature verification is becoming increasingly urgent. To meet this need, we propose an efficient SM9 aggregate signature scheme implemented on Field-Programmable Gate Array (FPGA). The scheme includes both fault-tolerant and non-fault-tolerant aggregate signature modes, which are designed to address challenges in various network environments. We provide security proofs for these two signature verification modes based on a K-ary Computational Additive Diffie-Hellman (K-CAA) difficult problem. To handle the numerous parallelizable elliptic curve point multiplication operations required during verification, we utilize FPGA's parallel processing capabilities to design an efficient parallel point multiplication architecture. By the Montgomery point multiplication algorithm and the Barrett modular reduction algorithm, we optimize the single-point multiplication computation unit, achieving a point multiplication speed of 70776 times per second. Finally, the overall scheme was simulated and analyzed on an FPGA platform. The experimental results and analysis indicate that under error-free conditions, the proposed non-fault-tolerant aggregate mode reduces the verification time by up to 97.1% compared to other schemes. In fault-tolerant conditions, the proposed fault-tolerant aggregate mode reduces the verification time by up to 77.2% compared to other schemes. When compared to other fault-tolerant aggregate schemes, its verification time is only 28.9% of their consumption, and even in the non-fault-tolerant aggregate mode, the verification time is reduced by at least 39.1%. Therefore, the proposed scheme demonstrates significant advantages in both error-free and fault-tolerant scenarios.