High-speed batch verification for discrete-logarithm-based signatures via Multi-Scalar Multiplication Algorithm

Abstract

Digital signatures are widely used in a variety of applications necessitating authentication. However, the amount of data is steadily increasing in domains like IoT, blockchain, e-commerce, etc. In such scenarios, the number of signatures could become extensive, resulting in considerable overhead in signature verification. Consequently, this bottleneck can hamper the responsiveness of transactions. Batch verification can verify numerous signatures simultaneously, effectively solving the challenge posed by the excessive overhead of verifying signatures. However, current state-of-the-art batch verification algorithms still require improvement when handling a large volume of signatures. In this paper, we propose an efficient algorithm for batch verification of discrete-logarithm-based signatures. Specifically, we propose an accelerated Multi-scalar Multiplication algorithm, which accounts for 99% cent of overheads in the batch verification process. When verifying a large number of signatures simultaneously, our algorithm significantly improves efficiency. For instance, when processing 10,000 signatures, our algorithm achieves a 3.6$\times$ speedup compared to the common algorithm. We applied our scheme to ECDSA, SM2 signature algorithm, and Schnorr signature algorithm, and simulation results show a significant improvement with our approach.