Hardware Implementation and Optimization of Critical Modules of SM9 Digital Signature Algorithm

SM9 is an identity-based cryptographic algorithm based on elliptic curves, which has high security and low management costs. However, its computational complexity restricts its development and application. This paper implements and optimizes the critical modules of SM9 digital signature algorithm based on FPGA. We simplify modular addition and subtraction, avoiding the use of large number comparators and saving approximately 50% of LUTs compared to traditional methods. The modular multiplication adopts the Montgomery modular multiplication algorithm, which only takes 0.24 \(\upmu \) s to realize modular multiplication operation on \(F_p\) . For complex modules, this paper analyzes the dependency relationship between calculations and parallelizes irrelevant operations to improve the parallelism within and between modules at different levels, greatly reducing the number of computation cycles required. In addition, this paper utilizes multiplexers to achieve resource reuse while ensuring computational performance. This research is not only of great significance for the high-performance implementation of SM9, but also has reference value for the implementation of other cryptographic algorithms based on elliptic curves.