TY - GEN
T1 - Hardware Implementation and Optimization of Critical Modules of SM9 Digital Signature Algorithm
AU - Shao, Yujie
AU - Chen, Tian
AU - Li, Ke
AU - Liu, Lu
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
PY - 2024
Y1 - 2024
N2 - 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 μ s to realize modular multiplication operation on Fp. 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.
AB - 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 μ s to realize modular multiplication operation on Fp. 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.
KW - FPGA
KW - Miller loop
KW - Montgomery modular multiplication
KW - R-ate bilinear pairing
KW - SM9
UR - http://www.scopus.com/inward/record.url?scp=85185704004&partnerID=8YFLogxK
U2 - 10.1007/978-981-99-9785-5_26
DO - 10.1007/978-981-99-9785-5_26
M3 - Conference contribution
AN - SCOPUS:85185704004
SN - 9789819997848
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 368
EP - 381
BT - Artificial Intelligence Security and Privacy - 1st International Conference on Artificial Intelligence Security and Privacy, AIS and P 2023, Proceedings
A2 - Vaidya, Jaideep
A2 - Gabbouj, Moncef
A2 - Li, Jin
PB - Springer Science and Business Media Deutschland GmbH
T2 - 1st International Conference on Artificial Intelligence Security and Privacy, AIS and P 2023
Y2 - 3 December 2023 through 5 December 2023
ER -
