Version 1
: Received: 11 September 2024 / Approved: 11 September 2024 / Online: 11 September 2024 (15:27:41 CEST)
Version 2
: Received: 12 September 2024 / Approved: 12 September 2024 / Online: 12 September 2024 (11:34:53 CEST)
How to cite:
Li, Y. Area-Time Efficient High-Radix Modular Inversion Algorithm and Hardware Implementation for ECC over Prime Fields. Preprints2024, 2024090891. https://doi.org/10.20944/preprints202409.0891.v2
Li, Y. Area-Time Efficient High-Radix Modular Inversion Algorithm and Hardware Implementation for ECC over Prime Fields. Preprints 2024, 2024090891. https://doi.org/10.20944/preprints202409.0891.v2
Li, Y. Area-Time Efficient High-Radix Modular Inversion Algorithm and Hardware Implementation for ECC over Prime Fields. Preprints2024, 2024090891. https://doi.org/10.20944/preprints202409.0891.v2
APA Style
Li, Y. (2024). Area-Time Efficient High-Radix Modular Inversion Algorithm and Hardware Implementation for ECC over Prime Fields. Preprints. https://doi.org/10.20944/preprints202409.0891.v2
Chicago/Turabian Style
Li, Y. 2024 "Area-Time Efficient High-Radix Modular Inversion Algorithm and Hardware Implementation for ECC over Prime Fields" Preprints. https://doi.org/10.20944/preprints202409.0891.v2
Abstract
Modular inversion on large operands is a time-consuming calculation used in elliptic curve cryptography. Its hardware implementation requires extensive hardware resources such as lookup tables and registers. We investigate state-of-the-art modular inversion algorithms and evaluate the performance and cost of the algorithms and their hardware implementations. We then propose a high-radix modular inversion algorithm aimed at short execution time and low hardware cost. We present a detailed radix-8 hardware implementation based on 256-bit primes in Verilog HDL and compare its cost performance with other implementations. Our implementation on the Altera Cyclone V FPGA chip uses 1227 ALMs (Adaptive logic modules) and 1037 registers. The modular inversion calculation takes 3.67 microseconds. The AT (Area time) factor is 8.30, outperforming other implementations. We also present an implementation of elliptic curve cryptography using the proposed radix-8 modular inversion algorithm. The implementation results also show that our modular inversion algorithm is more efficient in area time than other algorithms.
Computer Science and Mathematics, Computer Science
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
