A Hybrid Approach for Efficient and Secure Point Multiplication on Binary Edwards Curves

Abstract

The focus of this article is to present a novel crypto-accelerator architecture for a resource-constrained embedded system that utilizes elliptic curve cryptography (ECC). The architecture is built around Binary Edwards curves (BEC) to provide resistance against simple power analysis (SPA) attacks. Furthermore, the proposed architecture incorporates several optimizations to achieve efficient hardware resource utilization for the point multiplication process over GF(2m). This includes the use of a Montgomery radix-2 multiplier and the projective coordinate hybrid algorithm (combination of Montgomery ladder and double and add algorithm) for scalar multiplication. A two-stage pipelined architecture is employed to enhance throughput. The design is modeled in Verilog HDL and verified using Vivado and ISE design suites from Xilinx. The obtained results demonstrate that the proposed BEC accelerator offers significant performance improvements compared to existing solutions. The obtained throughput over area ratio for GF(2233) on Virtex-4, Virtex-5, Virtex-6, and Virtex-7 Xilinx FPGAs are 9.43, 14.39, 26.14, and 28.79, respectively. The computation time required for a single point multiplication operation on the Virtex-7 device is 19.61 µs. These findings indicate that the proposed architecture has the potential to address the challenges posed by resource-constrained embedded systems that require high throughput and efficient use of available resources.

Keywords

• elliptic curve cryptography
• binary Edwards curve
• scalar multiplication
• Montgomery radix-4 multiplier
• FPGA