An area-efficient ECC architecture over GF([formula omitted]) for resource-constrained applications

Abstract

Elliptic Curve Cryptography (ECC), an asymmetric-key cryptographic system, received extensive research and industry recognition owing to its reliable security with relatively smaller key sizes. It is most effective with resource-constrained applications. The very intensive function in ECC is point-multiplication. In this article, we propose a novel architecture for elliptic curve point-multiplication based on modified Lopez–Dahab–Montgomery(LDM) point-multiplication algorithm to achieve a reduction in hardware complexity and time complexity. The proposed architectural data-path is pipelined and organized to realize finite-field operations i.e., FF-multiplication and FF-square operations, in parallel to reduce the critical-path delay. The FF-operations are scheduled to perform each iteration of point-addition(PA) and point-doubling(PD) operations in eight clock-cycles without data-dependency. The elliptic curve-point-multiplication(ECPM) implementation over the National Institute of Standards and Technology(NIST) recommended binary curve GF(2163) shows that the proposed design achieves point-multiplication in 3.71μs utilizing 8529 LUTs on Xilinx Virtex-7 FPGA. In addition the design achieves an improvement of 36%, 32%, and 39% area-time efficiency when compared to the best existing designs in the literature when implemented over GF(2163), GF(2233) and GF(2283) respectively.