Innovative Dual-Binary-Field Architecture for Point Multiplication of Elliptic Curve Cryptography

High-performance Elliptic Curve Cryptography (ECC) implementation in encryption authentication severs has become a challenge due to the explosive growth of e-commerce’s demand for speed and security. Point multiplication (PM) is the most common and complex operation in ECC which directly determines the performance of the whole system. This article proposes a 6CC-6CC (clock cycle) dual-field PM architecture and a 6CC-4CC dual-field PM architecture based on maximizing utilization of Karatsuba multipliers and re-ordering schedule strategy in PM. The Montgomery Ladder algorithm used in PM is modified to a 4CC algorithm for better resource utilization and parallel computation. To solve the frequency drop problem while working on large finite field, the PM architectures for high and low field are carefully studied to have universal critical path length and balanced performance. Both of the architectures are implemented over GF(2
⁵⁷¹
) and GF(2
²⁸³
) on Xilinx Virtex-5 and Virtex-7 FPGAs (Field-Programmable Gate Array) for comparison. The 6CC-6CC architecture is shown to have the best performance on GF(2
⁵⁷¹
), which achieves one PM operation in
$17.44~\mu s$
using 81549 LUTs (Look-Up-Table) with the frequency of 197.2 MHz on Virtex-5, and
$12.55~\mu s$
using 80970 LUTs with the frequency of 274.1 MHz on Virtex-7. The 6CC-4CC architecture performs better on GF(2
²⁸³
) with the shortest computation time. It takes only
$3.21~\mu s$
to finish one PM operation on Virtex-5 and
$2.22~\mu s$
on Virtex-7, which are faster than all the previous designs. The implementation results prove that the proposed architectures have state-of-the-art performance as well as higher versatility for ECC designs.