High-Performance Elliptic Curve Scalar Multiplication Architecture Based on Interleaved Mechanism

Abstract

High-performance (HP) elliptic curve scalar multiplication (ECSM) hardware implementations hold significant importance in ensuring communication security in high-capacity and high-concurrence application scenarios. By analyzing the inherent priorities and parallelism in ECSMs, we proposed a novel HP ECSM algorithm and a partially parallel inversion algorithm based on the interleaved mechanism. With two dedicated multipliers and one interleaved multiplier, we introduced a compact hardware scheduling scheme to realize the consumption of four clock cycles within each loop of ECSM. The proposed HP ECSM architecture consists of two Karatsuba-Ofman multipliers (KOMs) and one classical multiplier (CM). The multiplexors and pipeline stages are meticulously designed to optimize the critical path (CP). The proposed architecture is implemented over Virtex-7 field-programmable gate array (FPGA), and the throughput reaches 158.03, 138.23, and 117.50 Mbps over $\text {GF}(2^{163})$ , $\text {GF}(2^{283})$ , and $\text {GF}(2^{571})$ using 8762, 20451, and 41974 slices, respectively. The comparisons with recent existing works demonstrate that the performance and throughput of our design are among the top.