Design and implementation of high-speed scalar multiplier for multi-elliptic curve

Bin YU; Hai HUANG; Zhiwei LIU; Shilei ZHAO; Ning NA

doi:10.11959/j.issn.1000-436X.2020226

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Design and implementation of high-speed scalar multiplier for multi-elliptic curve

Papers | 更新时间：2024-06-05

- Design and implementation of high-speed scalar multiplier for multi-elliptic curve
- Journal on Communications Vol. 41, Issue 12, Pages: 100-109(2020)
- 作者机构：
  
  哈尔滨理工大学软件与微电子学院，黑龙江哈尔滨 150080
- 作者简介：
- 基金信息：
  
  The Natural Science Foundation of Heilongjiang(YQ2019F010);The University Nursing Program for Young Scholars with Creative Talents in Heilongjiang(UNPYSCT-2017081);The National Key Research and Development Program of China(2018YFB2202100)
- DOI：10.11959/j.issn.1000-436X.2020226
  CLC： TN918；TP309
- Online First：2020-12，
  
  Published：25 December 2020
- 稿件说明：
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Bin YU, Hai HUANG, Zhiwei LIU, et al. Design and implementation of high-speed scalar multiplier for multi-elliptic curve[J]. Journal on Communications, 2020, 41(12): 100-109.
DOI：

Bin YU, Hai HUANG, Zhiwei LIU, et al. Design and implementation of high-speed scalar multiplier for multi-elliptic curve[J]. Journal on Communications, 2020, 41(12): 100-109. DOI： 10.11959/j.issn.1000-436X.2020226.

摘要

针对现有标量乘法器不能适用于多椭圆曲线且运算开销较大的问题，设计了一种能应用于两类素数域椭圆曲线的高速标量乘法器。首先，在标量乘算法上，对secp256r1曲线的基点采用Comb算法，对普通点采用Shamir算法，对 Curve25519 曲线使用蒙哥马利阶梯算法；然后，优化了点加和倍点运算的操作步骤，并对点加中 Z=1的情况进行简化设计，有效减少计算周期数；最后，采用快速模约简实现模乘，设计了 Curve25519 的快速模约简算法。整个设计充分考虑复用，在55 nm CMOS工艺下需1 022×10

个等效门，在secp256r1和Curve25519上计算普通点标量乘，运算速度分别为15.3万次/秒和15.8万次/秒，其中secp256r1上的运算速度是现有设计的1.9倍。

Abstract

Aiming at the problem that the existing scalar multiplier cannot be applied to multi-elliptic curve and the cost is expensive

a high-speed scalar multiplier was designed

applicable to two types of elliptic curves over prime fields.Firstly

in terms of the scalar multiplication

secp256r1 base points were processed with the comb algorithm

and the Shamir algorithm for ordinary points

and the Montgomery ladder algorithm for Curve25519.Secondly

the operation of point addition and point doubling was optimized

and the condition of Z=1 in point addition was simplified

thereby effectively reducing the number of calculation cycles.Lastly

a fast modular reduction algorithm of Curve25519 was designed for modular multiplication.Multiplexing was an important factor in the entire designing process.A 1022K equivalent gate was selected for the 55 nm CMOS process.This allowed ordinary point scalar multiplications performed on secp256r1 and Curve25519 respectively

calculating at the speeds of 153 000 times per second and 158 000 times per second

with the speed for secp256r1 1.9 times that of the existing designed one.

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references

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