Multi-Curve-Oriented General High-Performance ECC Processor Design

LIU Zhi-wei; LIU Lei-bo; HUANG Hai; ZHANG Qi; YU Bin; ZHAO Shi-lei; CUI Jian-bo

doi:10.12263/DZXB.20210967

您当前的位置：

首页 >

文章列表页 >

Multi-Curve-Oriented General High-Performance ECC Processor Design

PAPERS | 更新时间：2025-12-08

- Multi-Curve-Oriented General High-Performance ECC Processor Design
- ACTA ELECTRONICA SINICA Vol. 51, Issue 6, Pages: 1562-1571(2023)
- 作者机构：
  
  1.哈尔滨理工大学，黑龙江哈尔滨 150080
  2.清华大学集成电路学院，北京 100084
- 作者简介：
- 基金信息：
  
  Special Fund for Basic Scientific Research Business Expenses of Ordinary Colleges and Universities in Heilongjiang Province of China(2019KYYWF0214)
- DOI：10.12263/DZXB.20210967
  CLC： TN492;TP309
- Received：26 July 2021，
  
  Revised：2022-06-10，
  
  Published：25 June 2023
- 稿件说明：
移动端阅览
刘志伟,刘雷波,黄海等.面向多曲线的通用高性能ECC处理器设计[J].电子学报,2023,51(06):1562-1571.

LIU Zhi-wei,LIU Lei-bo,HUANG Hai,et al.Multi-Curve-Oriented General High-Performance ECC Processor Design[J].ACTA ELECTRONICA SINICA,2023,51(06):1562-1571.
刘志伟,刘雷波,黄海等.面向多曲线的通用高性能ECC处理器设计[J].电子学报,2023,51(06):1562-1571. DOI： 10.12263/DZXB.20210967.

LIU Zhi-wei,LIU Lei-bo,HUANG Hai,et al.Multi-Curve-Oriented General High-Performance ECC Processor Design[J].ACTA ELECTRONICA SINICA,2023,51(06):1562-1571. DOI： 10.12263/DZXB.20210967.

摘要

该文针对广泛应用的TLS1.3协议，提出了一种高性能的椭圆曲线密码处理器.该处理器支持TLS1.3协议中定义的两类素数域椭圆曲线的通用模数.通过对高基蒙哥马利算法的改进，提出了一种支持521 bit及以下位宽的模乘运算单元，并提出了一种双模乘单元并行结构的标量乘法器.基于该结构在两类椭圆曲线下设计了雅阁比坐标系下并行的点运算时序排布，使模乘单元的利用率在不同点运算情况下达到100%，95.4%和86.5%.与现有设计相比，本文中标量乘法运算消耗的周期更少，运算单元利用率更高，在相似的时间面积乘积前提下，具有更强的通用性和可配置性的优势.在TSMC 55 nm CMOS工艺下达到454 MHz的时钟频率，等效逻辑门数851k，Secp256r1曲线的标量乘运算速度为31 230 times/s.

Abstract

This paper proposes a high-performance elliptic curve cryptographic processor for the widely used TLS1.3 protocol. The processor supports two types of elliptic curve with general modulus in prime field defined in TLS1.3 protocol. Firstly

by modifying the high-radix Montgomery algorithm

a modular multiplication unit is proposed

which supports less than 521-bit width operators. Secondly

a parallel scalar multiplier structure with dual-modular multipliers is proposed. Based on this structure

to make full use of the two modular multipliers

a series of point operation timing arrangement is proposed in Jacobian coordinate

which supports two types of elliptic curves

makes the utilization rate of the modular multiplication unit reach 100%

95.4% and 86.5% under different types of point operations. Compared with the existing design

the scalar multiplier in this work has a less cycle cost and less time consumption

as well as stronger versatility and configurability with similar time-area products. Under TSMC 55 nm CMOS technology

the clock frequency reaches 454 MHz. The scalar multiplication costs 851k equivalent logic gates

and the calculation speed of Secp256r1 curve is 31 230 times/s.

关键词

Keywords

references

RESCORLA E . The Transport Layer Security (TLS) Protocol Version 1.3: RFC 8446 [S]. Fremont : IETF Trust , 2018 .

IEEE . IEEE Standard Specifications for Public Key Cryptography: IEEE 1363-2000 [S]. Piscataway : IEEE , 2000 .

LANGLEY A . Elliptic Curves for Security: RFC 7748 [S]. Fremont : IETF Trust , 2016 .

ANANYI K , ALRIMEIH H , RAKHMATOV D . Flexible hardware processor for elliptic curve cryptography over NIST prime fields [J]. IEEE Transactions on Very Large Scale Integration (VLSI) Systems , 2009 , 17 ( 8 ): 1099 - 1112 .

LOI K C C , KO S B . Scalable elliptic curve cryptosystem FPGA processor for NIST prime curves [J]. IEEE Transactions on Very Large Scale Integration (VLSI) Systems , 2015 , 23 ( 11 ): 2753 - 2756 .

SHAH Y A , JAVEED K , AZMAT S , et al . A high-speed RSD-based flexible ECC processor for arbitrary curves over general prime field [J]. International Journal of Circuit Theory and Applications , 2018 , 46 ( 10 ): 1858 - 1878 .

DING J N , LI S G . A reconfigurable high-speed ECC processor over NIST primes [C]// 2017 IEEE Trustcom/BigDataSE/ICESS . Sydney : IEEE , 2017 : 1064 - 1069 .

DING J N , LI S G , GU Z . High-speed ECC processor over NIST prime fields applied with toom-cook multiplication [J]. IEEE Transactions on Circuits and Systems I: Regular Papers , 2019 , 66 ( 3 ): 1003 - 1016 .

BERNSTEIN D J . Curve25519: New Diffie-Hellman speed records [M]// Public Key Cryptography - PKC 2006 . Berlin : Springer , 2006 : 207 - 228 .

COHEN H , MIYAJI A , ONO T . Efficient elliptic curve exponentiation using mixed coordinates [M]// Lecture Notes in Computer Science . Berlin : Springer , 1998 : 51 - 65 .

仲先海 . 并行可配置ECC协处理器关键技术研究 [D]. 郑州 : 解放军信息工程大学 , 2008 .

ZHONG X H . Research of Key Techniques on a Parallel and Reconfigurable ECC Coprocessor [D]. Zhengzhou : PLA Information Engineering University , 2008 . (in Chinese)

刘哲 , 王伊蕾 , 徐秋亮 . 最优素数域的优化蒙哥马利算法: 设计、分析与实现 [J]. 密码学报 , 2014 , 1 ( 2 ): 167 - 179 .

LIU Z , WANG Y L , XU Q L . Optimized Montgomery algorithms for optimal prime fields: Design, analysis and implementation [J]. Journal of Cryptologic Research , 2014 , 1 ( 2 ): 167 - 179 . (in Chinese)

MONTGOMERY P L . Modular multiplication without trial division [J]. Mathematics of Computation , 1985 , 44 ( 170 ): 519 - 521 .

BARRETT P . Implementing the Rivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor [M]// Advances in Cryptology - CRYPTO'86 . Berlin : Springer , 2007 : 311 - 323 .

KAYA KOC C , ACAR T , KALISKI B S . Analyzing and comparing Montgomery multiplication algorithms [J]. IEEE Micro , 1996 , 16 ( 3 ): 26 - 33 .

ELDRIDGE S E , WALTER C D . Hardware implementation of Montgomery's modular multiplication algorithm [J]. IEEE Transactions on Computers , 1993 , 42 ( 6 ): 693 - 699 .

HANKERSON D , MENEZES A J , VANSTONE S . Guide to Elliptic Curve Cryptography [M]. New York : Springer , 2004 .

CHOI P , LEE M K , KIM J H , et al . Low-complexity elliptic curve cryptography processor based on configurable partial modular reduction over NIST prime fields [J]. IEEE Transactions on Circuits and Systems II: Express Briefs , 2018 , 65 ( 11 ): 1703 - 1707 .

HOSSAIN M S , KONG Y N , SAEEDI E , et al . High-performance elliptic curve cryptography processor over NIST prime fields [J]. IET Computers & Digital Techniques , 2017 , 11 ( 1 ): 33 - 42 .

LEE J W , CHUNG S C , CHANG H C , et al . Efficient power-analysis-resistant dual-field elliptic curve cryptographic processor using heterogeneous dual-processing-element architecture [J]. IEEE Transactions on Very Large Scale Integration (VLSI) Systems , 2014 , 22 ( 1 ): 49 - 61 .

CHUNG S C , LEE J W , CHANG H C , et al . A high-performance elliptic curve cryptographic processor over GF(p) with SPA resistance [C]// 2012 IEEE International Symposium on Circuits and Systems (ISCAS) . Seoul : IEEE , 2012 : 1456 - 1459 .

黎明 , 吴丹 , 戴葵 , 等 . 高性能可扩展公钥密码协处理器研究与设计 [J]. 电子学报 , 2011 , 39 ( 3 ): 665 - 670 .

LI M , WU D , DAI K , et al . Research and design of a high-performance scalable public-key cipher coprocessor [J]. Acta Electronica Sinica , 2011 , 39 ( 3 ): 665 - 670 . (in Chinese)

CUI C , ZHAO Y , XIAO Y , et al . A hardware-efficient elliptic curve cryptographic architecture over GF(p) [J]. Mathematical Problems in Engineering , 2021 , 2021 : 1 - 7 .

HU X H , ZHENG X , ZHANG S S , et al . A low hardware consumption elliptic curve cryptographic architecture over GF(p) in embedded application [J]. Electronics , 2018 , 7 ( 7 ): 104 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Research on Efficient Implementation of SM2 for Mobile Devices

The Algorithm of New Five Elements Joint Sparse Form and Its Applications

Montgomery Modular Inversion Algorithm Based on Signed Digit System and Hardware Implementation

Related Author

LIU Zhe

YU Xuan

HUANG Jun-hao

ZHANG Ji-peng

WANG Nian-ping

CHEN Lin

SUN Wan-zhong

CHEN Xing-yuan

Related Institution

College of Computer Science and Technology， Nanjing University of Aeronautics and Astronautics

Hong Kong Baptist University

BNU-HKBU United International College

Zhejiang Laboratory

Institute of Electronic Technology, the PLA Information Engineering University

⁰