基于余数系统RSA密码算法快速实现

莫一奉; 李树国

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基于余数系统RSA密码算法快速实现

更新时间：2026-09-04

- 基于余数系统RSA密码算法快速实现
- Fast Implementation of RSA Algorithm Based on RNS
- 微电子学与计算机 2017年34卷第11期页码：11-15
- 作者机构：
  
  清华大学微电子学研究所,北京,100084
- 作者简介：
- 基金信息：
  
  国家自然科学基金项目 61674086
- DOI：
  中图分类号：
- 纸质出版：2017
- 稿件说明：
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莫一奉, 李树国. 基于余数系统RSA密码算法快速实现[J]. 微电子学与计算机, 2017, 34(11): 11-15.

MO Yi-feng, LI Shu-guo. Fast Implementation of RSA Algorithm Based on RNS[J]. 2017, 34(11): 11-15.
莫一奉, 李树国. 基于余数系统RSA密码算法快速实现[J]. 微电子学与计算机, 2017, 34(11): 11-15. DOI：

MO Yi-feng, LI Shu-guo. Fast Implementation of RSA Algorithm Based on RNS[J]. 2017, 34(11): 11-15. DOI：

摘要

本文基于余数系统实现了RSA密码算法.为每一个计算单元选择形式相近的四个模

基于这四个模的约减单元比常规方法选模对应的约减单元所需要面积更小

延时而更短.按照本文提出的方法选模

选了7组共28个位宽为74的模

应用这些模基于Cox-Rower结构设计了余数系统蒙哥马利模乘器

实现RSA密码算法.在SMIC 0.13 m标准单元库下进行综合

设计的RSA电路最高频率278 MHz.在该频率下

中国剩余定理模式下的1 024、2 048位RSA以及常规模式下1 024位RSA解密分别需要710 s、99 s、350 s

快于已发表的同类设计.

Abstract

In this paper

we implement RSA cryptographic using Residue number system (RNS). We choose four modulo similar in the form for every computational unit. The reduction unit supports these four modulo is smaller and shorter than the required reduction unit corresponding to the conventional method selection. According to our proposed method

we select seven groups of modulo with a width of 74

and design a RNS Montgomery multiplier based on Cox-Rower architecture to implement RSA cryptography. In the SMIC 0.13 m standard cell library

clock frequency reaches up to 278 MHz. At this frequency

1 024

2 048-bit RSA decryption in Chinese Remainder Theorem (CRT) mode and 1 024-bit RSA decryption require 710 s

99 s

350 s

respectively

faster than the published related designs.

关键词

Keywords

references

Shieh M D, Chen J H, Wu H H, et al. A new modular exponentiation architecture for efficient design of RSA cryptosystem[J]. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2008, 16(9): 1151-1161. DOI: 1151

Kawamura S, Koike M, Sano F, et al. Cox-rower architecture for fast parallel montgomery multiplication[C]// Advances in Cryptology - EUROCRYPT 2000, International Conference on the Theory and Application of Cryptographic Techniques. Bruges, Belgium, 2000: 523-538.

Montgomery P L. Modular multiplication without trial division[J]. Mathematics of Computation, 1985, 44(17): 519-521. DOI: 519

Néto J C, Tenca A F, Ruggiero W V. CRT RSA decryption: modular exponentiation based solely on montgomery multiplication[C]//Signals, Systems and Computers, 2015 49th Asilomar Conference on. Pacific Grove, CA, USA, IEEE, 2015: 431-436.

Nozaki H, Motoyama M, Shimbo A, et al. Implementation of RSA algorithm based on RNS montgomery multiplication[C]//International Workshop on Cryptographic Hardware and Embedded Systems. Springer, Berlin, Heidelberg, 2001: 364-376.

Rivest R L, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems[J]. Communications of the ACM, 1978, 21(2): 120-126. DOI: 120

Gandino F, Lamberti F, Paravati G, et al. An algorithmic and architectural study on Montgomery exponentiation in RNS[J]. IEEE Transactions on Computers, 2012, 61(8): 1071-1083. DOI: 1071

麻永新, 曾晓洋, 吴敏, 等. 基于Barrett模乘算法的RSA密码协处理器设计[J]. 系统工程与电子技术, 2006, 28(6): 830-833. DOI: 830

Tao W U, Shuguo L I, Liu L T. Fast RSA decryption through high-radix scalable montgomery modular multipliers[J]. Science China Information Sciences, 2015, 58(6): 1-16. DOI: 1

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