An Optimal Normal Basis Type Ⅱ Multiplier over GF(2<sup>n</sup>) for FPGAs

FANG Bing; FAN Hai-ning; DAI Yi-qi

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An Optimal Normal Basis Type Ⅱ Multiplier over GF(2ⁿ) for FPGAs

更新时间：2025-07-16

- An Optimal Normal Basis Type Ⅱ Multiplier over GF(2ⁿ) for FPGAs
- Acta Electronica Sinica Vol. 30, Issue S1, Pages: 2045-2048(2002)
- 作者机构：
  
  清华大学计算机科学与技术系网络所,北京,100084
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN47
- Published：2002
- 稿件说明：
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FANG Bing, FAN Hai-ning, DAI Yi-qi. An Optimal Normal Basis Type Ⅱ Multiplier over GF(2ⁿ) for FPGAs[J]. Acta Electronica Sinica, 2002, 30(S1): 2045-2048.
DOI：

FANG Bing, FAN Hai-ning, DAI Yi-qi. An Optimal Normal Basis Type Ⅱ Multiplier over GF(2ⁿ) for FPGAs[J]. Acta Electronica Sinica, 2002, 30(S1): 2045-2048. DOI：

摘要

有限域GF(2

)上的椭圆曲线密码体制以其密钥短

安全强度高的优点正在获得广泛的重视和应用.该密码体制最主要的运算是有限域上的乘法运算.本文提出了一种基于Ⅱ型优化正规基的乘法器

该乘法器具有Massey-Omura乘法器的优点

又避免了其不足

易于编程

适合FPGA实现.实验表明

该算法简单

快速.

Abstract

The elliptic curve cryptosystems over the fiute field GF(2

) receive considerable attention and are widely used because of their small key size and high security. Multiplication operation over the finite field GF(2

) is the crucial arithmetic operation. This paper presents a multiplication algorithm for the optimal normal basis type Ⅱ. The algorithm has the advantage of Massey-Omura multiplication algorithm and eliminate its deficiency.The test shows that this algorithm is simple

fast and is easy to be implemented by FPGA.

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Department of Electronics EngineeringSoutheast UniversityNanjing 210096China

Institute of Electronic Technology,the PLA University of Information Engineering

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An Optimal Normal Basis Type Ⅱ Multiplier over GF(2n) for FPGAs

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摘要

Abstract

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An Optimal Normal Basis Type Ⅱ Multiplier over GF(2ⁿ) for FPGAs