上海交通大学学报(自然版) ›› 2012, Vol. 46 ›› Issue (11): 1741-1745.

• 自动化技术、计算机技术 • 上一篇    下一篇

一种GF(3m)上立方运算电路的优化设计方法

汪小丁, 曹珍富   

  1. (上海交通大学 计算机科学与工程系, 上海 200240)
  • 收稿日期:2011-12-15 出版日期:2012-11-30 发布日期:2012-11-30
  • 基金资助:

    国家自然科学基金重点项目(61033014),国家自然科学基金项目(60970110,60972034)

A New Method for Optimizing Cubic Arithmetic Circuit in GF(3m)

 WANG  Xiao-Ding, CAO  Zhen-Fu   

  1. (Department of Computer Science and Engineering, Shanghai Jiaotong University,Shanghai 200240, China)
  • Received:2011-12-15 Online:2012-11-30 Published:2012-11-30

摘要: 提出了一个能优化GF(3m)上立方运算电路的浓缩法方法.采用该方法处理了580种GF(3m)有限域上立方运算电路,统计数据表明:若不可约多项式形如xm+ptxt+x0,m<256,除极少数情况外,浓缩法优化后的立方运算电路的加法器不超过1.35m个.给出212个不可约多项式,用浓缩法优化后的立方运算电路的加法器数量不超过m个.  

关键词: Tate配对, 有限域, 立方运算, 电路设计, 优化

Abstract: This paper proposed a new method for generating an optimized circuit for cubic arithmetic in Galois field GF(3m). After applying the method on 580 different cubic arithmetic circuits in Galois field GF(3m), the statistical data shows that for xm+ptxt+x0,m<256 most  irreducible polynomials, our method can generate a cubic arithmetic circuit with less than  1.35m adders. For 212 irreducible polynomials, our method can generate a cubic arithmetic circuit with less than m adders.  

Key words: Tate pairing, Galois field, cubic arithmetic, circuit design, optimization

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