Efficient multiplication for finite fields of p characteristic

LI Yin 1; CHEN Gong-liang1; LI Jian-hua1

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Efficient multiplication for finite fields of p characteristic

更新时间：2024-10-14

- Efficient multiplication for finite fields of p characteristic
- Vol. 30, Issue 11, Pages: 101-105(2009)
- 作者机构：
  
  1. 上海交通大学信息安全工程学院
  2. 上海交通大学电信学院
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN918.1
- Published：2009
- 稿件说明：
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LI Yin 1, CHEN Gong-liang1, LI Jian-hua1. Efficient multiplication for finite fields of p characteristic[J]. 2009, 30(11): 101-105.
DOI：

LI Yin 1, CHEN Gong-liang1, LI Jian-hua1. Efficient multiplication for finite fields of p characteristic[J]. 2009, 30(11): 101-105. DOI：

摘要

基于剩余算术理论构造了一类Fp[x]上的多项式PAPB

给出了该型不可约多项式的存在数量估计;然后

利用剩余算术和中国剩余定理

提出了一种模PAPB乘法的快速实现算法;最后给出结果分析。理论和实验结果表明

在一定条件下

给出算法的计算复杂度仅有O(k1.5)

优于常用模二项式乘法O(k2)的计算复杂度。因此

该类多项式在最优扩域和椭圆曲线算法中有较好的应用前景。

Abstract

Based on residue arithmetic

a new form of polynomial named PAPB in Fp[x] had been constructed.The amount and distribution of such irreducible polynomials had also been investigated.Then

an efficient algorithm for multiplication modulo PAPB had been proposed using residue arithmetic and Chinese remainder theorem.In the end

the result analysis was given.The theoretic analysis and simulation experiment show that for some finite field of medium prime characteristic

the given algorithm only costs O（k1.5） operations in Fp while the multiplication modulo irreducible binomial cost O（k2） operations

which shows a better performance.As a result

the work presents an interesting perspective for optimal extension field and elliptic curve cryptography.

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