通信学报2009，Vol.30Issue(11)：101-105,112,6.
P元扩域上的快速乘法
Efficient multiplication for finite fields of p characteristic
摘要
Abstract
Based on residue arithmetic, a new form of polynomial named PAPB in F_p[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(k~(1.5)) operations in F_p while the multiplication modulo irreducible binomial cost O(k~2) operations, which shows a better performance. As a result, the work presents an interesting perspective for optimal extension field and elliptic curve cryptography.关键词
密码学/不可约多项式/剩余算术/模乘Key words
cryptography/ irreducible polynomial/ residue arithmetic/ modular multiplication分类
信息技术与安全科学引用本文复制引用
李银,陈恭亮,李建华..P元扩域上的快速乘法[J].通信学报,2009,30(11):101-105,112,6.基金项目
国家自然科学基金资助项目(60672068) （60672068）
