Explicit formulae of polynomial basis squarer for pentanomials using weakly dual basis

Sun-Mi Park

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Explicit formulae of polynomial basis squarer for pentanomials using weakly dual basis

机译：五项式多项式基平方的显式使用弱对偶基

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I present a new method to compute a bit-parallel polynomial basis squarer for GF(2~m) generated by an arbitrary irreducible polynomial using weakly dual basis. I apply the proposed method to irreducible pentanomial and derive the explicit formulae for squarer. It is the first time that gives the explicit formulae and an upper complexity bound of squarer for irreducible pentanomials. Moreover, such formulae permit one to choose pentanomial for any odd me[19,2000] whose multiplier, as well as squarer, can be performed more efficiently.

机译：我提出了一种新的方法来计算使用弱对偶基由任意不可约多项式生成的GF（2〜m）的位并行多项式基平方。我将提出的方法应用于不可约的五项式，并推导了平方器的显式公式。这是第一次为不可归约的五项式给出明确的公式和平方的上限。而且，这样的公式允许人们为任何奇数我选择五项式[19,2000]，其乘数和平方可以更有效地执行。

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来源
《Integration》 |2012年第2期|p.205-210|共6页
作者
Sun-Mi Park;
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作者单位

KAIST, Department of Mathematics, 373-1 Cuseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
finite field arithmetic; pentanomials; bit-parallel squarer; polynomial basis; weakly dual basis;

机译：有限域算法五旬期位平行平方器多项式基础弱对偶;

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1. Explicit formulae for Mastrovito matrix and its corresponding Toeplitz matrix for all irreducible pentanomials using shifted polynomial basis [J] . Park Sun-Mi, Chang Ku-Young, Hong Dowon, Integration . 2016,第Mara期

机译：使用移位多项式基础的所有不可约五项式的Mastrovito矩阵及其对应的Toeplitz矩阵的显式公式
2. Fast Bit-Parallel Polynomial Basis Multiplier for GF(2~m) Defined by Pentanomials Using Weakly Dual Basis [J] . Sun-Mi PARK, Ku-Young CHANG, Dowon HONG, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences . 2013,第1期

机译：由五项式使用弱对偶基定义的GF（2〜m）快速位并行多项式基乘
3. GF(2n) bit-parallel squarer using generalised polynomial basis for new class of irreducible pentanomials [J] . Xi Xiong, Haining Fan Electronics Letters . 2014,第9期

机译：使用广义多项式基础的GF（2 n ）位并行平方器用于新型不可约五项式
4. Faster Polynomial Basis Finite Field Squaring and Inversion for GF(2{sup}m) With Cryptographic Software Application [C] . Athar Mahboob, Nassar Ikram International Symposium on Biometrics and Security Technologies . 2008

机译：具有加密软件应用的GF（2 {SUP} M）的多项式基础有限场平方和反转
5. An explicit proof of the weak finite basis theorem and applications to computing ranks of elliptic curves. [D] . Sharon, Zachery A. 2011

机译：弱有限基定理的明确证明及其在椭圆曲线秩计算中的应用。
6. Inhomogeneous basis set of symmetric polynomials defined by tableaux. [O] . L C Biedenharn, J D Louck 1990

机译：tableaux定义的对称多项式的不均匀基集。
7. High-speed polynomial basis multipliers over GF(2(m)) for special pentanomial. [O] . Imaña Pascual José Luis 2016

机译：特殊五项式在GF（2（m））上的高速多项式基乘数。

Explicit formulae of polynomial basis squarer for pentanomials using weakly dual basis

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