ON HARDWARE AND SOFTWARE IMPLEMENTATION OF ARITHMETIC IN FINITE FIELDS OF CHARACTERISTIC 7 FOR CALCULATION OF PAIRINGS

S. B. Gashkov; A. A. Bolotov; A. A. Burtsev; S. Yu. Zhebet; A. B. Frolov

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ON HARDWARE AND SOFTWARE IMPLEMENTATION OF ARITHMETIC IN FINITE FIELDS OF CHARACTERISTIC 7 FOR CALCULATION OF PAIRINGS

机译：特征对有限域7中算术的硬件和软件实现研究

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We study scheme (hardware) and program (software) methods of multiplication of polynomials over fields of characteristic 7 in order to apply them to pairing-based cryptographic protocols on hyperelliptic curves of genus three. We consider hardware and software implementations of arithmetic in GF(7), GF(7~2), GF(7~n), GF(7~(7n)), and GF(7~(14n)) and estimate the complexity of corresponding schemes and programs.

机译：我们研究在特征7的字段上多项式相乘的方案（硬件）和程序（软件）方法，以将其应用于属三的超椭圆曲线上的基于配对的加密协议。我们考虑GF（7），GF（7〜2），GF（7〜n），GF（7〜（7n））和GF（7〜（14n））中算术的硬件和软件实现，并估算复杂度相应的方案和程序。

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《Journal of Mathematical Sciences》 |2010年第1期|P.49-75|共27页
作者
S. B. Gashkov; A. A. Bolotov; A. A. Burtsev; S. Yu. Zhebet; A. B. Frolov;
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Lomonosov Moscow State University, Moscow, Russia;

rnLSI Corporation, Milpitas, California, USA;

rnMoscow Institute of Physics and Technology (State University), Moscow, Russia;

rnMoscow Power Engineering Institute (Technical University), Moscow, Russia;

rnMoscow Power Engineering Institute (Technical University), Moscow, Russia;

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1. A Custom Instruction Approach for Hardware and Software Implementations of Finite Field Arithmetic over F_(2~(163)) using Gaussian Normal Bases [J] . MARCIO JULIATO, GUIDO ARAUJO, JULIO LOPEZ, Journal of VLSI signal processing systems . 2007,第1期

机译：使用高斯正态基数的F_（2〜（163））上有限域算法的硬件和软件实现的自定义指令方法
2. Bit-Parallel Arithmetic Implementations over Finite Fields GF(2~m) with Reconfigurable Hardware [J] . Jose Luis Imana Acta Applicandae Mathematicae: An International Journal on Applying Mathematics and Mathematical Applications . 2002,第3期

机译：具有可重配置硬件的有限域GF（2〜m）的位并行算术实现
3. Bit-Parallel Arithmetic Implementations over Finite Fields GF(2 m ) with Reconfigurable Hardware [J] . José Luis Imaña Acta Applicandae Mathematicae . 2002,第3期

机译：具有可重配置硬件的有限域GF（2 m ）的位并行算术实现
4. On Hardware and Software Implementation of Arithmetic in Finite Fields of Characteristic 7 for Calculation of Pairings [C] . International Conference on Dependability of Computer Systems . 2009

机译：关于配对计算特性7的有限字段算法的硬件和软件实现
5. A geometric perspective on some arithmetic statistic questions over function fields over finite fields [D] . Matei, Vlad. 2017

机译：在有限字段上使用函数字段的一些算术统计问题的几何视角
6. Some fundamental groups in the arithmetic of algebraic curves over finite fields [O] . Yasutaka Ihara 1975

机译：有限域上代数曲线算法中的一些基本群
7. Software Implementation of Finite Fields of Characteristic Three, for Use in Pairing-based Cryptosystems [O] . K. Harrison, D. Page, N. P. Smart 2002

机译：软件实现特征三个特征领域，用于基于配对的密码系统

ON HARDWARE AND SOFTWARE IMPLEMENTATION OF ARITHMETIC IN FINITE FIELDS OF CHARACTERISTIC 7 FOR CALCULATION OF PAIRINGS

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