On the construction of irreducible polynomials over finite fields via odd prime degree endomorphisms of elliptic curves

Ugolini Simone

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On the construction of irreducible polynomials over finite fields via odd prime degree endomorphisms of elliptic curves

机译：椭圆曲线奇异性阶段内术中不可缩短的有限田的结构

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摘要

In this paper we present an iterative construction of irreducible polynomials over finite fields based on repeated applications of transforms induced by endomorphisms of odd prime degree of ordinary elliptic curves.

机译：本文基于普通椭圆曲线的奇数主要程度致奇异度诱导的转化诱导的转化诱导的反复应用，展现了在有限田间的迭代构造。

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来源
《Periodica Mathematica Hungarica: Journal of the Janos Bolyai Mathematical Society》 |2018年第1期|共12页
作者
Ugolini Simone;
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作者单位

Univ Trento Trento Italy;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Endomorphisms of elliptic curves; Iterative constructions; Irreducible polynomials; Finite fields;

机译：椭圆曲线的子元形;迭代结构;不可减少的多项式;有限田地;

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专利

1. On the construction of irreducible polynomials over finite fields via odd prime degree endomorphisms of elliptic curves [J] . Ugolini Simone Periodica Mathematica Hungarica: Journal of the Janos Bolyai Mathematical Society . 2018,第1期

机译：椭圆曲线奇异性阶段内术中不可缩短的有限田的结构
2. Sequences of irreducible polynomials without prescribed coefficients over odd prime fields [J] . S. Ugolini Designs, Codes and Crytography . 2015,第1期

机译：奇素域上没有规定系数的不可约多项式序列
3. Distribution of irreducible polynomials of small degrees over finite fields [J] . Ham KH., Mullen GL. Mathematics of computation . 1998,第221期

机译：有限域上小度不可约多项式的分布
4. One variable polynomial division approach for elliptic curve arithmetic over prime fields [C] . Santoshi Pote, Virendra Sule, B.K. Lande 2016 International Conference on Computing, Analytics and Security Trends . 2016

机译：素场上椭圆曲线算法的一种可变多项式除法
5. Endomorphism rings of elliptic curves over finite fields [D] . Kohel, David Russell 1996

机译：有限域上椭圆曲线的同胚环
6. Design and Realization of a Three Degrees of Freedom Displacement Measurement System Composed of Hall Sensors Based on Magnetic Field Fitting by an Elliptic Function [O] . Bo Zhao, Lei Wang, Jiu-Bin Tan 2015

机译：基于椭圆函数拟合的霍尔传感器三自由度位移测量系统的设计与实现
7. Sequences of irreducible polynomials over odd prime fields via elliptic curve endomorphisms [O] . Ugolini, Simone 2014

机译：椭圆上奇素数域上不可约多项式的序列曲线内同胚

On the construction of irreducible polynomials over finite fields via odd prime degree endomorphisms of elliptic curves

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