Multiplicative character sums of Fermat quotients and pseudorandom sequences

被引：52

作者：

Gomez, Domingo ^{[1
]}

Winterhof, Arne ^{[2
]}

机构：

[1] Univ Cantabria, E-39005 Santander, Spain

[2] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, A-4040 Linz, Austria

来源：

PERIODICA MATHEMATICA HUNGARICA | 2012年 / 64卷 / 02期

关键词：

Fermat quotients; finite fields; character sums; pseudorandom sequences; discrete logarithm; correlation measure; linear complexity; LINEAR COMPLEXITY; NUMBERS;

D O I：

10.1007/s10998-012-3747-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a bound on sums of products of multiplicative characters of shifted Fermat quotients modulo p. From this bound we derive results on the pseudorandomness of sequences of modular discrete logarithms of Fermat quotients modulo p: bounds on the well-distribution measure, the correlation measure of order a"", and the linear complexity.

引用

页码：161 / 168

页数：8

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