Multiplicative character sums of Fermat quotients and pseudorandom sequences

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 measu...

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Bibliographic Details
Published inPeriodica mathematica Hungarica Vol. 64; no. 2; pp. 161 - 168
Main Authors Gomez, Domingo, Winterhof, Arne
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2012
Subjects
Mathematics
Mathematics and Statistics
finite fields
linear complexity
11T71
correlation measure
11K45
11K36
pseudorandom sequences
discrete logarithm
11T24
94A55
Fermat quotients
character sums
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Summary: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 ℓ , and the linear complexity.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-012-3747-1