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# On the pseudorandomness of binary and quaternary sequences linked by the gray mapping

Periodica Mathematica Hungarica
Authors: Radwa Marzouk and Arne Winterhof

## Abstract

Binary and quaternary sequences are the most important sequences in view of many practical applications. Any quaternary sequence can be decomposed into two binary sequences and any two binary sequences can be combined into a quaternary sequence using the Gray mapping. We analyze the relation between the measures of pseudorandomness for the two binary sequences and the measures for the corresponding quaternary sequences, which were both introduced by Mauduit and Sárközy. Our results show that each ‘pseudorandom’ quaternary sequence corresponds to two ‘pseudorandom’ binary sequences which are ‘uncorrelated’.

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# Multiplicative character sums of Fermat quotients and pseudorandom sequences

Periodica Mathematica Hungarica
Authors: Domingo Gomez and Arne Winterhof

## Abstract

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 , and the linear complexity.

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# On a new class of inversive pseudorandom numbers for parallelized simulation methods

Periodica Mathematica Hungarica
Authors: Harald Niederreiter and Arne Winterhof
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# Linear complexity profile of binary sequences with small correlation measure

Periodica Mathematica Hungarica
Authors: Nina Brandstätter and Arne Winterhof

## Summary

A high linear complexity profile is a desirable feature of sequences used for cryptographical purposes. For a given binary sequence we estimate its linear complexity profile in terms of the correlation measure, which was introduced by Mauduit and Srkzy. We apply this result to certain periodic sequences including Legendre sequences, Sidelnikov sequences and other sequences related to the discrete logarithm.

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