Periodica Mathematica Hungarica

, Volume 51, Issue 2, pp 75–107

Modular constructions of pseudorandom binary sequences with composite moduli

  • Joël Rivat
  • András Sárközy

DOI: 10.1007/s10998-005-0031-7

Cite this article as:
Rivat, J. & Sárközy, A. Period Math Hung (2005) 51: 75. doi:10.1007/s10998-005-0031-7


Recently, Goubin, Mauduit, Rivat and Sárközy have given three constructions for large families of binary sequences. In each of these constructions the sequence is defined by modulo <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>p$ congruences where $p$ is a prime number. In this paper the three constructions are extended to the case when the modulus is of the form $pq$ where $p$, $q$ are two distinct primes not far apart (note that the well-known Blum-Blum-Shub and RSA constructions for pseudorandom sequences are also of this type). It is shown that these modulo $pq$ constructions also have certain strong pseudorandom properties but, e.g., the (``long range'') correlation of order $4$ is large (similar phenomenon may occur in other modulo $pq$ constructions as well).

correlationbinary sequencepseudo-randomadditive character

Copyright information

© Springer-Verlag/Akadémiai Kiadó 2005

Authors and Affiliations

  • Joël Rivat
    • 1
  • András Sárközy
    • 2
  1. 1.Institut de Mathématiques de Luminy CNRS-UMR 6206 Université de la Méditerranée
  2. 2.Depart. of Algebra and Number TheoryEötvös Loránd University Department of Algebra and Number Theory