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Construction of pseudorandom binary lattices based on multiplicative characters

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Abstract

In this paper a large family of pseudorandom binary lattices is constructed by using the multiplicative characters of finite fields. This construction generalizes several one-dimensional constructions to arbitrary dimensions.

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References

  1. L. Goubin, C. Mauduit and A. Sárközy, Construction of large families of pseudorandom binary sequences, J. Number Theory, 106 (2004), 56–69.

    Article  MATH  MathSciNet  Google Scholar 

  2. K. Gyarmati, A note to the earlier paper “On a fast version of a pseudorandom generator”, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 49 (2006), 87–93.

    MATH  MathSciNet  Google Scholar 

  3. K. Gyarmati, On a family of pseudorandom binary sequences, Period. Math. Hungar., 49 (2004), 45–63.

    Article  MATH  MathSciNet  Google Scholar 

  4. K. Gyarmati, On a fast version of a pseudorandom generator, General Theory of Information Transfer and Combinatorics, Lecture Notes in Computer Science 4123, Springer, Heidelberg, 2006, 326–342.

    Google Scholar 

  5. K. Gyarmati, C. Mauduit and A. Sárközy, Construction of pseudorandom binary lattices, submitted.

  6. K. Gyarmati, A. Sárközy and C. L. Stewart, On Legendre symbol lattices, submitted.

  7. P. Hubert, C. Mauduit and A. Sárközy, On pseudorandom binary lattices, Acta Arith., 125 (2006), 51–62.

    Article  MATH  MathSciNet  Google Scholar 

  8. C. Mauduit, J. Rivat and A. Sárközy, Construction of pseudorandom binary sequence using additive characters, Monatsh. Math., 141 (2004), 197–208.

    Article  MATH  MathSciNet  Google Scholar 

  9. C. Mauduit and A. Sárközy, On large families of pseudorandom binary lattices, Unif. Distrib. Theory, 2 (2007), 23–37.

    MATH  MathSciNet  Google Scholar 

  10. C. Mauduit and A. Sárközy, Construction of pseudorandom binary lattices by using the multiplicative inverse, Monatsh. Math., 153 (2008), 217–231.

    Article  MATH  MathSciNet  Google Scholar 

  11. C. Mauduit and A. Sárközy, Construction of pseudorandom binary sequences by using the multiplicative inverse, Acta Math. Hungar., 108 (2005), 239–252.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Mauduit and A. Sárközy, On finite pseudorandom binary sequences I: Measures of pseudorandomness, the Legendre symbol, Acta Arith., 82 (1997), 365–377.

    MATH  MathSciNet  Google Scholar 

  13. L. Mérai, Construction of large families of pseudorandom binary sequences, Ramanujan J., to appear.

  14. S. M. Oon, Construction des suites binaires pseudo-aléatories, PhD thesis, Nancy, 2005.

  15. S. M. Oon, On pseudo-random properties of certain Dirichlet series, Ramanujan J., 15 (2008), 19–30.

    Article  MATH  MathSciNet  Google Scholar 

  16. A. Sárközy, A finite pseudorandom binary sequence, Studia Sci. Math. Hungar., 38 (2001), 377–384.

    MATH  MathSciNet  Google Scholar 

  17. A. Sárközy, On finite pseudorandom binary sequences and their applications in cryptography, Tatra Mt. Math. Publ., 37 (2007), 123–136.

    MATH  Google Scholar 

  18. A. Winterhof, Some estimates for character sums and applications, Des. Codes Crytogr., 22 (2001), 123–131.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Algebra and Number Theory, Eötvös Loránd University, 1117, Budapest, Pázmány Péter sétány 1/c, Hungary

    László Mérai

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  1. László Mérai
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Correspondence to László Mérai.

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Communicated by Attila Pethő

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Mérai, L. Construction of pseudorandom binary lattices based on multiplicative characters. Period Math Hung 59, 43–51 (2009). https://doi.org/10.1007/s10998-009-9043-z

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  • DOI: https://doi.org/10.1007/s10998-009-9043-z

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