Advertisement

On Pseudorandom Sequences and Their Application

  • J. Rivat
  • András Sárközy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)

Abstract

A large family of finite pseudorandom binary sequences is presented, and also tested “theoretically” for pseudorandomness. The optimal way of implementation is discussed and running time analysis is given. Numerical calculations are also presented.

Keywords

Binary Sequence Pseudorandom Sequence Primitive Root Riemann Hypothesis Legendre Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahlswede, R., Khachatrian, L., Mauduit, C., Sárközy, A.: A complexity measure for families of binary sequences. Periodica Mathematica Hungarica 46, 107–118 (2003)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Blum, L., Blum, M., Shub, M.: A simple unpredictable pseudorandom number generator. SIAM Journal on Computing 15, 364–383 (1986)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudorandom bits. SIAM Journal on Computing 13, 850–864 (1984)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Burgess, D.A.: The distribution of quadratic residues and non residues. Mathematika 4, 106–112 (1957)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cassaigne, J., Mauduit, C., Sárközy, A.: On finite pseudorandom binary sequences VII: The measures of pseudorandomness. Acta Arithmetica 103, 97–118 (2002)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Goubin, L., Mauduit, C., Sárközy, A.: Construction of large families of pseudorandom binary sequences. Journal of Number Theory 106, 56–69 (2004)CrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    Gyarmati, K.: On a pseudorandom property of binary sequences. Ramanujan J. 8(3), 289–302 (2004)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Heath-Brown, D.R.: Artin’s conjecture for primitive roots. Quarterly Journal of Math. 37, 27–38 (1986)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hooley, C.: On Artin’s conjecture. J. reine angew. Math. 226, 209–220 (1967)CrossRefGoogle Scholar
  10. 10.
    Hooley, C.: Application of Sieve Methods to the Theory of Numbers, Cambridge Tracts in Mathematics (1970)Google Scholar
  11. 11.
    Knuth, D.E.: The Art of Computer Programming, 2nd edn., vol. 2. Addison Wesley, Reading (1981)MATHGoogle Scholar
  12. 12.
    Mauduit, C., Sárközy, A.: On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol. Acta Arithmetica 82, 365–377 (1997)MATHMathSciNetGoogle Scholar
  13. 13.
    Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Inc., Boca Raton (1997)MATHGoogle Scholar
  14. 14.
    Montgomery, H.L.: Topics in Multiplicative Number Theory. Springer, New-York (1971)MATHCrossRefGoogle Scholar
  15. 15.
    Montgomery, H.L., Vaughan, R.C.: Exponential sums with multiplicative coefficients. Inventiones Mathematicae 43, 69–82 (1977)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Montgomery, H.L., Vaughan, R.C.: Mean values of character sums. Canadian Journal of Mathematics 31, 476–487 (1979)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Murata, L.: On the magnitude of the least prime primitive root. Journal of Number Theory 37, 47–66 (1991)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Paley, R.E.A.C.: A theorem on characters. Journal London Math. Soc. 7, 28–32 (1932)MATHCrossRefGoogle Scholar
  19. 19.
    Schinzel, A.: Sur certaines hypothèses concernant les nombres premiers. Acta Arithmetica 7, 1–8 (1961/1962) (Remarks on the paper)Google Scholar
  20. 20.
    Schinzel, A., Sierpiński, W.: Sur certaines hypothèses concernant les nombres premiers. Acta Arithmetica 4, 185–208 (1958); Corrigendum: ibid 5, 259 (1959)Google Scholar
  21. 21.
    Sárközy, A.: A finite pseudorandom binary sequence. Studia Sci. Math. Hungar. 38, 377–384 (2001)MATHMathSciNetGoogle Scholar
  22. 22.
    Weil, A.: Sur les courbes algébriques et les variétés qui s’en déduisent. Act. Sci. Ind., vol. 1041, Hermann, Paris (1948)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • J. Rivat
  • András Sárközy

There are no affiliations available

Personalised recommendations