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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4123))

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Abstract

In an earlier paper I constructed a large family of pseudorandom sequences by using the discrete logarithm. While the sequences in this construction have strong pseudorandom properties, they can be generated very slowly since no fast algorithm is known to compute ind n. The purpose of this paper is to modify this family slightly so that the members of the new family can be generated much faster, and they have almost as good pseudorandom properties as the sequences in the original family.

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References

  1. Ahlswede, R., Mauduit, C., Sárközy, A.: Large families of pseudorandom sequences of k symbols and their complexity, Part I, Part II. In: Ahlswede, R., Bäumer, L., Cai, N., Aydinian, H., Blinovsky, V., Deppe, C., Mashurian, H. (eds.) General Theory of Information Transfer and Combinatorics. LNCS, vol. 4123, pp. 293–307, 308–325. Springer, Heidelberg (2006)

    Google Scholar 

  2. Ahlswede, R., Khachatrian, L.H., Mauduit, C., Sárközy, A.: A complexity measure for families of binary sequences. Periodica Math. Hungar. 46, 107–118 (2003)

    Article  MATH  Google Scholar 

  3. Cassaigne, J., Mauduit, C., Sárközy, A.: On finite pseudorandom binary sequences VII: The measures of pseudorandomness. Acta Arith. 103, 97–118 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Gyarmati, K.: On a family of pseudorandom binary sequences. Period. Math. Hungar. 49(2), 45–63 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gyarmati, K.: On a pseudorandom property of binary sequences. Ramanujan J. 8(3), 289–302 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Heath-Brown, D.R.: Zero-free regions for Dirichlet L-functions and the least prime in an arithmetic progression. Proc. London Math. Soc. 64, 265–338 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Koblitz, N.: A Course in Number Theory and Cryptography. Graduate Texts in Mathematics, vol. 114. Springer, New-York (1994)

    Book  MATH  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  10. Mauduit, C., Sárközy, A.: On the measures of pseudorandomness of binary sequences. Discrete Math. 271, 195–207 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Mauduit, C., Rivat, J., Sárközy, A.: Construction of pseudorandom binary sequences using additive characters. Monatshefte Math. 141(3), 197–208 (2004)

    Article  MATH  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  13. Weil, A.: Sur les courbes algébriques et les variétés qui s’en déduisent. Act. Sci. Ind. 1041, Hermann, Paris (1948)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Gyarmati, K. (2006). On a Fast Version of a Pseudorandom Generator. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_18

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  • DOI: https://doi.org/10.1007/11889342_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46244-6

  • Online ISBN: 978-3-540-46245-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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