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On the Distribution of the RSA Generator

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Book cover Sequences and their Applications

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

Abstract

Let 19, m and e be integers such that gcd(19, m) = 1. Then one can define the sequence (un) by the recurrence relation

$${{u}_{n}} \equiv u_{{n - 1}}^{e}\left( {\,\bmod \,m} \right),0{{u}_{n}}m - 1,n = 1,2,..., $$
(1)

with theinitial value \({{u}_{0}} = \nu \).

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References

  1. E. Bach, ‘Toward a theory of Pollard’s rho method’Inform. and Comp.90(1991), 139–155.

    Article  MathSciNet  MATH  Google Scholar 

  2. E. Bach and J. ShallitAlgorithmic Number TheoryMIT Press, 1996.

    Google Scholar 

  3. L. Blum, M. Blum and M. Shub, ‘A simple unpredictable pseudo-random number generator’SIAM J. Comp.15(1986), 364–383.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. J. Brennan and B. Geist, ‘Analysis of iterated modular exponentiation: The orbit of\({{x}^{\alpha }} \)mod N’Designs Codes and Cryptography 13(1998), 229–245.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Canetti, J. B. Friedlander, S. Konyagin, M. Larsen, D. Lieman and I. E. Shparlinski, ‘On the statistical properties of the Diffie-Hellman distribution’Israel J. Math.(to appear).

    Google Scholar 

  6. R. Canetti, J. B. Friedlander and I. E. Shparlinski, ‘On certain exponential sums and the distribution of Diffle-Hellman triples’J. London Math. Soc.(to appear).

    Google Scholar 

  7. J. H. H. Chalk ‘The Vinogradov-Mordell-Tietäväinen inequalities’Indag. Math.42(1980), 367–374.

    MathSciNet  MATH  Google Scholar 

  8. T. W. Cusick, ‘Properties of the x2modNpseudorandom number generator’IEEE Trans. Inform. Theory 41(1995), 1155–1159.

    Article  MathSciNet  MATH  Google Scholar 

  9. T. W. Cusick, C. Ding and A. RenvallStream CiphersandNumber TheoryElsevier, Amsterdam, 1998.

    MATH  Google Scholar 

  10. R. Fischlin and C. P. Schnorr, ‘Stronger security proofs for RSA and Rabin bits’Lect. Notes in Comp.Sci., Springer-Verlag, Berlin1233(1997), 267–279.

    Google Scholar 

  11. F. Griffin and I. E. Shparlinski, ‘On the linear complexity profile of the power generator’, Preprint, 1998, 1–11.

    Google Scholar 

  12. J. Hästad and M. Näslund, ‘The security of individual RSA bits’Proc 39th IEEE Symp. on Foundations of Comp. Sci.1998, 510–519.

    Google Scholar 

  13. J. C. Lagarias, ‘Pseudorandom number generators in cryptography and number theory’Proc. Symp. in Appl. Math.Amer. Math. Soc., Providence, RI42(1990), 115–143.

    MathSciNet  Google Scholar 

  14. A. J. Menezes, P. C. van Oorschot and S. A. VanstoneHandbook of CryptographyCRC Press, Boca Raton, FL, 1996.

    Book  Google Scholar 

  15. I. E. Shparlinski, ‘On the linear complexity of the power generator’Tech. Report. C/TR 98–12Dept. of Computing, Macquarie Uni., Sydney, 1998, 1–8.

    Google Scholar 

  16. D. R. StinsonCryptography: Theory and PracticeCRC Press, Boca Raton, FL, 1995.

    MATH  Google Scholar 

  17. I. M. VinogradovElements of Number TheoryDover Publ., NY, 1954.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto Toronto, Ontario, M5S 3G3, Canada

    John B. Friedlander

  2. Department of Mathematics, University of Missouri Columbia, MO, 65211, USA

    Daniel Lieman

  3. School of MPCE, Macquarie University Sydney, NSW, 2109, Australia

    Igor E. Shparlinski

Authors
  1. John B. Friedlander
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  2. Daniel Lieman
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  3. Igor E. Shparlinski
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Editor information

Editors and Affiliations

  1. Department of Computer Science, School of Computing, National University of Singapore, Lower Kent Ridge Road, Singapore, 119260

    C. Ding

  2. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    T. Helleseth

  3. Institute of Information Processing, Austrian Academy of Sciences, Sonnenfelsgasse 19, A01010, Vienna, Austria

    H. Niederreiter

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© 1999 Springer-Verlag London

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Friedlander, J.B., Lieman, D., Shparlinski, I.E. (1999). On the Distribution of the RSA Generator. In: Ding, C., Helleseth, T., Niederreiter, H. (eds) Sequences and their Applications. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0551-0_14

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  • DOI: https://doi.org/10.1007/978-1-4471-0551-0_14

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-196-2

  • Online ISBN: 978-1-4471-0551-0

  • eBook Packages: Springer Book Archive

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