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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Mefenza, Thierry and Vergnaud, Damien 2018. Polynomial interpolation of the generalized Diffie–Hellman and Naor–Reingold functions. Designs, Codes and Cryptography,
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    Chang, Seunghwan Kim, Bihtnara and Lee, Hyang-Sook 2015. POLYNOMIAL REPRESENTATIONS FOR n-TH ROOTS IN FINITE FIELDS. Journal of the Korean Mathematical Society, Vol. 52, Issue. 1, p. 209.
    Adelmann, Clemens and Winterhof, Arne 2006. Coding and Cryptography. Vol. 3969, Issue. , p. 144.
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    Satoh, Takakazu 2006. On Polynomial Interpolations related to Verheul Homomorphisms. LMS Journal of Computation and Mathematics, Vol. 9, Issue. , p. 135.
    Aly, Hassan and Winterhof, Arne 2006. Polynomial representations of the Lucas logarithm. Finite Fields and Their Applications, Vol. 12, Issue. 3, p. 413.
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On the interpolation of bivariate polynomials related to the Diffie-Hellman mapping

  • Eike Kiltz (a1) and Arne Winterhof (a2)
Extract

We obtain lower bounds on degree and weight of bivariate polynomials representing the Diffie-Hellman mapping for finite fields and the Diffie-Hellman mapping for elliptic curves over finite fields. This complements and improves several earlier results. We also consider some closely related bivariate mappings called P-Diffie-Hellman mappings introduced by the first author. We show that the existence of a low degree polynomial representing a P-Diffie-Hellman mapping would lead to an efficient algorithm for solving the Diffie-Hellman problem. Motivated by this result we prove lower bounds on weight and degree of such interpolation polynomials, as well.

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COPYRIGHT: © Australian Mathematical Society 2004
References
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[2]Blake, I.F., Seroussi, G. and Smart, N.P., Elliptic curves in cryptography (Cambridge University Press, New York, 1999).
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[5]Kiltz, E., ‘A tool box of cryptographic functions related to the Diffie-Hellman function’, Lecture Notes in Comput. Sci. 2247 (2001), 339–349.
[6]Kiltz, E. and Winterhof, A., ‘Polynomial interpolation of cryptographic functions related to the Diffie-Hellman problem’,in Proceedings of the International Workshop on Coding and Cryptography, WCC 2003, pp. 281–288.
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[8]Lange, T. and Winterhof, A., ‘Polynomial interpolation of the elliptic curve and XTR discrete logarithm’,in Proceedings COCOON'02, pp. 137–143.
[9]El Mahassni, E. and Shparlinski, I., ‘Polynomial representations of the Diffie-Hellman mapping’ Bull. Austral. Math. Soc. 63 (2001), 467–473.
[10]Meidl, W. and Winterhof, A., ‘A polynomial representation of the Diffie-Hellman mapping’, Appl. Algebra Engrg. Comm. Comput. 13 (313–318).
[11]Menezes, A.J., van Oorschot, P.C. and Vanstone, S.A., Handbook of applied cryptography (CRC Press, Boca Raton, 1997).
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[15]Winterhof, A., ‘A note on the interpolation of the Diffie-Hellman mapping’, Bull. Austral. Math. Soc. 64 (2001), 475–477.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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