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On the interpolation of bivariate polynomials related to the Diffie-Hellman mapping

Published online by Cambridge University Press:  17 April 2009

Eike Kiltz  and
Arne Winterhof
Eike Kiltz
Affiliation:
Lehrstuhl Mathematik & Informatik, Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany e-mail: [email protected]
Arne Winterhof
Affiliation:
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, c/o Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria e-mail: [email protected]
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 305 - 315
Copyright
Copyright © Australian Mathematical Society 2004

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