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Polynomial representations of the Diffie-Hellman mapping

Published online by Cambridge University Press:  17 April 2009

Edwin El Mahassni  and
Igor Shparlinski
Edwin El Mahassni
Affiliation:
Department of Computing, Macquarie University, New South Wales 2109, Australia, e-mail: eelmaha@ics.mq.edu.au, igor@ics.mq.edu.au
Igor Shparlinski
Affiliation:
Department of Computing, Macquarie University, New South Wales 2109, Australia, e-mail: eelmaha@ics.mq.edu.au, igor@ics.mq.edu.au
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Abstract

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We obtain lower bounds on the degrees of polynomials representing the Diffie-Hellman mapping (gx, gy) → gxy, where g is a primitive root of a finite field q of q elements. These bounds are exponential in terms of log q. In particular, these results can be used to obtain lower bounds on the parallel arithmetic complexity of breaking the Diffie-Hellman cryptosystem. The method is based on bounds of numbers of solutions of some polynomial equations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 467 - 473
Copyright
Copyright © Australian Mathematical Society 2001

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