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On general multi-quadratic function field extensions in the GHS attack

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On general multi-quadratic function field extensions in the GHS attack

Lavasani, Ahmad (2008) On general multi-quadratic function field extensions in the GHS attack. Masters thesis, Concordia University.

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Abstract

To date, elliptic curves offer the most efficient cryptographic solution. Particularly efficient among elliptic curves, are those defined over binary composite finite fields, such as GF ((2 r ) n ). These curves were no longer considered secure when, in 1998, Gerhard Frey innovated a concept which paved the road for the GHS attack. The idea behind the GHS attack is to map the Discrete Logarithm Problem (DLP) over such a curve to an equivalent DLP over the jacobian of another curve, defined over the smaller field GF (2 r ). In this thesis, we study the theoretical structure of the GHS attack for elliptic curves defined over fields of arbitrary characteristics. We study the GHS attack using general quadratic extensions for elliptic curves defined over composite fields of even characteristic and we estimate the genus of resulting function field. We also implement the GHS attack and present some computational results. Keywords . GHS Attack, Elliptic Curve Cryptography, Function Fields

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Lavasani, Ahmad
Pagination:xi, 101 leaves : ill. ; 29 cm.
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:2008
Thesis Supervisor(s):David, Chantal
ID Code:976115
Deposited By: Concordia University Library
Deposited On:22 Jan 2013 16:20
Last Modified:18 Jan 2018 17:41
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