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This thesis explores methods to generate cryptographically strong elliptic curves by tackling ECDLP.
The purpose of this thesis is an in-depth examination of the Elliptic Curve Discrete Logarithm Problem(ECDLP) including up-to-date techniques in attacking cryptosystems dependent on the ECDLP. The thesis is presented as a how-to guide and included are programs written in Pari/GP for various attacks. We then use the knowledge of these attacks in an attempt to generate cryptographically strong elliptic curves.
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Matthew Musson (2006) studied this question.
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