Ph.D. Database
The aim of the IACR Ph.D. database is twofold. On the first hand, we want to offer an overview of Ph.D. already completed
in the domain of cryptology. Where possible, this should also include a subject classification, an abstract, and
access to the full text.
On the second hand, it deals with Ph.D. subjects currently under investigation. This way, we provide a timely
map of contemporary research in cryptology.
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Details

Alfred Menezes (#334)

Name
Alfred Menezes

Personal Homepage
http://www.cacr.math.uwaterloo.ca/~ajmeneze

Topic of his/her doctorate.
Elliptic Curve Cryptosystems

Category
public-key cryptography

Year of completion
1992

Abstract
Elliptic curves have been extensively studied for many years. Recent interest
has revolved around their applicability to factoring integers and to
primality testing.
In 1985, N. Koblitz and V. Miller independently suggested using the group of
points on an elliptic curve over a finite field as a basis for public-key
cryptosystems. Elliptic curve cryptosystems have the potential to provide
equivalent security as the existing public-key schemes, but with much shorter
key lengths. The purpose of this thesis is to study
various issues that arise in the secure and
efficient implementation of these systems.
We first present a simple method of counting the number of non-isomorphic
elliptic curves over finite fields of characteristic two.

We then show how the discrete logarithm problem in some finite groups can be
efficiently reduced to the discrete logarithm problem in a finite field.
We present
a reduction of the elliptic curve logarithm problem to the logarithm problem
in some finite field. For the special class of supersingular curves, the
reduction takes probabilistic polynomial time, thus leading to a
probabilistic subexponential time algorithm for the logarithm problem in these
elliptic curves.

For some elliptic curves for which the logarithm problem is believed to be
intractable, we demonstrate that the cryptosystems that arise form these
curves are very practical, and are amenable to both software and hardware
implementation.

Finally, we present some heuristics for improving Schoof's polynomial time
algorithm for counting the number of points on elliptic curves
defined over finite
fields of characteristic two.

Last Change
2011-04-16 11:22:04

Alfred Menezes's Students Berkant Ustaoglu - Key establishment - security models, protocols and usage (cryptographic protocols)