Elliptic Curve Point Counting Algorithms and Cryptography
Abstract
As further technological advancements have been made over
the past few decades, our dependence on computers and
the Internet has increased. As a result, algebraic coding
theory has become a significant focus for today's world
in order to create channels over which private information
such as credit card and social security numbers are passed.
As interest in this field increases, mathematicians have
discovered the benefit of using elliptic curve cryptography
as the primary scheme for Internet security. It has thus
become a focus and an appeal to develop improved algorithms
that provide efficient means by which elliptic curve
cryptosystems can perform. Before doing so, mathematicians
had to confront the issue of solving the point counting
problem associated with elliptic curves generated over
large finite fields. One such result called the Schoof
Algorithm was developed, which was later followed and enhanced
by the Schoof-Elkies-Atkin Algorithm. The implementation
of these products has shown their efficiency and reliability
as seen through comparison with older models and brute-force
investigation.
Table of Contents
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