The Case for Curves: Unraveling Elliptic Curves

This site serves as the output of my research project, supervised by Dr. Jelena Schmalz at the University of New England (UNE), specifically for the unit SCI395 - Science Report. Here, you will find information organised to facilitate understanding, and exploration of elliptic curves.

Contents & Using This Site

Introduction Welcome to this guide to elliptic curves. Elliptic curves are a cornerstone of modern cryptographic systems. They have an...

Exploring Fundamental Abstract Algebra.

The Discrete Logarithm Problem is a foundational problem in the field of cryptography and number theory.

Elliptic curves over real numbers involve intricate & beautiful geometric properties & have applications in various mathematical fields.

How do we know that a line connecting P and Q will always intersect another point on the curve?

For every point P, on an Elliptic Curve, there exists a point P' (often denoted -P) for which P + P' = P + (-P) = P - P = the point at...

Adding and doubling points is an essential element of the algebra of Elliptic curves.

Taking the Weierstrass form of an Elliptic Curve, and translating our x-values and y-values, with functions, we can convert the...

Associativity on elliptic curves refers to a fundamental property of the addition operation defined on points of the curve (Washington,...

The projective plane plays a critical role in the study of elliptic curves, providing a broader framework that extends the usual...