Brief, fairly technical overview of what I’ve been working on these last few months.
Archive of posts filed under the Number Theory category.
The Extended Euclidean Algorithm
Some notes on Euclid’s algorithm and its extension for solving linear Diophantine equations in two variables.
Addition Chains
Fast addition (or exponentiation) via addition chains.
First Year Presentation
Slides and Report from my first year presentation on the point counting problem.
Geometry Club Talk: Hyperelliptic curves
Slides from my talk on the geometry of hyperelliptic curves in connection with cryptography.
Genus 2 jacobian group law in Maple
Maple procedures for working with the group of rational divisors of a genus 2 hyperelliptic curve; designed for compatibility with generic_group procedures.
Computation in the jacobian of hyperelliptic curves
Polynomial representation of divisors and the notion of rationality.
From points to divisors: the jacobian.
Extending the idea of the group of rational points of an elliptic curve to higher genus: the jacobian of a hyperelliptic curve.
Elliptic Curve group law in Maple
Maple procedures for working with the group of rational points of an elliptic curve; designed for compatibility with generic_group procedures.
Baby Steps, Giant Steps, and element orders
Establishing the order of an element by BSGS.
