# crypto

## Fundamental Concepts Underlying Elliptic Curves (Level 2): Divisors and Pairings

Elliptic curve has a lot of nice structures attached to it. One of them is the idea of divisors. Using divisors, we can construct an example of a pairing, wh...

## Fundamental Concepts Underlying Elliptic Curves (Level 1): Projective Coordinates

Last time we mentioned the basic concepts of Elliptic curves. However, there were some lingering questions about the weird representation of points in sage b...

## Fundamental Concepts Underlying Elliptic Curves (Level 0): High-level Overview

Elliptic Curve is one of the biggest topic in mathematics, for example number theory and geometry, and is used to, for example, proof the famous Fermat’s Las...

## Coppersmith’s Method (Part II): Choosing the Right Lattice (1)

This time we will be proving the Coppersmith’s theorem using the proof method of Howgrave-Graham. We will use lattices and the lattice basis reduction algori...

## Coppersmith’s Method (Part I): Introduction

The Coppersmith’s method is an application of lattice basis reduction algorithms (like LLL) to find small solutions to polynomials modulo (N). The applicatio...