crypto

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

56 minute read ★★★☆☆

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

85 minute read ★★★☆☆

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

39 minute read ★★☆☆☆

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)

59 minute read ★★★☆☆

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

49 minute read ★★★☆☆

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

Basics of Lattice-based Cryptography

55 minute read ★★★☆☆

Lattice is a very important construct for modern day cryptography, especially when we know that in the future, quantum computers will break both ECC and RSA,...

HKCERT CTF 2021 Selected Write-ups

29 minute read ★★☆☆☆

Last Friday to Sunday there was the HKCERT CTF competition 2021 held by HKCERT. I am not allowed to join the competition (for obvious reasons). Nonetheless I...