# Posts by Tag

## 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, prove 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...

## 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,...

## 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, prove the famous Fermat’s Las...

## 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, prove the famous Fermat’s Las...

## Zetta-CTF: 🥥

38 minute read ★★☆☆☆

The following challenge is from the Zetta-CTF PHP: Horrific Puzzle, during the VXCON in Hong Kong, 27 Apr - 28 Apr 2019. The challenge is named 🥥. btw no one...

## 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...

## 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...

## Zetta-CTF: 🥥

38 minute read ★★☆☆☆

The following challenge is from the Zetta-CTF PHP: Horrific Puzzle, during the VXCON in Hong Kong, 27 Apr - 28 Apr 2019. The challenge is named 🥥. btw no one...

## 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...