## 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...

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...

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...

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...

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

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,...

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...

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...

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...