## Trusted Setup with Isogenies

Trusted parties are fundamental in setting up secure communication among parties. For instance, a trusted setup is needed when establishing a trusted relationship between users and certain public information in a public-key infrastructure (PKI) for public-key encryption and signature schemes.
The risk with placing trust on a third party can be ...

## Pseudorandom Functions from Isogenies

In this blogpost we will assume knowledge of CSIDH (see previous blogpost). Basic knowledge of pseudorandom functions will be useful.
What is a Pseudorandom Function?
Intuitively, a pseudorandom function (PRF) is a function that “looks like” a random function. We now define it more formally.
Firstly, we let $F: ${$0,1$}$^* \times ${$0,1$}$^*...

## CSIDH

For this blogpost we will assume knowledge of
Preview blogpost on Isogenies for Cryptography
Optional: Previous blogpost on SIDH
We will also need a basic understanding of ideal class groups.
Ideal Class Groups
We briefly introduce ideal class groups in the context needed for CSIDH. For a more general treatment and prec...

## Asiacrypt 2020

This year at Asiacrypt a total of 7 papers on isogeny-based cryptography were presented. For those who couldn’t attend, I’ve briefly described each paper. I also give links to the papers and corresponding talks (on YouTube) for more details.
SQISign: Compact Post Quantum signatures from Quaternions and Isogenies
[Paper]
Winning the best paper ...

## SIDH

SIDH
Stolbunov proposed a Diffie-Hellman type scheme based on the difficulty of computing isogenies between ordinary elliptic curves, with the aim of obtaining quantum-resistant cryptographic protocols 1. The fastest known classical probabilitic algorithm for solving this problem is an algorithm of Galbraith and Stolbunov 2, which is exponentia...

## Vélu's Formulas for SIDH

In this blog post I will assume knowledge on:
Elliptic curves (over finite fields)
A previous blogpost on isogenies for cryptography
Polynomials
Suppose we have an elliptic curve $E_1$ over a finite field $\mathbb{F}_{p^2}$. Given the kernel of an isogeny (a finite subgroup of the group of points on $E_1$), Vélu’s formulas give us a wa...

## Isogenies for Cryptography

On July 22, 2020, the Round 3 finalists for the NIST Post-quantum Cryptography Standardization effort were announced. One of the alternate candidates for public-key encryption and key-establishement algorithms is SIKE, a key encapsulation mechanism (KEM) based on isogenies. A non-specialist wanting a basic understanding of the schemes may find t...