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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 ...

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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...

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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 ...

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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...

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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...

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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...

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