On Isogeny-based identifications protocols and proof of isogeny knowledge
2022-07-25 08:00 - 10:00 | INF 220 https://plan.epfl.ch/?room==INF%20220
Laurane Marco
EDIC candidacy exam
Exam president: Prof. Bryan Ford
Thesis advisor: Prof. Serge Vaudenay
Co-examiner: Prof. Alessandro Chiesa

Abstract
Isogeny-based cryptography is a branch of post-quantum cryptography. In this paper we explore identification protocols based on an isogeny protocol called SIDH \cite{sidh}. Identification protocols are a tool for authentication, and can be used as a basis for digital signatures.
A key building block of this SIDH-based identification protocol is a proof of isogeny-knowledge, which can additionally act as a countermeasure to prevent some active attacks in the context of public-key encryption. We show however that obtaining a sound zero-knowledge proof of knowledge is not easy, as highlighted by Ghantous et al. and De Feo et al. and explore their possible solutions. Finally, we highlight possible research directions to improve upon the current state of the art in terms of isogeny-based identifications protocols, digital signatures and proofs of knowledge.

Background papers
1- Towards quantum-resistant crypto systems from super singular elliptic curve isogenies - Lucas de Feo, David Jao, Jérôme Plût https://eprint.iacr.org/2011/506.pdf

2- Collisions in Supersingular Isogeny Graphs and the SIDH-based Identification protocol - Wissam Ghantous, Shuichi Katsumata, Federico Pintore, Mattia Veroni https://eprint.iacr.org/2021/1051.pdf

3- Side Proof of knowledge - Luca De Feo, Samuel Dobson, Steven D. Galbraith, Lukas Zobernig https://eprint.iacr.org/2021/1023.pdf
