Isogeny-based Toolbox for Post-quantum Cryptography

A quantum computer exploits quantum-mechanical effects such as superposition to solve hard mathematical problems that are intractable on classical computers.

The most prominent example is Shor's algorithm that renders all widely deployed cryptographic systems such as included in TLS totally insecure, and thus also all digital services that crucially rely on them.Post-quantum cryptography deals with the design and analysis of cryptographic algorithms that remain secure against attacks not only by classical computers, but also by quantum computers.

The threat of quantum computers is a very real and pressing issue as evidenced by the ongoing NIST standardization effort for post-quantum cryptographic algorithms.Isogenies are maps between elliptic curves, and hard problems related to the computation of such maps, have recently been proposed as a candidate for post-quantum cryptography.

Due to its versatility, isogeny-based cryptography has the potential to become the only fully fledged alternative to lattice-based cryptography, providing much needed diversity.The goal of ISOCRYPT is to develop the full potential of isogeny-based cryptography into a secure, efficient and practical approach to post-quantum cryptography, and to provide a toolbox to easily instantiate secure isogeny-based applications.

To achieve this goal, a number of key research challenges need to be solved: determining the exact security of isogeny-based systems, providing efficientand secure implementations and building a suite isogeny-based post-quantum secure applications.

Our approach to solving these challenges relies on a deep exploration of the mathematical properties of isogenies, guided by the functionalities needed to build practical applications.This proposal will build on the renowned expertise of the PI and his team in mathematical foundations of post-quantum cryptography to ready isogeny-based cryptography for real world deployment.