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AGATHA CRYPTY

Financiado

Algebraic groups at the heart of post-quantum cryptography

Contemporary public-key cryptography builds its foundations on a handful of computational problems rooted in arithmetic and geometry. The vast majority of deployed cryptosystems rely on two classical problems (computing discrete l... ver más

31/12/2028

CNRS

1M€

Presupuesto del proyecto: 1M€

Líder del proyecto

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Financiación concedida El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2023-11-17

ERC-2023-STG: ERC STARTING GRANTS Scope:Objectives

I+D

Cerrada hace 2 años

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1 Participantes

CNRS

1.45M€ | Lider

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Duración del proyecto: 61 meses Fecha Inicio: 2023-11-17
Fecha Fin: 2028-12-31

Líder del proyecto

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 1M€

Descripción del proyecto Contemporary public-key cryptography builds its foundations on a handful of computational problems rooted in arithmetic and geometry. The vast majority of deployed cryptosystems rely on two classical problems (computing discrete logarithms, and factoring integers) that would not resist a large-scale quantum computer. Research on quantum technology is accelerating, endangering the world's information systems. New foundations are being proposed by the cryptologic community, promising post-quantum security, but suffering in many aspects from the lack of adequate scrutiny. Emerging post-quantum candidates can be naturally embedded into rich and modern mathematical theories. It is the case of lattice-based and isogeny-based cryptography, which share surprising connections once recast in the world of algebraic groups. Algebraic groups are at the forefront of modern mathematics. Their study across the past century has blossomed with the development of powerful theories, such as representation theory and automorphic forms. Yet, the dialogue between arithmeticians and cryptologists has been sparse, and the link between algebraic groups and the objects of post-quantum cryptography has been mostly anecdotal. This project brings this connection to the forefront, observing that the theory of algebraic groups shines a powerful light on problems raised by lattice-based and isogeny-based cryptography. It has the unique ability to turn the set of all instances of a computational problem into one meaningful object in itself — a 'moduli space' — with an arithmetic structure, a geometry, a topology, a harmonic theory. Exposing these problems to the powerful artillery of modern arithmetic will lead to cryptanalytic breakthroughs, security proofs, and the construction of cutting-edge cryptosystems.

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