Description du projet
L’application de nouvelles méthodes pour les problèmes modérément difficiles inaugure une nouvelle ère de la cryptographie
Conserver les données en toute sécurité malgré le mode de traitement des données de plus en plus complexe et décentralisé représente un besoin pressant dont l’impact se fait sentir à tous les niveaux, de la sécurité des données à caractère personnel à la sécurité nationale. Les méthodes de cryptographie traditionnelles traitaient des problèmes plutôt noirs et blancs – faciles ou difficiles – alors que les problèmes «modérément difficiles» sont légion. Le projet FGC, financé par l’UE, étudie l’application d’une théorie de la complexité «à grain fin» récemment élaborée pour les problèmes modérément difficiles et les outils d’analyse des cas moyens à plusieurs niveaux de tâches cryptographiques et d’applications cryptographiques avancées.
Objectif
Encryption and authentication have long been the workhorse of secure systems, but with the shift towards a decentralized mode of data processing, contemporary cryptographic tools such as secure computation and homomorphic encryption are taking center stage. Unlike their “private-key” counterparts, for which efficient candidate instantiations abound, these “public-key” types of primitives rely on a remarkably narrow base of computational hardness assumptions. Developing and understanding new assumptions upon which such primitives can be based is a necessity; the Fine-Grained Cryptography project aims to do exactly that.
Traditionally, cryptography has been based on problems for which there is a conjectured exponential complexity gap between the “easy” and “hard” directions; in contrast, we propose to investigate alternatives where the underlying gap is a sufficiently large polynomial. Practically speaking, fixed polynomial gaps should suffice for concrete security parameter instantiations. From a theoretical standpoint, they yield meaningful results even if P = NP -- a scenario in which most cryptography is (asymptotically) broken.
While a rich “fine-grained” complexity theory of moderately hard problems has been developed in the past two decades, its consequences to cryptography remain relatively unexplored. Moderately hard problems abound, and many of them enjoy algebraic and combinatorial structure. This, combined with the existence of tools for average-case analysis, points to their promise as a new base for advanced cryptographic applications.
Our initial focus will be on lower-level cryptographic primitives, such as one-way functions and public-key encryption. However, we expect our approach to also have direct impact on the feasibility and practical efficiency of higher-level cryptographic tasks, including advanced forms of encryption and even obfuscation.
Champ scientifique
Programme(s)
Thème(s)
Régime de financement
ERC-ADG - Advanced GrantInstitution d’accueil
20136 Milano
Italie