Opis projektu
Zastosowanie nowych metod rozwiązywania umiarkowanie złożonych problemów początkiem nowej ery kryptografii
W obliczu coraz bardziej złożonych i zdecentralizowanych metod przetwarzania danych istnieje pilna potrzeba zapewnienia wysokiego poziomu ich bezpieczeństwa, gdyż wpływa to na bezpieczeństwo zarówno obywateli, jak i państwa. Tradycyjna kryptografia uporała się z problemami, które można określić mianem „czarno-białych”, a więc takich, które są albo proste, albo trudne. Tymczasem problemy „umiarkowanie złożone” pozostają nierozwiązane. Zespół finansowanego ze środków UE projektu FGC bada zastosowanie niedawno opracowanej teorii złożoności drobnoziarnistej problemów umiarkowanie trudnych oraz narzędzi do analizy przypadków średnich na potrzeby zadań kryptograficznych o różnych poziomach złożoności i zaawansowanych zastosowań kryptograficznych.
Cel
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.
Dziedzina nauki
Program(-y)
Temat(-y)
System finansowania
ERC-ADG - Advanced GrantInstytucja przyjmująca
20136 Milano
Włochy