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A tale of SNARKs : quantum resilience, knowledge extractability and data privacy

Anca Nitulescu 1, 2
2 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : The contributions detailed in this thesis focus on the design and the analysis of Succinct non-interactive arguments of knowledge, known as SNARKs. SNARKs enable a party with large computational resources to prove to a weaker party that a particular statement is true in an efficient way without further interaction and under a minimal communication requirement. Our results deal with three different aspects of SNARK protocols: the postquantum security of SNARKs, the composability of SNARKs with other cryptographic primitives and the confidentiality of the inputs in the computations verified by SNARKs. First, we propose a new framework that allows the instantiation of a quantumresilient SNARK scheme from lattice assumptions. We also study the notion of extractability that is part of the soundness definition for SNARKs. We remark some limitations of this definition and we address this problem, by introducing and studying a new notion, O-SNARKs. Finally, to achieve data privacy in delegated computation, we study the possibility of constructing SNARKs that enables verification of computations over encrypted data.
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Anca Nitulescu. A tale of SNARKs : quantum resilience, knowledge extractability and data privacy. Cryptography and Security [cs.CR]. Université Paris sciences et lettres, 2019. English. ⟨NNT : 2019PSLEE014⟩. ⟨tel-02129544v2⟩

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