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Non-interactive arguments of knowledge

Michele Orrù 1, 2, 3
1 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 : This thesis studies non-interactive arguments of knowledge, a cryptographic primitive that allows a prover to convince a verifier of the truth of a certain statement. It focuses on cryptographic constructions that allow a user to prove knowledge of a so-called witness x that satisfies a circuit C, while simultaneously hiding it. First, we prove the existence of non-interactive witness-indistinguishable arguments of knowledge in the standard model. Our proof system is an argument of knowledge that is secure even if an adversary subverts the initial parameters. Secondly, we revisit a family of zero-knowledge arguments of knowledge (SNARKs), and show that it can be moved to post-quantum assumptions, as long as the verifier is known in advance. Lastly, we consider a novel, anonymous cryptocurrency whose security can be guaranteed via arguments of knowledge: Mimblewimble. The cryptocurrency was proposed by an anonymous author in 2016. We provide the first formal analysis of it, fixing a security issue present in the initial proposal.
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Michele Orrù. Non-interactive arguments of knowledge. Cryptography and Security [cs.CR]. ENS Paris, 2020. English. ⟨tel-02947185⟩

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