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Preuves de connaissances interactives et non-interactives

Olivier Blazy 1, 2
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, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : In this thesis, we create new building blocks and use them to present new efficient protocols via a modular design. We first begin by using the Groth-Sahai methodology for non-interactive proofs to design various group signature protocols in the standard model. We also present a new approach allowing to sign ciphertext and then under the knowledge of a secret independent from the signature protocol we show how a user can recover the signature on the plaintext, creating this way some sort of commutative property between signature and encryption where a decryption of a signature on a ciphertext provides a signature on the associated plaintext. This approach allows us to build a Round-Optimal Blind Signature scheme where the user can ultimately exploit a regular signature. We prove the security of this construction under classical hypotheses in the standard model. We then present a new methodology for implicit proofs of knowledge in an interactive environment without random oracle. For that we use Smooth Projective Hash Functions, first to instantiate Oblivious Signature-Based Envelope schemes, and then to create Authenticated Key Exchange scheme. Throughout this process we further refine the notion of language, and greatly widen the set of languages manageable via SPHF. This last result allows us to introduce the concept of LAKE (Language Authenticated Key Exchange), a new AKE design where two users will be able to share a common key if they both possess a secret word in a language expected by the other. We then show how to build standard AKE schemes (like Password Authenticated Key Exchange) using our framework, and show that our design leads to an increment in efficiency from pre existing solutions. We prove the security of our design in the UC framework under regular hypotheses.
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Submitted on : Monday, December 24, 2012 - 12:12:02 AM
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Olivier Blazy. Preuves de connaissances interactives et non-interactives. Cryptographie et sécurité [cs.CR]. Université Paris-Diderot - Paris VII, 2012. Français. ⟨tel-00768787⟩

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