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Efficient Smooth Projective Hash Functions and Applications

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In 2008, Groth and Sahai proposed a powerful suite of techniques for constructing non-interactive zero-knowledge proofs in bilinear groups. Their proof systems have found numerous applications, including group signature schemes, anonymous voting, and anonymous credentials.

In this talk, we demonstrate that the notion of smooth projective hash functions is an efficient alternative for interactive protocols. We show that this approach provides suitable proofs for designing schemes that rely on standard security assumptions in the standard model with a common-reference string and are more efficient than those obtained using the Groth-Sahai methodology when interactions are already required by the primitive itself.

As an illustration of our design principle, we describe efficient blind signature schemes, as well as an oblivious signature-based envelope scheme, but also the new notion of Language-based Authenticated Key Exchange, that includes Password-based Authenticated Key Exchange, Secret Handshakes and Credential Authenticated Key Exchange.

This is a joint work with Olivier Blazy, Cline Chevalier and Damien Vergnaud.

This talk is part of the Isaac Newton Institute Seminar Series series.

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