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2018 | OriginalPaper | Buchkapitel

Efficient Designated-Verifier Non-interactive Zero-Knowledge Proofs of Knowledge

verfasst von : Pyrros Chaidos, Geoffroy Couteau

Erschienen in: Advances in Cryptology – EUROCRYPT 2018

Verlag: Springer International Publishing

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Abstract

We propose a framework for constructing efficient designated-verifier non-interactive zero-knowledge proofs (\(\mathsf {DVNIZK}\)) for a wide class of algebraic languages over abelian groups, under standard assumptions. The proofs obtained via our framework are proofs of knowledge, enjoy statistical, and unbounded soundness (the soundness holds even when the prover receives arbitrary feedbacks on previous proofs). Previously, no efficient \(\mathsf {DVNIZK}\) system satisfying any of those three properties was known. Our framework allows proving arbitrary relations between cryptographic primitives such as Pedersen commitments, ElGamal encryptions, or Paillier encryptions, in an efficient way. For the latter, we further exhibit the first non-interactive zero-knowledge proof system in the standard model that is more efficient than proofs obtained via the Fiat-Shamir transform, with still-meaningful security guarantees and under standard assumptions. Our framework has numerous applications, in particular for the design of efficient privacy-preserving non-interactive authentication.

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Vorheriges Kapitel Overdrive: Making SPDZ Great Again

Nächstes Kapitel Quasi-Optimal SNARGs via Linear Multi-Prover Interactive Proofs

More formally, this proof only satisfies zero-knowledge against honest verifiers, but this property is sufficient for the construction of [23].

These applications typically require a proof-friendly signature scheme, but designated-verifier variants of such scheme can easily be constructed (without pairings) from algebraic MACs [18, 40], by committing to the secret key of the MAC and proving knowledge of the committed value with a \(\mathsf {DVNIZK}\); such statements are naturally handled by our framework.

In the variant we consider here, we must restrict our attention to elements of \(\mathbb {Z}^*_{n ^2}\) which have Jacobi symbol 1 when reduced modulo \(n \) as \(g \in \mathbb {J}_n \), but this can be checked in polynomial time anyway.

In view of our previous observation on \(\mathsf {IND\text {-}CPA}\) security for strongly additive cryptosystems, this implies that R is secret.

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Titel: Efficient Designated-Verifier Non-interactive Zero-Knowledge Proofs of Knowledge
verfasst von: Pyrros Chaidos
Geoffroy Couteau
Verlag: Springer International Publishing
Buch: Advances in Cryptology – EUROCRYPT 2018
Print ISBN: 978-3-319-78371-0

Electronic ISBN: 978-3-319-78372-7

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-78372-7_7

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