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Communication Dans Un Congrès Année : 2020

Shorter Non-interactive Zero-Knowledge Arguments and ZAPs for Algebraic Languages

Geoffroy Couteau
Dominik Hartmann
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Résumé

We put forth a new framework for building pairing-based non-interactive zeroknowledge (NIZK) arguments for a wide class of algebraic languages, which are an extension of linear languages, containing disjunctions of linear languages and more. Our approach differs from the Groth-Sahai methodology, in that we rely on pairings to compile a Σ-protocol into a NIZK. Our framework enjoys a number of interesting features: conceptual simplicity, parameters derive from the Σ-protocol; proofs as short as resulting from the Fiat-Shamir heuristic applied to the underlying Σprotocol; fully adaptive soundness and perfect zero-knowledge in the common random string model with a single random group element as CRS; yields simple and efficient two-round, public coin, publicly-verifiable perfect witness-indistinguishable (WI) arguments(ZAPs) in the plain model. To our knowledge, this is the first construction of two-rounds statistical witness-indistinguishable arguments from pairing assumptions. Our proof system relies on a new (static, falsifiable) assumption over pairing groups which generalizes the standard kernel Diffie-Hellman assumption in a natural way and holds in the generic group model (GGM) and in the algebraic group model (AGM). Replacing Groth-Sahai NIZKs with our new proof system allows to improve several important cryptographic primitives. In particular, we obtain the shortest tightly-secure structurepreserving signature scheme (which are a core component in anonymous credentials), the shortest tightly-secure quasi-adaptive NIZK with unbounded simulation soundness (which in turns implies the shortest tightly-mCCA-secure cryptosystem), and shorter ring signatures.
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Dates et versions

hal-03374157 , version 1 (11-10-2021)

Identifiants

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Geoffroy Couteau, Dominik Hartmann. Shorter Non-interactive Zero-Knowledge Arguments and ZAPs for Algebraic Languages. CRYPTO 2020 - Annual International Cryptology Conference, Aug 2020, Santa Barbara, United States. pp.768-798, ⟨10.1007/978-3-030-56877-1_27⟩. ⟨hal-03374157⟩
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