1,235 research outputs found
Efficient Designated-Verifier Non-Interactive Zero-Knowledge Proofs of Knowledge
We propose a framework for constructing efficient designated-verifier non-interactive zero-knowledge proofs (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 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
Making Sigma-Protocols Non-interactive Without Random Oracles
Damg˚ard, Fazio and Nicolosi (TCC 2006) gave a transformation of Sigma-protocols, 3-move honest verifier zero-knowledge proofs, into efficient non-interactive zero-knowledge arguments for a designated verifier. Their transformation uses additively homomorphic encryption
to encrypt the verifier’s challenge, which the prover uses to compute an encrypted answer. The transformation does not rely on the random oracle model but proving soundness requires a complexity leveraging assumption.
We propose an alternative instantiation of their transformation and show that it achieves culpable soundness without complexity leveraging. This
improves upon an earlier result by Ventre and Visconti (Africacrypt 2009), who used a different construction which achieved weak culpable soundness.
We demonstrate how our construction can be used to prove validity of encrypted votes in a referendum. This yields a voting system with homomorphic tallying that does not rely on the Fiat-Shamir heuristic
Line-Point Zero Knowledge and Its Applications
We introduce and study a simple kind of proof system called line-point zero knowledge (LPZK). In an LPZK proof, the prover encodes the witness as an affine line in a vector space , and the verifier queries the line at a single random point . LPZK is motivated by recent practical protocols for vector oblivious linear evaluation (VOLE), which can be used to compile LPZK proof systems into lightweight designated-verifier NIZK protocols.
We construct LPZK systems for proving satisfiability of arithmetic circuits with attractive efficiency features. These give rise to designated-verifier NIZK protocols that require only 2-5 times the computation of evaluating the circuit in the clear (following an input-independent preprocessing phase), and where the prover communicates roughly 2 field elements per multiplication gate, or roughly 1 element in the random oracle model with a modestly higher computation cost. On the theoretical side, our LPZK systems give rise to the first linear interactive proofs (Bitansky et al., TCC 2013) that are zero knowledge against a malicious verifier.
We then apply LPZK towards simplifying and improving recent constructions of reusable non-interactive secure computation (NISC) from VOLE (Chase et al., Crypto 2019). As an application, we give concretely efficient and reusable NISC protocols over VOLE for bounded inner product, where the sender\u27s input vector should have a bounded -norm
Lattice-based Zero-knowledge SNARGs for Arithmetic Circuits
Succinct non-interactive arguments (SNARGs) enable verifying NP computations
with substantially lower complexity than that required
for classical NP verification. In this work, we construct a zero-knowledge
SNARG candidate that relies only on lattice-based assumptions
which are claimed to hold even in the presence of quantum computers.
Central to this new construction is the notion of linear-targeted malleability introduced
by Bitansky et al. (TCC 2013) and the conjecture that
variants of Regev encryption satisfy this property. Then, using
the efficient characterization of NP languages as
Square Arithmetic Programs we build the first quantum-resilient zk-SNARG for
arithmetic circuits with a constant-size proof consisting
of only 2 lattice-based ciphertexts.
Our protocol is designated-verifier, achieves zero-knowledge and has shorter
proofs and shorter CRS than the previous such schemes, e.g. Boneh et al.
(Eurocrypt 2017)
Perfect zero knowledge for quantum multiprover interactive proofs
In this work we consider the interplay between multiprover interactive
proofs, quantum entanglement, and zero knowledge proofs - notions that are
central pillars of complexity theory, quantum information and cryptography. In
particular, we study the relationship between the complexity class MIP, the
set of languages decidable by multiprover interactive proofs with quantumly
entangled provers, and the class PZKMIP, which is the set of languages
decidable by MIP protocols that furthermore possess the perfect zero
knowledge property.
Our main result is that the two classes are equal, i.e., MIP
PZKMIP. This result provides a quantum analogue of the celebrated result of
Ben-Or, Goldwasser, Kilian, and Wigderson (STOC 1988) who show that MIP
PZKMIP (in other words, all classical multiprover interactive protocols can be
made zero knowledge). We prove our result by showing that every MIP
protocol can be efficiently transformed into an equivalent zero knowledge
MIP protocol in a manner that preserves the completeness-soundness gap.
Combining our transformation with previous results by Slofstra (Forum of
Mathematics, Pi 2019) and Fitzsimons, Ji, Vidick and Yuen (STOC 2019), we
obtain the corollary that all co-recursively enumerable languages (which
include undecidable problems as well as all decidable problems) have zero
knowledge MIP protocols with vanishing promise gap
A Practical Set-Membership Proof for Privacy-Preserving NFC Mobile Ticketing
To ensure the privacy of users in transport systems, researchers are working
on new protocols providing the best security guarantees while respecting
functional requirements of transport operators. In this paper, we design a
secure NFC m-ticketing protocol for public transport that preserves users'
anonymity and prevents transport operators from tracing their customers' trips.
To this end, we introduce a new practical set-membership proof that does not
require provers nor verifiers (but in a specific scenario for verifiers) to
perform pairing computations. It is therefore particularly suitable for our
(ticketing) setting where provers hold SIM/UICC cards that do not support such
costly computations. We also propose several optimizations of Boneh-Boyen type
signature schemes, which are of independent interest, increasing their
performance and efficiency during NFC transactions. Our m-ticketing protocol
offers greater flexibility compared to previous solutions as it enables the
post-payment and the off-line validation of m-tickets. By implementing a
prototype using a standard NFC SIM card, we show that it fulfils the stringent
functional requirement imposed by transport operators whilst using strong
security parameters. In particular, a validation can be completed in 184.25 ms
when the mobile is switched on, and in 266.52 ms when the mobile is switched
off or its battery is flat
Lattice-Based zk-SNARKs from Square Span Programs
Zero-knowledge SNARKs (zk-SNARKs) are non-interactive proof systems with short (i.e., independent of the size of the witness) and efficiently verifiable proofs. They elegantly resolve the juxtaposition of individual privacy and public trust, by providing an efficient way of demonstrating knowledge of secret information without actually revealing it. To this day, zk-SNARKs are widely deployed all over the planet and are used to keep alive a system worth billion of euros, namely the cryptocurrency Zcash. However, all current SNARKs implementations rely on so-called pre-quantum assumptions and, for this reason, are not expected to withstand cryptanalitic efforts over the next few decades.
In this work, we introduce a new zk-SNARK that can be instantiated from lattice-based assumptions, and which is thus believed to be post-quantum secure. We provide a generalization in the spirit of Gennaro et al. (Eurocrypt'13) to the SNARK of Danezis et al. (Asiacrypt'14) that is based on Square Span Programs (SSP) and relies on weaker computational assumptions. We focus on designated-verifier proofs and propose a protocol in which a proof consists of just 5 LWE encodings. We provide a concrete choice of parameters, showing that our construction is practically instantiable
Anonymous Single-Sign-On for n designated services with traceability
Anonymous Single-Sign-On authentication schemes have been proposed to allow
users to access a service protected by a verifier without revealing their
identity which has become more important due to the introduction of strong
privacy regulations. In this paper we describe a new approach whereby anonymous
authentication to different verifiers is achieved via authorisation tags and
pseudonyms. The particular innovation of our scheme is authentication can only
occur between a user and its designated verifier for a service, and the
verification cannot be performed by any other verifier. The benefit of this
authentication approach is that it prevents information leakage of a user's
service access information, even if the verifiers for these services collude
which each other. Our scheme also supports a trusted third party who is
authorised to de-anonymise the user and reveal her whole services access
information if required. Furthermore, our scheme is lightweight because it does
not rely on attribute or policy-based signature schemes to enable access to
multiple services. The scheme's security model is given together with a
security proof, an implementation and a performance evaluation.Comment: 3
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