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 $\mathbf{v}(t) := \mathbf{a}t + \mathbf{b}$ in a vector space $\mathbb{F}^n$, and the verifier queries the line at a single random point $t=\alpha$. 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 $L_2$-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

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

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

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