Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model

We consider a type of zero-knowledge protocols that are of interest for their practical applications within networks like the Internet: efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks. In an effort to reduce the setup assumptions required for efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks, we consider a model, which we call the Authenticated Public-Key (APK) model. The APK model seems to significantly reduce the setup assumptions made by the CRS model (as no trusted party or honest execution of a centralized algorithm are required), and can be seen as a slightly stronger variation of the Bare Public-Key (BPK) model from \cite{CGGM,MR}, and a weaker variation of the registered public-key model used in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK model. Our main result is a constant-round concurrent non-malleable zero-knowledge argument of knowledge for any polynomial-time relation (associated to a language in $\mathcal{NP}$), under the (minimal) assumption of the existence of a one-way function family. Furthermore,We show time-efficient instantiations of our protocol based on known number-theoretic assumptions. We also note a negative result with respect to further reducing the setup assumptions of our protocol to those in the (unauthenticated) BPK model, by showing that concurrently non-malleable zero-knowledge arguments of knowledge in the BPK model are only possible for trivial languages

Efficient Zero-Knowledge Proofs and Applications

Zero-knowledge proofs provide a means for a prover to convince a verifier that some claim is true and nothing more. The ability to prove statements while conveying zero information beyond their veracity has profound implications for cryptography and, especially, for its applicability to privacy-enhancing technologies. Unfortunately, the most common zero-knowledge techniques in the literature suffer from poor scalability, which limits their usefulness in many otherwise promising applications. This dissertation addresses the problem of designing communication- and computation-efficient protocols for zero-knowledge proofs and arguments of propositions that comprise many "simple" predicates. In particular, we propose a new formal model in which to analyze batch zero-knowledge protocols and perform the first systematic study of systems for batch zero-knowledge proofs and arguments of knowledge. In the course of this study, we suggest a general construction for batch zero-knowledge proof systems and use it to realize several new protocols suitable for proving knowledge of and relationships among large batches of discrete logarithm (DL) representations in prime-order groups. Our new protocols improve on existing protocols in several ways; for example, among the new protocols is one with lower asymptotic computation cost than any other such system in the literature. We also tackle the problem of constructing batch proofs of partial knowledge, proposing new protocols to prove knowledge of a DL that is equal to at least k-out-of-n other DLs, at most k-out-of-n other DLs, or exactly k-out-of-n other DLs. These constructions are particularly interesting as they prove some propositions that appear difficult to prove using existing techniques, even when efficiency is not a primary consideration. We illustrate the applicability of our new techniques by using them to construct efficient protocols for anonymous blacklisting and reputation systems

A Note on Non-Interactive Zero-Knowledge from CDH

We build non-interactive zero-knowledge (NIZK) and ZAP arguments for all $\mathsf{NP}$ where soundness holds for infinitely-many security parameters, and against uniform adversaries, assuming the subexponential hardness of the Computational Diffie-Hellman (CDH) assumption. We additionally prove the existence of NIZK arguments with these same properties assuming the polynomial hardness of both CDH and the Learning Parity with Noise (LPN) assumption. In both cases, the CDH assumption does not require a group equipped with a pairing. Infinitely-often uniform security is a standard byproduct of commonly used non-black-box techniques that build on disjunction arguments on the (in)security of some primitive. In the course of proving our results, we develop a new variant of this non-black-box technique that yields improved guarantees: we obtain explicit constructions (previous works generally only obtained existential results) where security holds for a relatively dense set of security parameters (as opposed to an arbitrary infinite set of security parameters). We demonstrate that our technique can have applications beyond our main results

Zero-Knowledge Proofs of Proximity

Interactive proofs of proximity (IPPs) are interactive proofs in which the verifier runs in time sub-linear in the input length. Since the verifier cannot even read the entire input, following the property testing literature, we only require that the verifier reject inputs that are far from the language (and, as usual, accept inputs that are in the language). In this work, we initiate the study of zero-knowledge proofs of proximity (ZKPP). A ZKPP convinces a sub-linear time verifier that the input is close to the language (similarly to an IPP) while simultaneously guaranteeing a natural zero-knowledge property. Specifically, the verifier learns nothing beyond (1) the fact that the input is in the language, and (2) what it could additionally infer by reading a few bits of the input. Our main focus is the setting of statistical zero-knowledge where we show that the following hold unconditionally (where N denotes the input length): - Statistical ZKPPs can be sub-exponentially more efficient than property testers (or even non-interactive IPPs): We show a natural property which has a statistical ZKPP with a polylog(N) time verifier, but requires Omega(sqrt(N)) queries (and hence also runtime) for every property tester. - Statistical ZKPPs can be sub-exponentially less efficient than IPPs: We show a property which has an IPP with a polylog(N) time verifier, but cannot have a statistical ZKPP with even an N^(o(1)) time verifier. - Statistical ZKPPs for some graph-based properties such as promise versions of expansion and bipartiteness, in the bounded degree graph model, with polylog(N) time verifiers exist. Lastly, we also consider the computational setting where we show that: - Assuming the existence of one-way functions, every language computable either in (logspace uniform) NC or in SC, has a computational ZKPP with a (roughly) sqrt(N) time verifier. - Assuming the existence of collision-resistant hash functions, every language in NP has a statistical zero-knowledge argument of proximity with a polylog(N) time verifier

Limbo: Efficient Zero-knowledge MPCitH-based Arguments

This work introduces a new interactive oracle proof system based on the MPC-in-the-Head paradigm. To improve concrete efficiency and offer flexibility between computation time and communication size, a generic proof construction based on multi-round MPC protocols is proposed, instantiated with a specific protocol and implemented and compared to similar proof systems. Performance gains over previous work derive from a multi-party multiplication check optimized for the multi-round and MPC-in-the-Head settings. Of most interest among implementation optimizations is the use of identical randomness across repeated MPC protocol executions in order to accelerate computation without excessive cost to the soundness error. The new system creates proofs of SHA-256 pre-images of 43KB in 53ms with 16 MPC parties, or 23KB in 188ms for 128 parties. As a signature scheme, the non-interactive variant produces signatures, based on the AES-128 circuit, of 19KB in 4.2ms; this is 35% faster and 33 % larger than the Picnic3 scheme (13kB in 5.3ms for 16 parties) which is based on the 90% smaller LowMC circuit

On a New, Efficient Framework for Falsifiable Non-interactive Zero-Knowledge Arguments

Et kunnskapsløst bevis er en protokoll mellom en bevisfører og en attestant. Bevisføreren har som mål å overbevise attestanten om at visse utsagn er korrekte, som besittelse av kortnummeret til et gyldig kredittkort, uten å avsløre noen private opplysninger, som for eksempel kortnummeret selv. I mange anvendelser er det ønskelig å bruke IIK-bevis (Ikke-interaktive kunnskapsløse bevis), der bevisføreren produserer kun en enkelt melding som kan bekreftes av mange attestanter. En ulempe er at sikre IIK-bevis for ikke-trivielle språk kun kan eksistere ved tilstedeværelsen av en pålitelig tredjepart som beregner en felles referansestreng som blir gjort tilgjengelig for både bevisføreren og attestanten. Når ingen slik part eksisterer liter man av og til på ikke-interaktiv vitne-uskillbarhet, en svakere form for personvern. Studiet av effektive og sikre IIK-bevis er en kritisk del av kryptografi som har blomstret opp i det siste grunnet anvendelser i blokkjeder. I den første artikkelen konstruerer vi et nytt IIK-bevis for språkene som består av alle felles nullpunkter for en endelig mengde polynomer over en endelig kropp. Vi demonstrerer nytteverdien av beviset ved flerfoldige eksempler på anvendelser. Særlig verdt å merke seg er at det er mulig å gå nesten automatisk fra en beskrivelse av et språk på et høyt nivå til definisjonen av IIK-beviset, som minsker behovet for dedikert kryptografisk ekspertise. I den andre artikkelen konstruerer vi et IIV-bevis ved å bruke en ny kompilator. Vi utforsker begrepet Kunnskapslydighet (et sterkere sikkerhetsbegrep enn lydighet) for noen konstruksjoner av IIK-bevis. I den tredje artikkelen utvider vi arbeidet fra den første artikkelen ved å konstruere et nytt IIK-bevis for mengde-medlemskap som lar oss bevise at et element ligger, eller ikke ligger, i den gitte mengden. Flere nye konstruksjoner har bedre effektivitet sammenlignet med allerede kjente konstruksjoner.A zero-knowledge proof is a protocol between a prover, and a verifier. The prover aims to convince the verifier of the truth of some statement, such as possessing credentials for a valid credit card, without revealing any private information, such as the credentials themselves. In many applications, it is desirable to use NIZKs (Non-Interactive Zero Knowledge) proofs, where the prover sends outputs only a single message that can be verified by many verifiers. As a drawback, secure NIZKs for non-trivial languages can only exist in the presence of a trusted third party that computes a common reference string and makes it available to both the prover and verifier. When no such party exists, one sometimes relies on non interactive witness indistinguishability (NIWI), a weaker notion of privacy. The study of efficient and secure NIZKs is a crucial part of cryptography that has been thriving recently due to blockchain applications. In the first paper, we construct a new NIZK for the language of common zeros of a finite set of polynomials over a finite field. We demonstrate its usefulness by giving a large number of example applications. Notably, it is possible to go from a high-level language description to the definition of the NIZK almost automatically, lessening the need for dedicated cryptographic expertise. In the second paper, we construct a NIWI using a new compiler. We explore the notion of Knowledge Soundness (a security notion stronger than soundness) of some NIZK constructions. In the third paper, we extended the first paper’s work by constructing a new set (non-)membership NIZK that allows us to prove that an element belongs or does not belong to the given set. Many new constructions have better efficiency compared to already-known constructions.Doktorgradsavhandlin

Efficient Zero-Knowledge Proofs and their Applications

A zero-knowledge proof is a fundamental cryptographic primitive that enables the verification of statements without revealing unnecessary information. Zero-knowledge proofs are a key component of many cryptographic protocols and, often, one of their main efficiency bottlenecks. In recent years there have been great advances in improving the efficiency of zero-knowledge proofs, bring them closer to wide deployability. In this thesis we make another step towards the construction of computationally-efficient zero-knowledge proofs. Specifically, we construct efficient zero-knowledge proofs for the satisfiability of arithmetic circuits for which the computational cost of the prover is only a constant factor more expensive than direct evaluation of the circuit. We also construct efficient zero-knowledge proofs to check the correct execution of (Tiny)RAM programs. In this case the computational cost for the prover is a superconstant factor larger than executing the program directly. Our proofs also support efficient verification and small proof sizes. For security, they rely on symmetric primitives and could potentially withstand attacks from quantum computers. On a different research direction, we look at group signatures, a fundamental primitive which relies on zero-knowledge proofs. A group signature enables users to sign anonymously on behalf of a group of users. In case of dispute a Manager can identify the author of a signature and potentially banish the user from the group. In this thesis we address the fundamental question of defining the security of fully dynamic group signatures, for which the users can join and leave at any time. Differently from other restricted settings, this case has been largely overlooked in the past. Our security model is general, does not implicitly assume existing design paradigms and captures the security of existing models for more restricted settings