Non-Uniformly Sound Certificates with Applications to Concurrent Zero-Knowledge

We introduce the notion of non-uniformly sound certificates: succinct single-message (unidirectional) argument systems that satisfy a ``best-possible security\u27\u27 against non-uniform polynomial-time attackers. In particular, no polynomial-time attacker with s bits of non-uniform advice can find significantly more than s accepting proofs for false statements. Our first result is a construction of non-uniformly sound certificates for all NP in the random oracle model, where the attacker\u27s advice can depend arbitrarily on the random oracle. We next show that the existence of non-uniformly sound certificates for P (and collision resistant hash functions) yields a public-coin constant-round fully concurrent zero-knowledge argument for NP

Constant-Round Concurrent Zero-Knowledge From Falsifiable Assumptions

We present a constant-round concurrent zero-knowledge protocol for \NP. Our protocol is sound against uniform polynomial-time attackers, and relies on the existence of families of collision-resistant hash functions, and a new (but in our eyes, natural) falsifiable intractability assumption: Roughly speaking, that Micali's non-interactive CS-proofs are sound for languages in $\P$

Constant-Round Concurrent Zero-knowledge from Indistinguishability Obfuscation

We present a constant-round concurrent zero-knowledge protocol for NP. Our protocol relies on the existence of families of collision-resistant hash functions, one-way permutations, and indistinguishability obfuscators for P/poly (with slightly super-polynomial security)

3-Message Zero Knowledge Against Human Ignorance

The notion of Zero Knowledge has driven the field of cryptography since its conception over thirty years ago. It is well established that two-message zero-knowledge protocols for NP do not exist, and that four-message zero-knowledge arguments exist under the minimal assumption of one-way functions. Resolving the precise round complexity of zero-knowledge has been an outstanding open problem for far too long. In this work, we present a three-message zero-knowledge argument system with soundness against uniform polynomial-time cheating provers. The main component in our construction is the recent delegation protocol for RAM computations (Kalai and Paneth, TCC 2016B and Brakerski, Holmgren and Kalai, ePrint 2016). Concretely, we rely on a three-message variant of their protocol based on a key-less collision-resistant hash functions secure against uniform adversaries as well as other standard primitives. More generally, beyond uniform provers, our protocol provides a natural and meaningful security guarantee against real-world adversaries, which we formalize following Rogaway’s “human-ignorance” approach (VIETCRYPT 2006): in a nutshell, we give an explicit uniform reduction from any adversary breaking the soundness of our protocol to finding collisions in the underlying hash function.National Science Foundation (U.S.) (Award CNS-1350619)National Science Foundation (U.S.) (Award CNS-1413964

Short Concurrent Covert Authenticated Key Exchange (Short cAKE)

Von Ahn, Hopper and Langford introduced the notion of steganographic a.k.a. covert computation, to capture distributed computation where the attackers must not be able to distinguish honest parties from entities emitting random bitstrings. This indistinguishability should hold for the duration of the computation except for what is revealed by the intended outputs of the computed functionality. An important case of covert computation is mutually authenticated key exchange, a.k.a. mutual authentication. Mutual authentication is a fundamental primitive often preceding more complex secure protocols used for distributed computation. However, standard authentication implementations are not covert, which allows a network adversary to target or block parties who engage in authentication. Therefore, mutual authentication is one of the premier use cases of covert computation and has numerous real-world applications, e.g., for enabling authentication over steganographic channels in a network controlled by a discriminatory entity. We improve on the state of the art in covert authentication by presenting a protocol that retains covertness and security under concurrent composition, has minimal message complexity, and reduces protocol bandwidth by an order of magnitude compared to previous constructions. To model the security of our scheme we develop a UC model which captures standard features of secure mutual authentication but extends them to covertness. We prove our construction secure in this UC model. We also provide a proof-of-concept implementation of our scheme

Digital certificates and threshold cryptography

This dissertation discusses the use of secret sharing cryptographic protocols for distributing and sharing of secret documents, in our case PDF documents. We discuss the advantages and uses of such a system in the context of collaborative environments. Description of the cryptographic protocol involved and the necessary Public Key Infrastructure (PKI) shall be presented. We also provide an implementation of this framework as a “proof of concept” and fundament the use of a certificate extension as the basis for threshold cryptography. Details of the shared secret distribution protocol and shared secret recovery protocol shall be given as well as the associated technical implementation details. The actual secret sharing algorithm implemented at this stage is based on an existing well known secret sharing scheme that uses polynomial interpolation over a finite field. Finally we conclude with a practical assessment of our prototype

Zero-Knowledge Arguments for Matrix-Vector Relations and Lattice-Based Group Encryption

International audienceGroup encryption (GE) is the natural encryption analogue of group signatures in that it allows verifiably encrypting messages for some anonymous member of a group while providing evidence that the receiver is a properly certified group member. Should the need arise, an opening authority is capable of identifying the receiver of any ciphertext. As introduced by Kiayias, Tsiounis and Yung (Asiacrypt'07), GE is motivated by applications in the context of oblivious retriever storage systems, anonymous third parties and hierarchical group signatures. This paper provides the first realization of group encryption under lattice assumptions. Our construction is proved secure in the standard model (assuming interaction in the proving phase) under the Learning-With-Errors (LWE) and Short-Integer-Solution (SIS) assumptions. As a crucial component of our system, we describe a new zero-knowledge argument system allowing to demonstrate that a given ciphertext is a valid encryption under some hidden but certified public key, which incurs to prove quadratic statements about LWE relations. Specifically, our protocol allows arguing knowledge of witnesses consisting of X ∈ Z m×n q , s ∈ Z n q and a small-norm e ∈ Z m which underlie a public vector b = X · s + e ∈ Z m q while simultaneously proving that the matrix X ∈ Z m×n q has been correctly certified. We believe our proof system to be useful in other applications involving zero-knowledge proofs in the lattice setting

Multisignatures secure under the discrete logarithm assumption and a generalized forking lemma

Multisignatures allow n signers to produce a short joint signature on a single message. Multisignatures were achieved in the plain model with a non-interactive protocol in groups with bilinear maps, by Boneh et al [4], and by a three-round protocol under the Discrete Logarithm (DL) assumption, by Bellare and Neven [3], with mul-tisignature verification cost of, respectively, O(n) pairings or ex-ponentiations. In addition, multisignatures with O(1) verification were shown in so-called Key Verification (KV) model, where each public key is accompanied by a short proof of well-formedness, again either with a non-interactive protocol using bilinear maps, by Ristenpart and Yilek [15], or with a three-round protocol under the Diffie-Hellman assumption, by Bagherzandi and Jarecki [1]. We improve on these results in two ways: First, we show a two-round O(n)-verification multisignature secure under the DL as

New Notions of Soundness and Simultaneous Resettability in the Public-Key Model

I n this paper, some new notions of soundness in public-key model are presented. We clarify the relationships among our new notions of soundness and the original 4 soundness notions presented by Micali and Reyzin. Our new soundness notions also characterize a new model for ZK protocols in public key model: weak soundness model. By ``weak” we mean for each common input x selected by a malicious prover on the fly, x is used by the malicious prover at most a-priori bounded polynomial times. The weak soundness model just lies in between BPK model and UPK model. Namely, it is weaker than BPK model but stronger than UPK model. In the weak soundness model (also in the UPK model, since weak soundness model implies UPK model), we get a 3-round black-box rZK arguments with weak resettable soundness for NP. Note that simultaneous resettability is an important open problem in the field of ZK protocols. And Reyzin has proven that there are no ZK protocols with resettable soundness in the BPK model. It means that to achieve simultaneous resettability one needs to augment the BPK model in a reasonable fashion. Although Barak et al. [BGGL01] have proven that any language which has a black-box ZK arguments with resettable soundness is in BPP. It is the weak soundness that makes us to get simultaneous resettability. More interestingly, our protocols work in a somewhat ``parallel repetition” manner to reduce the error probability and the verifier indeed has secret information with respect to historical transcripts. Note that in general the error probability of such protocols can not be reduced by parallel repetition. [BIN97] At last, we give a 3-round non-black-box rZK arguments system with resettable soundness for NP in the preprocessing model in which a trusted third party is assumed. Our construction for such protocol is quite simple. Note that although the preprocessing model is quite imposing but it is still quite reasonable as indicated in [CGGM00]. For example, in many e-commerce setting a trusted third party is often assumed. The critical tools used in this paper are: verifiable pseudorandom functions, zap and complexity leveraging. To our knowledge, our protocols are also the second application of verifiable pseudorandom functions. The first application is the 3-round rZK arguments with one-time soundness for NP in the public-key model as indicated by Micali and Reyzin [MR01a]