This paper deals with efficient non-malleable zero-knowledge proofs forNP, based on general assumptions. We construct a simulation-sound zero-knowledge (ZK) protocol for NP, based only on the black-box use of one-way functions. Constructing such a proof system has been an open question ever since the original work of Dolev, Dwork, and Naor [DDN91]. In addition to the feasibility result, our protocol has a constant number of rounds, which is asymptotically optimal. Traditionally, the term non-malleable zero-knowledge (NmZK) refers to the original definition of [DDN91]; but today it is used loosely to also refer to simulation-soundness (SimSound) [Sah99], and simulation-extractability (SimExt) [PR05b]. While SimExt implies NmZK, the common perception is that SimExt is strongest of the three notions. A formal study of the definitional relationship between these three notions, however, has never been done. In the second part of this work, we try to correct this situation by initiating such a study. We show that in the âstaticâ case, if an NmZK protocol is also an argument-of-knowledge, then it is in fact SimExt. Furthermore, in the most strict sense of the definition, SimSound does not necessarily follow from SimExt. These results are somewhat surprising because they are opposite to the common perception that SimExt is the strongest of the three notions.
We present a method to compile Yaoâs two-player garbled circuit protocol into one that is secure against malicious adversaries that relies on witness indistinguishability. Our approach can enjoy lower communication and computation overhead than methods based on cut-andchoose [13] and lower overhead than methods based on zero-knowledge proofs [8] (or ÎŁ-protocols [14]). To do so, we develop and analyze new solutions to issues arising with this transformation: â How to guarantee the generatorâs input consistency â How to support different outputs for each player without adding extra gates to the circuit of the function f being computed â How the evaluator can retrieve input keys but avoid selective failure attacks â Challenging 3/5 of the circuits is near optimal for cut-and-choose (and better than challenging 1/2) Our protocols require the existence of secure-OT and claw-free functions that have a weak malleability property. We discuss an experimental implementation of our protocol to validate our efficiency claims.
Sanjam Garg, Rafail Ostrovsky, Ivan Visconti, Akshay Wadia
Abstract Two central notions of Zero Knowledge that provide very strong, yet seemingly incomparable security guarantees against malicious verifiers are those of Statistical Zero Knowledge and Resettable Zero Knowledge. The current state of the art includes several feasibility and impossibility results about the two notions separately. However, the challenging question of achieving Resettable Statistical Zero Knowledge (i.e., Resettable Zero Knowledge and Statistical Zero Knowledge simultaneously) for non-trivial languages is still open. In this paper, we show:- Resettable Statistical Zero Knowledge with efficient provers: Efficient-prover Resettable Statistical Zero-Knowledge proof systems exist for all languages that admit hash proof systems (e.g., QNR, QR, DDH, DCR). Furthermore, for these languages, as an application of our technique, we also construct a two-round resettable statistical witness-indistinguishable argument system.- Resettable Statistical Zero Knowledge with unbounded provers: Under the assumption that sub-exponentially hard one-way functions exist, rSZK = SZK. In other words, every language that admits a Statistical Zero-Knowledge (SZK) proof system also admits a Resettable Statistical Zero-Knowledge (rSZK) proof system. (Further, the result can be re-stated unconditionally provided there exists a sub-exponentially hard language in SZK). Moreover, under the assumption that (standard) one-way functions exist, all languages L such that the complement of L is random self reducible, admit a rSZK, in other words: co-RSR â rSZK. The round complexity of all our proof systems is Ă(log Îș), where Îș is the security parameter, and all our simulators are black-box. 1
A non-interactive zero-knowledge proof can be used to demonstrate the truth of a statement without revealing anything else. It has been shown under standard cryptographic assumptions that non-interactive zero-knowledge proofs of membership exist for all languages in NP. However, known non-interactive zero-knowledge proofs of membership of NP-languages yield proofs that are larger than the corresponding membership witnesses. We investigate the question of minimizing the communication overhead involved in making non-interactive zero-knowledge proofs and show that if fully homomorphic encryption exists then it is possible to minimize the size of non-interactive zero-knowledge proofs and get proofs that are of the same size as the witnesses. Our technique is applicable to many types of non-interactive zero-knowledge proofs. We apply it to both standard non-interactive zero-knowledge proofs and to universally composable non-interactive zero-knowledge proofs. The technique can also be applied outside the realm of non-interactive zero-knowledge proofs, for instance to get witness-size interactive zero-knowledge proofs in the plain model without any setup. Keywords: Non-interactive zero-knowledge proofs, fully homomorphic encryption. 1
In this paper, based on the verifiable pair and identity-based threshold cryptography, a novel identity-based (ID-based) threshold decryption scheme (IDTDS) is proposed, which is provably secure against adaptive chosen ciphertext attack under the computational bilinear Diffie-Hellman (CBDH) problem assumption in the random oracle. The pubic checkability of ciphertext in the IDTDS is given by simply creating a signed ElGamal encryption instead of a noninteractive zero-knowledge proof. Furthermore, we introduce a modified verifiable pairing to ensure all decryption shares are consistent. Our scheme is more efficient in verification than the schemes considered previously.
Markus RĂŒckert, Michael Schneider, Dominique Schröder
Verifiably encrypted signature schemes (VES) allow a signer to encrypt his or her signature under the public key of a trusted third party, while maintaining public signature verifiability. With our work, we propose two generic constructions based on Merkle authentication trees that do not require non-interactive zero-knowledge proofs (NIZKs) for maintaining verifiability. Both are stateful and secure in the standard model. Furthermore, we extend the specification for VES, bringing it closer to real-world needs. We also argue that statefulness can be a feature in common business scenarios.
Our constructions rely on the assumption that CPA (even slightly weaker) secure encryption, maskable CMA secure signatures, and collision resistant hash functions exist. Maskable means that a signature can be hidden in a verifiable way using a secret masking value. Unmasking the signature is hard without knowing the secret masking value. We show that our constructions can be instantiated with a broad range of efficient signature and encryption schemes, including two lattice-based primitives. Thus, VES schemes can be based on the hardness of worstcase lattice problems, making them secure against subexponential and quantum-computer attacks. Among others, we provide the first efficient pairing-free instantiation in the standard model.
Multiparty computation protocols have been known for more than twenty years now, but due to their lack of efficiency their use is still limited in real-world applications: the goal of this paper is the design of efficient two and multi party computation protocols aimed to fill the gap between theory and practice. We propose a new protocol to securely evaluate reactive arithmetic circuits, that offers security against an active adversary in the universally composable security framework. Instead of the âdo-and-compileâ approach (where the parties use zero-knowledge proofs to show that they are following the protocol) our key ingredient is an efficient version of the âcut-and-chooseâ technique, that allow us to achieve active security for just a (small) constant amount of work more than for passive security.
Vipul Goyal, Yuval Ishai, Mohammad Mahmoody, Amit Sahai
Motivated by the question of basing cryptographic protocols on stateless tamper-proof hardware tokens, we revisit the question of unconditional two-prover zero-knowledge proofs for NP. We show that such protocols exist in the interactive PCP model of Kalai and Raz (ICALP â08), where one of the provers is replaced by a PCP oracle. This strengthens the feasibility result of Ben-Or, Goldwasser, Kilian, and Wigderson (STOC â88) which requires two stateful provers. In contrast to previous zero-knowledge PCPs of Kilian, Petrank, and Tardos (STOC â97), in our protocol both the prover and the PCP oracle are efficient given an NP witness. Our main technical tool is a new primitive that we call interactive locking, an efficient realization of an unconditionally secure commitment scheme in the interactive PCP model. We implement interactive locking by adapting previous constructions of interactive hashing protocols to our setting, and also provide a direct construction which uses a minimal amount of interaction and improves over our interactive hashing based constructions. Finally, we apply the above results towards showing the feasibility of basing unconditional cryptography on stateless tamper-proof hardware tokens, and obtain the following results:
In this note, we show the existence of constant-round computational zero-knowledge proofs of knowledge for all N P. The existence of constant-round zero-knowledge proofs was proven by Goldreich and Kahan (Journal of Cryptology, 1996), and the existence of constant-round zeroknowledge arguments of knowledge was proven by Feige and Shamir (CRYPTO 1989). Although it is widely believed that there exist constant-round zero-knowledge proofs of knowledge for all N P, to the best of our knowledge, no proof of this fact has been published. 1