Zero-knowledge Proof System Research Articles

Verifiably encrypted signatures with short keys based on the decisional linear problem and obfuscation for encrypted VES

Verifiably encrypted signatures (VES) are encrypted signatures under a public key of a trusted third party. We can verify their validity without decryption. VES has useful applications such as online contract signing and optimistic fair exchange. We propose a VES scheme that is secure under the decisional linear (DLIN) assumption in the standard model. We also propose new obfuscators for encrypted signatures (ES) and encrypted VES (EVES) that are secure under the DLIN assumption. All previous VES schemes in the standard model are either secure under standard assumptions (such as the computational Diffie–Hellman assumption) with large verification (or secret) keys or secure under non-standard dynamic $$q$$ -type assumptions (such as the $$q$$ -strong Diffie–Hellman extraction assumption) with short verification keys. Our scheme is the first VES scheme with short verification (and secret) keys secure under the DLIN assumption (standard assumption). We construct new obfuscators for ES/EVES as byproducts of our new VES scheme. They are more efficient than previous obfuscators with respect to public key size. Previous obfuscators for EVES are secure under non-standard assumption and use zero-knowledge (ZK) proof systems and Fiat–Shamir heuristics to obtain non-interactive ZK, i.e., its security is considered in the random oracle model. Thus, our scheme also has an advantage with respect to assumptions and the security model. Our new obfuscator for ES is obtained from our new obfuscator for EVES.

A Survey of Noninteractive Zero Knowledge Proof System and Its Applications

Zero knowledge proof system which has received extensive attention since it was proposed is an important branch of cryptography and computational complexity theory. Thereinto, noninteractive zero knowledge proof system contains only one message sent by the prover to the verifier. It is widely used in the construction of various types of cryptographic protocols and cryptographic algorithms because of its good privacy, authentication, and lower interactive complexity. This paper reviews and analyzes the basic principles of noninteractive zero knowledge proof system, and summarizes the research progress achieved by noninteractive zero knowledge proof system on the following aspects: the definition and related models of noninteractive zero knowledge proof system, noninteractive zero knowledge proof system of NP problems, noninteractive statistical and perfect zero knowledge, the connection between noninteractive zero knowledge proof system, interactive zero knowledge proof system, and zap, and the specific applications of noninteractive zero knowledge proof system. This paper also points out the future research directions.

Advanced Cooperative Provable Data Possession based Data Integrity Verification for Multi-Cloud Storage

Cloud computing is an emerging field which is raising its importance in the field of storage of data. Every individual, firm or organization wants to store data that has the limited storage capacity. For that purpose, there is need to outsource data to some Cloud Service Provider, there arises a problem of security of data. Security comes with 3 main parameters confidentiality, integrity and availability. For these issues, there is term called Provable Data Possession, it is nothing but the proof given by service provider to the data owner when there is demand by owner. Paper proposes an effective PDP model for integrity verification of data on distributed multicloud storage by using web-servers and Trusted Third Party. Here proposed the use of techniques such as, Advanced Cooperative Provable Data Possession (Advanced CPDP), Homomorphic Verifiable Response and Hash Index Hierarchy for Multiprover Zero Knowledge Proof System which is an Interactive Proof System. General Terms Security, Data Integrity on multi cloud

Latest Research Progress on Non-interactive Zero Knowledge Proof System

Latest Research Progress on Non-interactive Zero Knowledge Proof System

Cooperative Demonstrable Data Retention for Integrity Verification in Multi-Cloud Storage

Demonstrable data retention (DDR) is a technique which certain the integrity of data in storage outsourcing. In this paper we propose an efficient DDR protocol that prevent attacker in gaining information from multiple cloud storage node. Our technique is for distributed cloud storage and support the scalability of services and data migration. This technique Cooperative store and maintain the client’s data on multi cloud storage. To insure the security of our technique we use zero-knowledge proof system, which satisfies zero-knowledge properties, knowledge soundness and completeness. We present a Cooperative DDR (CDDR) protocol based on hash index hierarchy and homomorphic verification response. In order to optimize the performance of our technique we use a novel technique for selecting optimal parameter values to reduce the storage overhead and computation costs of client for service providers. Keyword: Demonstrable Data Retention, homomorphic, zero knowledge, storage outsourcing, multiple cloud, Cooperative, data Retention.

Cooperative Provable Data Possession for Integrity Verification in Multicloud Storage

Provable data possession (PDP) is a technique for ensuring the integrity of data in storage outsourcing. In this paper, we address the construction of an efficient PDP scheme for distributed cloud storage to support the scalability of service and data migration, in which we consider the existence of multiple cloud service providers to cooperatively store and maintain the clients' data. We present a cooperative PDP (CPDP) scheme based on homomorphic verifiable response and hash index hierarchy. We prove the security of our scheme based on multiprover zero-knowledge proof system, which can satisfy completeness, knowledge soundness, and zero-knowledge properties. In addition, we articulate performance optimization mechanisms for our scheme, and in particular present an efficient method for selecting optimal parameter values to minimize the computation costs of clients and storage service providers. Our experiments show that our solution introduces lower computation and communication overheads in comparison with noncooperative approaches.

SECURE COLLABORATIVE INTEGRITY VERIFICATION FOR HYBRID CLOUD ENVIRONMENTS

A hybrid cloud is a cloud computing environment in which an organization provides and manages some internal resources and has others provided externally. However, this new environment could bring irretrievable losses to the clients due to a lack of integrity verification mechanism for distributed data outsourcing. To support scalable service and data migration, in this paper we address the construction of a collaborative integrity verification mechanism in hybrid clouds where we consider the existence of multiple cloud service providers to collaboratively store and maintain the clients' data. We propose a collaborative provable data possession scheme adopting the techniques of homomorphic verifiable responses and hash index hierarchy. In addition, we articulate the performance optimization mechanisms for our scheme and prove the security of our scheme based on multi-prover zero-knowledge proof system, which can satisfy the properties of completeness, knowledge soundness, and zero-knowledge. Our experiments also show that our proposed solution only incurs a small constant amount of communications overhead.

New Techniques for Noninteractive Zero-Knowledge

Noninteractive zero-knowledge (NIZK) proof systems are fundamental primitives used in many cryptographic constructions, including public-key encryption secure against chosen ciphertext attack, digital signatures, and various other cryptographic protocols. We introduce new techniques for constructing NIZK proofs based on groups with a bilinear map. Compared to previous constructions of NIZK proofs, our techniques yield dramatic reduction in the length of the common reference string (proportional to security parameter) and the size of the proofs (proportional to security parameter times the circuit size). Our novel techniques allow us to answer several long-standing open questions in the theory of noninteractive proofs. We construct the first perfect NIZK argument system for all NP. We construct the first universally composable NIZK argument for all NP in the presence of an adaptive adversary. We construct a non-interactive zap for all NP, which is the first that is based on a standard cryptographic security assumption.

Attack against a batch zero-knowledge proof system

Chida and Yamamoto propose a batch proof algorithm to enhance the performance of multiple instances of zero knowledge proof of partial knowledge. When multiple instances of zero knowledge proof of partial knowledge need to be proved simultaneously, their proof algorithm employs a batching mechanism to reduce the cost in computation and communication. Unfortunately, their batch proof algorithm is not sound and vulnerable to an attack, which completely breaks soundness of the proof. More precisely, an adversary can design the multiple partial knowledge statements in a special way such that no matter how he is challenged he can always pass the verification as a prover in the batch proof scheme while he does not have the knowledge he claims. The attack is presented and is formally illustrated to always succeed.

Efficient audit service outsourcing for data integrity in clouds

Cloud-based outsourced storage relieves the client's burden for storage management and maintenance by providing a comparably low-cost, scalable, location-independent platform. However, the fact that clients no longer have physical possession of data indicates that they are facing a potentially formidable risk for missing or corrupted data. To avoid the security risks, audit services are critical to ensure the integrity and availability of outsourced data and to achieve digital forensics and credibility on cloud computing. Provable data possession (PDP), which is a cryptographic technique for verifying the integrity of data without retrieving it at an untrusted server, can be used to realize audit services.In this paper, profiting from the interactive zero-knowledge proof system, we address the construction of an interactive PDP protocol to prevent the fraudulence of prover (soundness property) and the leakage of verified data (zero-knowledge property). We prove that our construction holds these properties based on the computation Diffie–Hellman assumption and the rewindable black-box knowledge extractor. We also propose an efficient mechanism with respect to probabilistic queries and periodic verification to reduce the audit costs per verification and implement abnormal detection timely. In addition, we present an efficient method for selecting an optimal parameter value to minimize computational overheads of cloud audit services. Our experimental results demonstrate the effectiveness of our approach.

On constant-round concurrent non-malleable proof systems

Security under man-in-the-middle attacks is extremely important when protocols are executed on asynchronous networks, as the Internet. Focusing on interactive proof systems, one would like also to achieve unconditional soundness, so that proving a false statement is not possible even for a computationally unbounded adversarial prover. Motivated by such requirements, in this paper we address the problem of designing constant-round protocols in the plain model that enjoy simultaneously non-malleability (i.e., security against man-in-the-middle attacks) and unconditional soundness (i.e., they are proof systems). We first give a construction of a constant-round one–many (i.e., one honest prover, many honest verifiers) concurrent non-malleable zero-knowledge proof (in contrast to argument) system for every NP language in the plain model. We then give a construction of a constant-round concurrent non-malleable witness-indistinguishable proof system for every NP language. Compared with previous results, our constructions are the first constant-round proof systems that in the plain model guarantee simultaneously security against some non-trivial concurrent man-in-the-middle attacks and against unbounded malicious provers.

Which Languages Have 4-Round Zero-Knowledge Proofs?

We show that if a language L has a 4-round, black-box, computational zero-knowledge proof system with negligible soundness error, then $\bar{L}\in \mathsf{MA}$ . Assuming the polynomial hierarchy does not collapse, this means in particular that NP-complete languages do not have 4-round zero-knowledge proofs with black-box simulation.

Computational soundness of symbolic zero-knowledge proofs*

The abstraction of cryptographic operations by term algebras, called Dolev-Yao models, is essential in almost all tool-supported methods for proving security protocols. Recently significant progress was made in proving that Dolev-Yao models offering the core cryptographic operations such as encryption and digital signatures can be sound with respect to actual cryptographic realizations and security definitions. Recent work, however, has started to extend Dolev-Yao models to more sophisticated operations with unique security features. Zero-knowledge proofs arguably constitute the most amazing such extension. In this paper, we first identify which additional properties a cryptographic (non-interactive) zero-knowledge proof needs to fulfill in order to serve as a computationally sound implementation of symbolic (Dolev-Yao style) zero-knowledge proofs; this leads to the novel definition of a symbolically-sound zero-knowledge proof system. We prove that even in the presence of arbitrary active adversaries, such proof systems constitute computationally sound implementations of symbolic zero-knowledge proofs. This yields the first computational soundness result for symbolic zero-knowledge proofs and the first such result against fully active adversaries of Dolev-Yao models that go beyond the core cryptographic operations.

Quantum protocols for zero-knowledge systems

Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. An intrinsic characteristic of a zero-knowledge systems is the assumption that is impossible for the verifier to show to a third party that he has interacted with the prover. However, it has been shown that using quantum correlations the impossibility of transferring proofs can be successfully attacked. In this work we show two new protocols for proof transference, being the first one based on teleportation and the second one without using entangled states. In this last case, we assume that the third party can communicate in advance with both verifier and prover. Following, we present a quantum zero-knowledge protocol based on quantum bit commitment that can be implemented with today technology.

Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles

We consider cryptographic and physical zero-knowledge proof schemes for Sudoku, a popular combinatorial puzzle. We discuss methods that allow one party, the prover, to convince another party, the verifier, that the prover has solved a Sudoku puzzle, without revealing the solution to the verifier. The question of interest is how a prover can show: (i) that there is a solution to the given puzzle, and (ii) that he knows the solution, while not giving away any information about the solution to the verifier. In this paper we consider several protocols that achieve these goals. Broadly speaking, the protocols are either cryptographic or physical. By a cryptographic protocol we mean one in the usual model found in the foundations of cryptography literature. In this model, two machines exchange messages, and the security of the protocol relies on computational hardness. By a physical protocol we mean one that is implementable by humans using common objects, and preferably without the aid of computers. In particular, our physical protocols utilize items such as scratch-off cards, similar to those used in lotteries, or even just simple playing cards. The cryptographic protocols are direct and efficient, and do not involve a reduction to other problems. The physical protocols are meant to be understood by “lay-people” and implementable without the use of computers.

Existence of 3-round zero-knowledge proof systems for NP

This paper considers the existence of 3-round zero-knowledge proof systems for NP. Whether there exist 3-round non-black-box zero-knowledge proof systems for NP language is an open problem. By introducing a new interactive proof model, we construct a 3-round zero-knowledge proof system for graph 3-coloring under standard assumptions. Our protocol is a non-black-box zero-knowledge proof because we adopt a special strategy to prove the zero-knowledge property. Consequently, our construction shows the existence of 3-round non-black-box zero-knowledge proof for all languages in NP under the DDH assumption.

Hybrid commitments and their applications to zero-knowledge proof systems

We introduce the notion of hybrid trapdoor commitment schemes. Intuitively a hybrid trapdoor commitment scheme is a primitive which can be either an unconditionally binding commitment scheme or a trapdoor commitment scheme depending on the distribution of commitment parameters. Moreover, such two possible distributions are computationally indistinguishable. Hybrid trapdoor commitments are related but different with respect to mixed commitments (introduced by Damgård and Nielsen at Crypto 2002). In particular hybrid trapdoor commitments can either be polynomially trapdoor commitments or unconditionally binding commitments, while mixed commitments can be either trapdoor commitments or extractable commitments. In this paper we show that strong notions (e.g., simulation sound, multi-trapdoor) of hybrid trapdoor commitments admit constructions based on the sole assumption that one-way functions exist as well as efficient constructions based on standard number-theoretic assumptions. To further stress the difference between hybrid and mixed commitments, we remark here that mixed commitments seem to require stronger theoretical assumptions (and the known number-theoretic constructions are less efficient). Our main result, is to show how to construct concurrent and simulation-sound zero-knowledge proof systems (in contrast to the arguments recently presented in [I. Damgård, Efficient concurrent zero-knowledge in the auxiliary string model, in: Advances in Cryptology — Eurocrypt’00, in: Lecture Notes in Computer Science, vol. 1807, Springer-Verlag, 2000, pp. 418–430; P. MacKenzie, K. Yang, On simulation-sound trapdoor commitments, in: Advances in Cryptology — Eurocrypt’04, in: Lecture Notes in Computer Science, vol. 3027, Springer-Verlag, 2004, pp. 382–400; R. Gennaro, Multi-trapdoor commitments and their applications to proofs of knowledge secure under concurrent man-in-the-middle attacks, in: Advances in Cryptology — Crypto’04, in: Lecture Notes in Computer Science, vol. 3152, Springer-Verlag, 2004, pp. 220–236]) in the common reference string model. We crucially use hybrid trapdoor commitments since we present general constructions based on the sole assumption that one-way functions exist and very efficient constructions based on number-theoretic assumptions.

Lower bounds for non-black-box zero knowledge

We show new lower bounds and impossibility results for general (possibly non-black-box) zero-knowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions: 1. There does not exist a two-round zero-knowledge proof system with perfect completeness for an NP -complete language. The previous impossibility result for two-round zero knowledge, by Goldreich and Oren [J. Cryptol. 7(1) (1994) 1–32] was only for the case of auxiliary-input zero-knowledge proofs and arguments. 2. There does not exist a constant-round zero-knowledge strong proof or argument of knowledge (as defined by Goldreich [Foundations of Cryptography: Basic Tools, Cambridge University Press, Cambridge, 2001.]) for a non-trivial language. 3. There does not exist a constant-round public-coin proof system for a non-trivial language that is resettable zero knowledge. This result also extends to bounded-resettable zero knowledge, in which the number of resets is a priori bounded by a polynomial in the input length and prover-to-verifier communication. In contrast, we show that under reasonable assumptions, there does exist such a (computationally sound) argument system that is bounded-resettable zero knowledge. The complexity assumptions we use are not commonly used in cryptography. However, in all cases, we show that assumptions similar to ours are necessary for the above results. Most previously known lower bounds, such as those of Goldreich and Krawczyk [SIAM J. Comput. 25(1) (1996) 169–192], were only for black-box zero knowledge. However, a result of Barak (Proceedings of the 42nd FOCS, IEEE, 2001, pp. 106–115) shows that many (or even most) of these black-box lower bounds do not extend to the case of general zero knowledge.

Memorizable interactive proof and zero-knowledge proof systems

Interactive proof and zero-knowledge proof systems are two important concepts in cryptography and complexity theory. In the past two decades, a great number of interactive proof and zero-knowledge proof protocols have been designed and applied in practice. In this paper, a simple memorizable zero-knowledge protocol is proposed for graph non-isomorphism problem, based on the memorizable interactive proof system, which is extended from the original definition of interactive proof and is more applicable in reality.

Reduction zero-knowledge*

Abstract The nature of zero-knowledge is re-examined and the evidence for the following belief is shown: the classic simulation based definitions of zero- knowledge (simulation zero-knowledge) may be somewhat too strong to include some “nice” protocols in which the malicious verifier seems to learn nothing but we do not know how to construct a zero-knowledge simulator for it. To overcome this problem a new relaxation of zero-knowledge, reduction zero-knowledge, is introduced. It is shown that reduction zero- knowledge just lies between simulation zero-knowledge and witness indistinguishability. Under the assumption of existence of one-way permutations a 4-round public-coin reduction zero-knowledge proof system for NP is presented and in practice this protocol works in 3 rounds since the first verifier's message can be fixed once and for all.