Zero-knowledge Interactive Proof Research Articles

GOTzilla: Efficient Disjunctive Zero-Knowledge Proofs from MPC in the Head, with Application to Proofs of Assets in Cryptocurrencies

We present gOTzilla, a protocol for interactive zero-knowledge proofs for very large disjunctive statements of the following format: given publicly known circuit C, and set of values Y = {y1 , . . . , yn }, prove knowledge of a witness x such that C(x) = y1 ∨ C(x) = y2 ∨ · · · ∨ C(x) = yn . These type of statements are extremely important for the proof of assets (PoA) problem in cryptocurrencies where a prover wants to prove the knowledge of a secret key sk that associates with the hash of a public key H(pk) posted on the ledger. We note that the size of n in popular cryptocurrencies, such as Bitcoin, is estimated to 80 million. For the construction of gOTzilla, we start by observing that if we restructure the proof statement to an equivalent of proving knowledge of (x, y) such that (C(x) = y) ∧ (y = y1 ∨ · · · ∨ y = yn )), then we can reduce the disjunction of equalities to 1-out-of-N oblivious transfer (OT). Our overall protocol is based on the MPC in the head (MPCitH) paradigm. We additionally provide a concrete, efficient extension of our protocol for the case where C combines algebraic and non-algebraic statements (which is the case in the PoA application). We achieve an asymptotic communication cost of O(log n) plus the proof size of the underlying MPCitH protocol. While related work has similar asymptotic complexity, our approach results in concrete performance improvements. We implement our protocol and provide benchmarks. Concretely, for a set of size 1 million entries, the total run-time of our protocol is 14.89 seconds using 48 threads, with 6.18 MB total communication, which is about 4x faster compared to the state of the art when considering a disjunctive statement with algebraic and non-algebraic elements.

SpyChain: A Lightweight Blockchain for Authentication and Anonymous Authorization in IoD

In this paper, we have proposed a lightweight blockchain based model to provide distributed authentication and anonymous authorization in IoD. We have proposed four different approaches to hide the identity of unmanned aerial vehicles UAV during the message exchanges using the blockchain. Non Interactive Zero Knowledge Proof (NIZKP) with bilinear map has been used to provide anonymity of UAV on the blockchain. The first approach describes a mechanism for the unlinkability of user identities. The second approach provides resistance against malleability attack together with unlinkability. The third approach ensures sender trackability to the receiver. In the fourth scheme, a UAV can delegate its task of tracking transactions to GCS in such a way that GCS can track the transaction of UAV but cannot claim the transaction’s authority. Relevant proofs of security for Signature Unforgeability and Unlinkability in Ciphertext (UN-C) are given to prove the strength of the techniques.

A Blockchain based ITS framework with Privacy Preserving for Secure and Reliable Communication

With the omnipresence of technology, intelligent transportation system (ITS) is no more a distant dream but has become an achievable reality. One of the fundamental challenges in the implementation of an ITS is the proper management of security and privacy issues, especially how the system confirms the validity of its users. Most of the existing security mechanisms are based on a centralized framework and assume the registration authority and roadside units to be trustful. Therefore, a distributed framework using Blockchain and, a very lightweight and privacy-preserving authentication protocol employing an interactive zero-knowledge proof (ZKP) based on elliptic curve cryptography (ECC) is proposed. An in-depth analysis of the protocol demonstrates that it meets all the security and privacy requisites of an ITS. In addition, the suggested protocol is also validated using the widely used AVISPA tool. The reliability and effectiveness of the protocol are analyzed through simulation using NS2 which proves the practicality of the protocol.

Towards Large-Scale and Privacy-Preserving Contact Tracing in COVID-19 Pandemic: A Blockchain Perspective.

Activity-tracking applications and location-based services using short-range communication (SRC) techniques have been abruptly demanded in the COVID-19 pandemic, especially for automated contact tracing. The attention from both public and policy keeps raising on related practical problems, including 1) how to protect data security and location privacy? 2) how to efficiently and dynamically deploy SRC Internet of Thing (IoT) witnesses to monitor large areas? To answer these questions, in this paper, we propose a decentralized and permissionless blockchain protocol, named Bychain. Specifically, 1) a privacy-preserving SRC protocol for activity-tracking and corresponding generalized block structure is developed, by connecting an interactive zero-knowledge proof protocol and the key escrow mechanism. As a result, connections between personal identity and the ownership of on-chain location information are decoupled. Meanwhile, the owner of the on-chain location data can still claim its ownership without revealing the private key to anyone else. 2) An artificial potential field-based incentive allocation mechanism is proposed to incentivize IoT witnesses to pursue the maximum monitoring coverage deployment. We implemented and evaluated the proposed blockchain protocol in the real-world using the Bluetooth 5.0. The storage, CPU utilization, power consumption, time delay, and security of each procedure and performance of activities are analyzed. The experiment and security analysis is shown to provide a real-world performance evaluation.

A Identification and Key Establishment Scheme based on Self-Certified Public Key for MANETs

Due to the mobility of nodes, lack of infrastructure and limited computing and storage resources in mobile ad hoc networks (MANETs), this scheme uses the self-certification public key, combined with the interactive zero-knowledge proof and KEA+ key exchange method in the GPS identity authentication protocol, uses four interactions to complete the two-way identity authentication and key exchange of both parties, and which security is analyzed subsequently. The scheme effectively reduces the leakage of the claimant’s secret knowledge in the identity authentication process, and enhances the reliability of the identity authentication and key exchange process.

AN EFFICIENT AUTHENTICATION PROTOCOL USING ZERO KNOWLEDGE PROPERTY AND PAIRING ON ELLIPTIC CURVES

The systematic introduction to zero knowledge proof protocol has important theoretical guidance and practical significance on attracting more scholars involved in research as well as expanding application fields. Zero-knowledge proofs were first conceived in 1985 by Shafi Golwasser, Silvio Micalli and Charles Rackoff in a draft of the knowledge complexity of interactive proof systems. The goal of the present paper is to introduce a new identity based scheme which is a combination of zero-knowledge interactive proof and weil pairing on elliptic curves. The concept of weil pairing was first introduced by Andre Weil in 1940. It plays an important role in the theoretical study of the arithmetic of elliptic curves and Abelian varieties. It has also recently become extremely useful in cryptologic constructions related to these objects.

Brandt’s fully private auction protocol revisited

Auctions have a long history, having been recorded as early as 500 B.C. [17]. Nowadays, electronic auctions have been a great success and are increasingly used. Many cryptographic protocols have been proposed to address the various security requirements of these electronic transactions, in particular to ensure privacy. Brandt [4] developed a protocol that computes the winner using homomorphic operations on a distributed ElGamal encryption of the bids. He claimed that it ensures full privacy of the bidders, i.e. no information apart from the winner and the winning price is leaked. We first show that this protocol – when using malleable interactive zero-knowledge proofs – is vulnerable to attacks by dishonest bidders. Such bidders can manipulate the publicly available data in a way that allows the seller to deduce all participants’ bids. Additionally we discuss some issues with verifiability as well as attacks on non-repudiation, fairness and the privacy of individual bidders exploiting authentication problems.

Delegating Computation

In this work we study interactive proofs for tractable languages. The (honest) prover should be efficient and run in polynomial time or, in other words, a “muggle”.1 The verifier should be super-efficient and run in nearly linear time. These proof systems can be used for delegating computation: a server can run a computation for a client and interactively prove the correctness of the result. The client can verify the result’s correctness in nearly linear time (instead of running the entire computation itself). Previously, related questions were considered in the holographic proof setting by Babai et al. [1991b] in the argument setting under computational assumptions by Kilian, and in the random oracle model by Micali [1994]. Our focus, however, is on the original interactive proof model where no assumptions are made on the computational power or adaptiveness of dishonest provers. Our main technical theorem gives a public coin interactive proof for any language computable by a log-space uniform boolean circuit with depth d and input length n . The verifier runs in time n · poly( d , log( n )) and space O (log( n )), the communication complexity is poly( d , log( n )), and the prover runs in time poly( n ). In particular, for languages computable by log-space uniform NC (circuits of polylog( n ) depth), the prover is efficient, the verifier runs in time n · polylog( n ) and space O (log( n )), and the communication complexity is polylog( n ). Using this theorem we make progress on several questions. --- We show how to construct 1-round computationally sound arguments with polylog communication for any log-space uniform NC computation. The verifier runs in quasi-linear time. This result uses a recent transformation of Kalai and Raz from public coin interactive proofs to 1-round arguments . The soundness of the argument system is based on the existence of a PIR scheme with polylog communication. --- We construct interactive proofs with public coin, log-space, poly-time verifiers for all of P are given. This settles an open question regarding the expressive power of proof systems with such verifiers. --- We construct zero-knowledge interactive proofs are given with communication complexity quasi-linear in the witness length for any NP language verifiable in NC , based on the existence of 1-way functions. --- We construct probabilistically checkable arguments (a model due to Kalai and Raz) of size polynomial in the witness length (rather than instance length) for any NP language verifiable in NC , under computational assumptions, are provided.

Secret Sharing Member Expansion Protocol Based on ECC

The protocols for member expansion in secret sharing schemes are very useful for key management in dynamic topology networks. In order to reduce the computation complexity of the existed protocols for member expansion in secret sharing schemes, a new protocol is proposed based on the problem of elliptic curve discrete logarithm. This paper exam- ines fifteen most recent patens that were awarded in the area of secret sharing. Unlike traditional detailed patent reviews that are focused on applying the simple secret sharing method, the proposed protocol has the following merits: 1) there is no trust center ; 2) only requesting broadcast 21 t + times to generate the sub-secret for the new participant and the new participant can verify the truth of the sub-secret; 3) the old participants can verify the new sub-secret by the non- interactive zero-knowledge proof protocol; 4) In the sub-secret generation stage, not only sub-secrets of old participants but also the sub-secret of new participant is secure. Compared to the existed protocols, the proposed protocol has lower computational complexity and less communications. Therefore, the proposed protocol has higher performance and is suit- able for resource-constrained terminals of dynamic networks.

Secure and Efficient Audit Service Outsourcing for Data Integrity in Clouds

Cloud-based outsourced storage relieves the client’s load for storage management and maintenance by providing a comparably low-cost, scalable, location-independent platform. Though, the information that clients no longer have physical control of data specifies that they are facing a potentially formidable risk for missing or corrupted data. To avoid the security risks, inspection services are serious to ensure the integrity and availability of outsourced data and to achieve digital forensics and reliability on cloud computing. Provable data possession (PDP), which is a cryptographic method for validating the reliability of data without retrieving it at an untrusted server, can be used to realize audit services. In this project, profiting from the interactive zero-knowledge proof system, the construction of an interactive PDP protocol to prevent the fraudulence of prover (soundness property) and the leakage of verified data (zero knowledge property).To prove that our construction holds these properties based on the computation Diffie–Hellman assumption and the rewindable black-box knowledge extractor. An efficient mechanism on probabilistic queries and periodic verification is proposed to reduce the audit costs per verification and implement abnormal detection timely. Also, we present an efficient method for choosing an optimal parameter value to reduce computational overheads of cloud audit services.

Using Fully Homomorphic Hybrid Encryption to Minimize Non-interative Zero-Knowledge Proofs

A non-interactive zero-knowledge (NIZK) proof can be used to demonstrate the truth of a statement without revealing anything else. It has been shown under standard cryptographic assumptions that NIZK proofs of membership exist for all languages in NP. While there is evidence that such proofs cannot be much shorter than the corresponding membership witnesses, all known NIZK proofs for NP languages are considerably longer than the witnesses. Soon after Gentry's construction of fully homomorphic encryption, several groups independently contemplated the use of hybrid encryption to optimize the size of NIZK proofs and discussed this idea within the cryptographic community. This article formally explores this idea of using fully homomorphic hybrid encryption to optimize NIZK proofs and other related cryptographic primitives. We investigate the question of minimizing the communication overhead of NIZK proofs for NP and show that if fully homomorphic encryption exists then it is possible to get proofs that are roughly of the same size as the witnesses. Our technique consists in constructing a fully homomorphic hybrid encryption scheme with ciphertext size $$|m|+{\mathrm {poly}}(k)$$|m|+poly(k), where $$m$$m is the plaintext and $$k$$k is the security parameter. Encrypting the witness for an NP-statement allows us to evaluate the NP-relation in a communication-efficient manner. We apply this technique 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 or to minimize the communication in secure computation protocols.

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.

Authentication Schemes Using Polynomials Over Non-Commutative Rings

Authentication is a process by which an entity,which could be a person or intended computer,establishes its identity to another entity.In private and public computer networks including the Internet,authentication is commonly done through the use of logon passwords. Knowledge of the password is assumed to guarantee that the user is authentic.Internet business and many other transactions require a more stringent authentication process. The aim of this paper is to propose two authentication schemes based on general non-commutative rings. The key idea of the schemes is that for a given non-commutative ring; one can build polynomials on additive structure and takes them as underlying work structure. By doing so, one can implement authentication schemes, one of them being zero-knowledge interactive proofs of knowledge, on multiplicative structure of the ring. The security of the schemes is based on the intractability of the polynomial symmetrical decomposition problem over the given non-commutative ring.

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.

Public Watermark Detection Resistant to Sensitivity Attacks

A public watermark detection scheme using verifiable secret sharing is proposed. It removes the expensive zero-knowledge interactive proofs and replaces the traditional trusted third party with a group of proxies. Moreover, the scheme is secure against sensitivity attacks and very efficient in terms of computation cost, the number of rounds and bandwidth required in the communications.

Adaptively Secure Threshold Signature Scheme in the Standard Model

We propose a distributed key generation protocol for pairing-based cryptosystems which is adaptively secure in the erasure-free and secure channel model, and at the same time completely avoids the use of interactive zero-knowledge proofs. Utilizing it as the threshold key generation protocol, we present a secure (t,n) threshold signature scheme based on the Waters' signature scheme. We prove that our scheme is unforgeable and robust against any adaptive adversary who can choose players for corruption at any time during the run of the protocols and make adaptive chosen-message attacks. And the security proof of ours is in the standard model (without random oracles). In addition our scheme achieves optimal resilience, that is, the adversary can corrupt any t<n/2 players.

Challenging epistemology: Interactive proofs and zero knowledge

This essay explores what (if anything) research on interactive zero knowledge proofs has to teach philosophers about the epistemology of mathematics and theoretical computer science. Though such proof systems initially appear ‘revolutionary’ and are a nonstandard conception of ‘proof’, I will argue that they do not have much philosophical import. Possible lessons from this work for the epistemology of mathematics—our models of mathematical proof should incorporate interaction, our theories of mathematical evidence must account for probabilistic evidence, our valuation of a mathematical proof should solely focus on its persuasive power—are either misguided or old hat. And while the differences between interactive and mathematical proofs suggest the need to develop a separate epistemology of theoretical computer science (or at least complexity theory) that differs from our theory of mathematical knowledge, a casual look at the actual practice of complexity theory indicates that such a distinct epistemology may not be necessary.

On Monotone Formula Composition of Perfect Zero-Knowledge Languages

We investigate structural properties of interactive perfect zero-knowledge (PZK) proofs. Specifically, we look into the closure properties of PZK languages under monotone boolean formula composition. This gives rise to new protocol techniques. We show that interactive PZK for random self-reducible (RSR) (and for co-RSR) languages is closed under monotone boolean formula composition. Namely, we present PZK proofs for monotone boolean formulae whose atoms are statements about membership in a PZK language which is RSR (or whose complement is RSR). We also discuss extensions, recent applications, and generalizations of the techniques.

Signcryption with Non-interactive Non-repudiation

Signcryption [33] is a public key primitive that achieves the functionality of both an encryption scheme and a signature scheme simultaneously. It does this more efficiently than a composition of public key encryption and public key signature. We present a model of security for signcryption schemes that offer non-interactive non-repudiation. This is non-repudiation in which the judge settling a repudiation dispute does not have to get involved in an interactive zero-knowledge proof. Our model applies to many existing schemes in the literature Bao and Deng, [4] He and Wu, [22] Peterson and Michels, [28]. We explain why the scheme proposed in Bao and Deng, [4] is insecure under any definition of privacy based on the idea of indistinguishable encryptions Goldwasser and Micali, [20]. We describe a modified scheme to overcome the problem. Proofs of security are given for the scheme in the random oracle model Bellare and Rogaway, [10].

Entity authentication schemes using braid word reduction

Artin's braid groups currently provide a promising background for cryptographical applications, since the first cryptosystems using braids were introduced in [I. Anshel, M. Anshel, D. Goldfeld, An algebraic method for public-key cryptography, Math. Res. Lett. 6 (1999) 287–291, I. Anshel, M. Anshel, B. Fisher, D. Goldfeld, New key agreement schemes in braid group cryptography, RSA 2001, K.H. Ko, S.J. Lee, J.H. Cheon, J.W. Han, J.S. Kang, C. Park, New public-key cryptosystem using braid groups, Crypto 2000, pp. 166–184] (see also [V.M. Sidelnikov, M.A. Cherepnev, V.Y. Yashcenko, Systems of open distribution of keys on the basis of noncommutative semigroups, Ross. Acad. Nauk Dokl. 332-5 (1993); English translation: Russian Acad. Sci. Dokl. Math. 48-2 (1194) 384–386]). A variety of key agreement protocols based on braids have been described, but few authentication or signature schemes have been proposed so far. We introduce three authentication schemes based on braids, two of them being zero-knowledge interactive proofs of knowledge. Then we discuss their possible implementations, involving normal forms or an alternative braid algorithm, called handle reduction, which can achieve good efficiency under specific requirements.