Blockchain Papers

Eleanor Birrell, Salil Vadhan

No abstract is available for this record.

Steven Gordon, Hoeteck Wee, David Xiao, Arkady Yerukhimovich

No abstract is available for this record.

Rafael Pass, Muthuramakrishnan Venkitasubramaniam

No abstract is available for this record.

Benoît Libert, Moti Yung

No abstract is available for this record.

Jens Groth

No abstract is available for this record.

Eric Ayeh

Zero-knowledge proofs protocols are effective interactive methods to prove a node's identity without disclosing any additional information other than the veracity of the proof. They are implementable in several ways. In this thesis, I investigate the graph isomorphism based zero-knowledge proofs protocol. My experiments and analyses suggest that graph isomorphism can easily be solved for many types of graphs and hence is not an ideal solution for implementing ZKP.

K. Subramani

In this article, we introduce a Prover–Verifier model for analysing the computational complexity of a class of constraint satisfaction problems (CSPs) termed boolean binary constraint satisfaction problems (BBCSPs). BBCSPs represent an extremely general class of CSPs and find applications in a wide variety of domains including constraint programming, puzzle solving and program testing. The constraints in a BBCSP permit the combination of multiple theories as opposed to traditional constraint systems in which all constraints belong to the same theory. We establish that each instance of a BBCSP admits a coin-flipping Turing machine that halts in time polynomial in the size of the input. Furthermore, the algorithm is oblivious in that it never sees more than one constraint at a time. The prover, P, in the Prover–Verifier model is endowed with very limited powers. In particular, it has no memory and it can only pose restricted queries to the verifier. The verifier, on the other hand, is both omniscient in that it is cognisant of all the problem details and insincere in that it does not have to decide a priori on the intended proof. However, the verifier must stay consistent in its responses, i.e. it cannot rule out a certain possibility in one response to a query from the prover and then rule in the same possibility in response to a subsequent query. We note that the combination of the resources required by the prover and the type of certificate demanded of the verifier, determine the resources required by an algorithm. Inasmuch as our provers will be memoryless and our verifiers will be asked for extremely simple certificates, our work establishes the existence of a simple, randomised algorithm for BBCSPs. Our model itself serves as a basis for the design of zero-knowledge machine learning algorithms in that the prover ends up learning the proof desired by the verifier. Likewise, our work finds applications in the domain of certifying algorithm design, wherein the goal is to provide a proof of correctness of the algorithm on the input instance by providing an easily checkable certificate.

Joseph Y. Halpern, Rafael Pass, Vasumathi Raman

Halpern, Moses and Tuttle presented a definition of interactive proofs using a notion they called practical knowledge, but left open the question of finding an epistemic formula that completely characterizes zero knowledge; that is, a formula that holds iff a proof is zero knowledge. We present such a formula, and show that it does characterize zero knowledge. Moreover, we show that variants of the formula characterize variants of zero knowledge such as concurrent zero knowledge [Dwork, Naor, and Sahai 2004] and proofs of knowledge [Feige, Fiat, and Shamir 1987; Tompa and Woll 1987].

Rahul Jain, Alexandra Kolla, Gatis Midrijānis, Ben W. Reichardt

Let $L$ be a language decided by a constant-round quantum Arthur-Merlin ($\QAM$) protocol with negligible soundness error and all but possibly the last message being classical. We prove that if this protocol is zero knowledge with a black-box, quantum simulator $\cS$, then $L \in \BQP$. Our result also applies to any language having a three-round quantum interactive proof ($\QIP$), with all but possibly the last message being classical, with negligible soundness error and a black-box quantum simulator. These results in particular make it unlikely that certain protocols can be composed in parallel in order to reduce soundness error, while maintaining zero knowledge with a black-box quantum simulator. They generalize analogous classical results of Goldreich and Krawczyk (1990). Our proof goes via a reduction to quantum black-box search. We show that the existence of a black-box quantum simulator for such protocols when $L \notin \BQP$ would imply an impossibly-good quantum search algorithm.

Jianwei Ye, Xu-lu Jiao, Yuge Zhang

Based on the verifiable encryption and zero-knowledge proof protocols of Jarecki and Shmatikov and Pedersen’s verifiable threshold secret sharing scheme, this paper proposes a new full fair secure two-party computation protocols. For getting full fair, the new protocol employs a group of third-party servers. We prove that when more than two-thirds of the third-party servers are honest, the new protocol guarantees that two parties can get their correct outputs full fairly. In the new protocol, the computation is performed in the form of garbled circuit, and only two added interaction rounds are needed for full fairness.

Sheng Zhong

Tompa and Woll constructed a zero-knowledge proof of knowing a square root of $X$ mod $N$, where $N$ is the product of two large, secret primes. In this paper, we construct a zero-knowledge proof of knowing a square root of $X_1$ or $X_2$ mod $N$. Compared with the existing solution to this problem, ours is significantly simpler.

Jong-Ho Ryu, Jung-Chan Na

This paper present an alternative scheme to key escrow scheme which allows probabilistic law enforcement access to reveal the encrypted communications. Namely, key escrow authority can reveal the information between communication parties partially. Our scheme allows law enforcement access with probability p for each message. The scheme in this paper is basically the complemented scheme of Mihir Bellare and Ronald L. Rivest [2], and combine a publicly verifiable encryption technique and translucent cryptography based on non-interactive fractional oblivious transfer. This protocol allows such access with probability for each message, for a parameter between 0 and 1, which should be chosen to provide an appropriate balance between concerns for individual privacy and the need for such law enforcement access by government. This paper induct a set of distributed key escrow authorities(DEA). The scheme is based on the El-Gamal encryption, a proof scheme of knowledge of common exponent in publicly verifiable El-Gamal public-key encryption, and a set of distributed escrow authorities. In session key recovery phase by DEA, use only partial parameters from each key escrow authorities required for session key recovery that have been passed through zero-knowledge(ZK) interactive proof protocol. The scheme allows both the law enforcement access with probability and DEA to recover the session key used to encrypt communication by User A.

Stephen R. Tate, Roopa Vishwanathan

At the heart of many fair exchange problems is verifiable escrow: a sender encrypts some value using the public key of a trusted party (called the recovery agent), and then must convince the receiver of the ciphertext that the corresponding plaintext satisfies some property (e.g., it contains the sender’s signature on a contract). Previous solutions to this problem are interactive, and often rely on communication-intensive cut-and-choose zero-knowledge proofs. In this paper, we provide a solution that uses generic trusted hardware to create an efficient, non-interactive verifiable escrow scheme. Our solution allows the protocol to use a set of recovery agents with a threshold access structure, the verifiable group escrow notion which was informally introduced by Camenisch and Damgard and which is formalized here. Finally, this paper shows how this new non-interactive verifiable escrow scheme can be used to create an efficient optimistic protocol for fair exchange of signatures.

Jianhong Zhang, Hua Chen, Qin Geng

Certificate-based cryptography solves certificate revocation problem and eliminate third-party queries in the traditional PKI and avoid key escrow in the ID-based cryptography. It is a better alternative for the traditional public key system. In this paper, we proposed an efficient certificate based signature scheme based on Schnorr signature and zero-knowledge proof technique. Our proposed scheme doesn't use pairing operator which is the most expensive computation. Then we show that our proposed scheme is proven to be against two forgeable attacks in the random oracles model, and the security is related to that of Schnorr signature.

David Xiao

Learning is a central task in computer science, and there are various formalisms for capturing the notion. One important model studied in computational learning theory is the PAC model of Valiant (CACM 1984). On the other hand, in cryptography the notion of "learning nothing'' is often modelled by the simulation paradigm: in an interactive protocol, a party learns nothing if it can produce a transcript of the protocol by itself that is indistinguishable from what it gets by interacting with other parties. The most famous example of this paradigm is zero knowledge proofs, introduced by Goldwasser, Micali, and Rackoff (SICOMP 1989). Applebaum et al. (FOCS 2008) observed that a theorem of Ostrovsky and Wigderson (ISTCS 1993) combined with the transformation of one-way functions to pseudo-random functions (Hastad et al. SICOMP 1999, Goldreich et al. J. ACM 1986) implies that if there exist non-trivial languages with zero-knowledge arguments, then no efficient algorithm can PAC learn polynomial-size circuits. They also prove a weak reverse implication, that if a certain non-standard learning task is hard, then zero knowledge is non-trivial. This motivates the question we explore here: can one prove that hardness of PAC learning is equivalent to non-triviality of zero-knowledge? We show that this statement cannot be proven via the following techniques: 1. Relativizing techniques: there exists an oracle relative to which learning polynomial-size circuits is hard and yet the class of languages with zero knowledge arguments is trivial. 2. Semi-black-box techniques: if there is a black-box construction of a zero-knowledge argument for an NP-complete language (possibly with a non-black-box security reduction) based on hardness of PAC learning, then NP has statistical zero knowledge proofs, namely NP is contained in SZK. Under the standard conjecture that NP is not contained in SZK, our results imply that most standard techniques do not suffice to prove the equivalence between the non-triviality of zero knowledge and the hardness of PAC learning. Our results hold even when considering non-uniform hardness of PAC learning with membership queries. In addition, our technique relies on a new kind of separating oracle that may be of independent interest.

Zecheng Wang, Haifeng Qian, Zhibin Li

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.

Rafael Dowsley, Jörn Müller‐Quade, Akira Otsuka, Goichiro Hanaoka · 6 authors

Abstract. This paper presents a non-interactive verifiable secret sharing scheme (VSS) tolerating a dishonest majority based on data predistributed by a trusted authority. As an application of this VSS scheme we present very efficient unconditionally secure multiparty protocols based on pre-distributed data which generalize two-party computations based on linear pre-distributed bit commitments. The main results of this paper are a non-interactive VSS where the amount of data which needs to be pre-distributed to each player depends on the number of tolerable cheaters only, a simplified multiplication protocol for shared values based on pre-distributed random products, and non-interactive zero knowledge proofs for arbitrary polynomial relations. The security of the schemes are proved using the UC framework.

Markus Rückert

No abstract is available for this record.

Kun Peng, Feng Bao

No abstract is available for this record.

Tsz Hon Yuen, Qiong Huang, Yi Mu, Willy Susilo · 6 authors

No abstract is available for this record.

Mira Belenkiy, Melissa Chase, Markulf Kohlweiss, Anna Lysyanskaya

Abstract. Efficient non-interactive zero-knowledge proofs are a powerful tool for solving many cryptographic problems. We apply the recent Groth-Sahai (GS) proof system for pairing product equations (Eurocrypt 2008) to two related cryptographic problems: compact e-cash (Eurocrypt 2005) and simulatable verifiable random functions (CRYPTO 2007). We present the first efficient compact e-cash scheme that does not rely on a random oracle. To this end we construct efficient GS proofs for signature possession, pseudo randomness and set membership. The GS proofs for pseudorandom functions give rise to a much cleaner and substantially faster construction of simulatable verifiable random functions (sVRF) under a weaker number theoretic assumption. We obtain the first efficient fully simulatable sVRF with a polynomial sized output domain (in the security parameter). 1

Rafael Pass, Wei-Lung Dustin Tseng, Douglas Wikström

We show that only languages in BPP have public-coin black-box zero-knowledge protocols that are secure under an unbounded (polynomial) number of parallel repetitions. This result holds both in the plain model (without any setup) and in the bare public key model (where the prover and the verifier have registered public keys). We complement this result by constructing a public-coin black-box zero-knowledge proof based on one-way functions that remains secure under any a priori bounded number of concurrent executions. A key step (of independent interest) in the analysis of our lower bound shows that any public-coin protocol, when repeated sufficiently in parallel, satisfies a notion of “resettable soundness” if the verifier picks its random coins using a pseudorandom function.

Ronald Cramer, Ivan Damgård, Marcel Keller

No abstract is available for this record.

Mira Belenkiy, Jan Camenisch, Melissa Chase, Markulf Kohlweiss · 6 authors

No abstract is available for this record.