Georg Fuchsbauer, Christian Hanser, Daniel Slamanig
Structure-preserving signatures (SPS) are a powerful building block for cryptographic protocols. We introduce SPS on equivalence classes (SPS-EQ), which allow joint randomization of messages and signatures. Messages are projective equivalence classes defined on group-element vectors, so multiplying a vector by a scalar yields a different representative of the same class. Our scheme lets one adapt a signature for one representative to a signature for another representative without knowledge of any secret. Moreover, given a signature, an adapted signature for a different representative is indistinguishable from a fresh signature on a random message. We propose a definitional framework for SPS-EQ and an efficient construction in Type-3 bilinear groups, which we prove secure against generic forgers. We also introduce set-commitment schemes that let one open subsets of the committed set. From this and SPS-EQ, we then build an efficient multi-show attribute-based anonymous credential system for an arbitrary number of attributes. Our ABC system avoids costly zero-knowledge proofs and only requires a short interactive proof to thwart replay attacks. It is the first credential system whose bandwidth required for credential showing is independent of the number of its attributes, i.e., constant-size. We propose strengthened game-based security definitions for ABC and prove our scheme anonymous against malicious organizations in the standard model; finally, we discuss a concurrently secure variant in the CRS model.
The notion of Zero Knowledge introduced by Goldwasser, Micali and Rackoff in STOC 1985 is fundamental in Cryptography. Motivated by conceptual and practical reasons, this notion has been explored under stronger definitions. We will consider the following two main strengthened notions. Statistical Zero Knowledge: here the zero-knowledge property will last forever, even in case in future the adversary will have unlimited power. Concurrent Non-Malleable Zero Knowledge: here the zero-knowledge property is combined with non-transferability and the adversary fails in mounting a concurrent man-inthe-middle attack aiming at transferring zero-knowledge proofs/arguments. Besides the well-known importance of both notions, it is still unknown whether one can design a zero-knowledge protocol that satisfies both notions simultaneously. In this work we shed light on this question in a very strong sense. We show a statistical concurrent non-malleable zero-knowledge argument system for N P with a black-box simulatorextractor. 1
Michel Abdalla⋆, Fabrice Benhamouda, David Pointcheval
Abstract. Smooth Projective Hash Functions (SPHFs), also known as Hash Proof Systems, were first introduced by Cramer and Shoup (Eurocrypt’02) as a tool to construct efficient IND-CCA secure encryption schemes. Since then, SPHFs have been used in various applications, including password authenticated key exchange, oblivious transfer, and zero-knowledge arguments. What makes SPHFs so interesting and powerful is that they can be seen as implicit proofs of membership for certain languages. As a result, by extending the family of languages that they can handle, one often obtains new applications or new ways to understand existent schemes. In this paper, we show how to construct SPHFs for the disjunction of languages defined generically over cyclic, bilinear, and multilinear groups. Among other applications, this enables us to construct the most efficient one-time simulation-sound (quasi-adaptive) non-interactive zero-knowledge arguments for linear languages over cyclic groups, and the first one-round group password-authenticated key exchange without random oracles.
Abstract. We construct a 3-move public coin special honest verifier zero-knowledge proof, a so-called Sigma-protocol, for a list of commitments having at least one commit-ment that opens to 0. It is not required for the prover to know openings of the other commitments. The proof system is efficient, in particular in terms of communication requiring only the transmission of a logarithmic number of commitments. We use our proof system to instantiate both ring signatures and zerocoin, a novel mech-anism for bitcoin privacy. We use our Sigma-protocol as a (linkable) ad-hoc group identi-fication scheme where the users have public keys that are commitments and demonstrate knowledge of an opening for one of the commitments to unlinkably identify themselves (once) as belonging to the group. Applying the Fiat-Shamir transform on the group identification scheme gives rise to ring signatures, applying it to the linkable group iden-tification scheme gives rise to zerocoin. Our ring signatures are very small compared to other ring signature schemes and we only assume the users ’ secret keys to be the discrete logarithms of single group elements so the setup is quite realistic. Similarly, compared with the original zerocoin protocol we rely on a weak cryptographic assumption and do not require a trusted setup. A third application of our Sigma protocol is an efficient proof of membership of a secret committed value u belonging to a public list L = {λ1,..., λN}.
Watrous (STOC 2006) proved that plugging classical bit commitment scheme that is secure against quantum attack into the GMW-type construction of zero-knowledge gives a classical zero-knowledge proof that is secure against quantum attack. In this paper, we showed that plugging quantum bit commitment scheme (allowing quantum computation and communication) into the GMW-type construction also gives a quantum zero-knowledge proof, as one expects. However, since the binding condition of quantum bit commitment scheme is inherently different from its classical counterpart, compared with Watrous ’ security proof, here we encounter new difficulty in soundness analysis. To overcome the difficulty, we take a geometric approach, managing to reduce quantum soundness analysis to classical soundness analysis. We also propose a formalization of non-interactive quantum bit commitment scheme, which may come in handy in other places. Moreover, inspired by our formalization, we generalize Naor’s construction of bit commitment scheme to the quantum setting, achieving non-interactive commit stage. We hope quantum bit commitment scheme can find more applications in quantum cryptog-raphy. 1
A probabilistically Checkable Proof (PCP) allows a randomized verifier, with oracle access to a purported proof, to probabilistically verify an input statement of the form “x ∈ L” by querying only few bits of the proof. A PCP of proximity (PCPP) has the additional feature of allowing the verifier to query only few bits of the input x, where if the input is accepted then the verifier is guaranteed that (with high probability) the input is close to some x′ ∈ L.
In this paper we discuss Bitcoin, the leader among the existing cryptocurrencies, to analyse its trends, success factors, current challenges and probable solutions to make it even better. In the introduction section, we discuss the history and working mechanism of Bitcoin. In the background section, we develop the ideas that evolved in the process of making a stable cryptocurrency. We also analyze the survey matrices of the present day cryptocurrencies. This survey clearly shows that Bitcoin is the clear winner among its kind. Section 3 is about the success factors of Bitcoin and the proceeding sections are a discussion about current challenges which pose as hurdles in making Bitcoin a better currency in the digital world. We finally discuss the balance between anonymity and reduced trust in the cryptocurrency world, before concluding the survey.
Jan 1, 2014·25th IET Irish Signals & Systems Conference 2014 and 2014 China-Ireland International Conference on Information and Communities Technologies (ISSC 2014/CIICT 2014)
The advent of the IoT with an estimated 50 billion internet enabled devices by the year 2020 raises questions about the suitability and scalability of existing mechanisms to provide privacy, data integrity and end-entity authentication between communicating peers. In this paper we present a new protocol that combines zero-knowledge proofs and key exchange mechanisms to provide secure and authenticated communication in static M2M networks, therefore addressing all the above problems. The protocol is suitable for devices with limited computational resources and can be deployed in wireless sensor networks. While the protocol requires an a-priori knowledge about the network setup and structure, it guarantees perfect forward secrecy.
We show how to realize two-factor authentication for a Bitcoin wallet employing the two-party ECDSA signature protocol adapted from MacKenzie & Reiter (2004). We also present a prototypic implementation of a Bitcoin wallet that offers both: two-factor authentication and verification over a separate channel. Since we use a smart phone as the second authentication factor, our solution can be used with hardware already available to most users and the user experience is quite similar to the existing online banking authentication methods.
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.
Fabrice Benhamouda, Stephan Krenn, Vadim Lyubashevsky, Krzysztof Pietrzak
Abstract. We design an efficient commitment scheme, and companion zero-knowledge proofs of knowledge, based on the learning with errors over rings (RLWE) problem. In particular, for rings in which almost all elements have inverses, we construct a perfectly binding commitment scheme whose hiding property relies on the RLWE assumption. Our scheme maps elements from the ring (or equivalently, n elements from Fq) to a small constant number of ring elements. We then construct Σ-protocols for proving, in a zero-knowledge manner, knowledge of the message contained in a commitment. We are able to further extend our basic protocol to allow us to prove additive and multiplicative relations among committed values. Our protocols have a communication complexity of O(Mn log q) and achieve a negligible knowledge error in one run. Here M is the constant from a rejection sampling technique that we employ, and can be set close to 1 by adjusting other parameters. Previously known Σ-protocols for LWE-related languages either relied on “smudging ” out the error (which necessitates working over large fields, resulting in poor efficiency) or only achieved a noticeable or even constant knowledge error (thus requiring many repetitions of the protocol).
We present a construction for non-interactive zero-knowledge proofs of knowledge in the random oracle model from general sigma-protocols. Our construction is secure against quantum adversaries. Prior constructions (by Fiat-Shamir and by Fischlin) are only known to be secure against classical adversaries, and Ambainis, Rosmanis, Unruh (FOCS 2014) gave evidence that those constructions might not be secure against quantum adversaries in general. To prove security of our constructions, we additionally develop new techniques for adaptively programming the quantum random oracle.
It is a widely spread belief that crypto-currencies implementing a proof of stake transaction validation system are less vulnerable to a 51% attack than crypto-currencies implementing a proof of work transaction validation system. In this article, we show that it is not the case and that, in fact, if the attacker's motivation is large enough (and this is common knowledge), he will succeed in his attack at no cost.