On Constant-Round Concurrent Zero-Knowledge from a Knowledge Assumption

In this work, we consider the long-standing open question of constructing constant-round concurrent zero-knowledge protocols in the plain model. Resolving this question is known to require non-black-box techniques. We consider non-black-box techniques for zero-knowledge based on knowledge assumptions, a line of thinking initiated by the work of Hada and Tanaka (CRYPTO 1998). Prior to our work, it was not known whether knowledge assumptions could be used for achieving security in the concurrent setting, due to a number of significant limitations that we discuss here. Nevertheless, we obtain the following results: 1. We obtain the first constant round concurrent zero-knowledge argument for \textbf{NP} in the plain model based on a new variant of knowledge of exponent assumption. Furthermore, our construction avoids the inefficiency inherent in previous non-black-box techniques such that those of Barak (FOCS 2001); we obtain our result through an efficient protocol compiler. 2. Unlike Hada and Tanaka, we do not require a knowledge assumption to argue the soundness of our protocol. Instead, we use a discrete log like assumption, which we call Diffie-Hellman Logarithm Assumption, to prove the soundness of our protocol. 3. We give evidence that our new variant of knowledge of exponent assumption is in fact plausible. In particular, we show that our assumption holds in the generic group model. 4. Knowledge assumptions are especially delicate assumptions whose plausibility may be hard to gauge. We give a novel framework to express knowledge assumptions in a more flexible way, which may allow for formulation of plausible assumptions and exploration of their impact and application in cryptography.Comment: 30 pages, 3 figure

Universally Composable Quantum Multi-Party Computation

The Universal Composability model (UC) by Canetti (FOCS 2001) allows for secure composition of arbitrary protocols. We present a quantum version of the UC model which enjoys the same compositionality guarantees. We prove that in this model statistically secure oblivious transfer protocols can be constructed from commitments. Furthermore, we show that every statistically classically UC secure protocol is also statistically quantum UC secure. Such implications are not known for other quantum security definitions. As a corollary, we get that quantum UC secure protocols for general multi-party computation can be constructed from commitments

Quantum Cryptography Beyond Quantum Key Distribution

Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries---including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference

New Notions of Security: Achieving Universal Composability without Trusted Setup

We propose a modification to the framework of Universally Composable (UC) security [3]. Our new notion, involves comparing the protocol executions with an ideal execution involving ideal functionalities (just as in UC-security), but allowing the environment and adversary access to some super-polynomial computational power. We argue the meaningfulness of the new notion, which in particular subsumes many of the traditional notions of security. We generalize the Universal Composition theorem of [3] to the new setting. Then under new computational assumptions, we realize secure multi-party computation (for static adversaries) without a common reference string or any other set-up assumptions, in the new framework. This is known to be impossible under the UC framework.

3-Message Zero Knowledge Against Human Ignorance

The notion of Zero Knowledge has driven the field of cryptography since its conception over thirty years ago. It is well established that two-message zero-knowledge protocols for NP do not exist, and that four-message zero-knowledge arguments exist under the minimal assumption of one-way functions. Resolving the precise round complexity of zero-knowledge has been an outstanding open problem for far too long. In this work, we present a three-message zero-knowledge argument system with soundness against uniform polynomial-time cheating provers. The main component in our construction is the recent delegation protocol for RAM computations (Kalai and Paneth, TCC 2016B and Brakerski, Holmgren and Kalai, ePrint 2016). Concretely, we rely on a three-message variant of their protocol based on a key-less collision-resistant hash functions secure against uniform adversaries as well as other standard primitives. More generally, beyond uniform provers, our protocol provides a natural and meaningful security guarantee against real-world adversaries, which we formalize following Rogaway’s “human-ignorance” approach (VIETCRYPT 2006): in a nutshell, we give an explicit uniform reduction from any adversary breaking the soundness of our protocol to finding collisions in the underlying hash function.National Science Foundation (U.S.) (Award CNS-1350619)National Science Foundation (U.S.) (Award CNS-1413964

Founding Secure Computation on Blockchains

We study the foundations of secure computation in the blockchain-hybrid model, where a blockchain -- modeled as a global functionality -- is available as an Oracle to all the participants of a cryptographic protocol. We demonstrate both destructive and constructive applications of blockchains: - We show that classical rewinding-based simulation techniques used in many security proofs fail against blockchain-active adversaries that have read and post access to a global blockchain. In particular, we show that zero-knowledge (ZK) proofs with black-box simulation are impossible against blockchain-active adversaries. - Nevertheless, we show that achieving security against blockchain-active adversaries is possible if the honest parties are also blockchain active. We construct an $\omega(1)$-round ZK protocol with black-box simulation. We show that this result is tight by proving the impossibility of constant-round ZK with black-box simulation. - Finally, we demonstrate a novel application of blockchains to overcome the known impossibility results for concurrent secure computation in the plain model. We construct a concurrent self-composable secure computation protocol for general functionalities in the blockchain-hybrid model based on standard cryptographic assumptions. We develop a suite of techniques for constructing secure protocols in the blockchain-hybrid model that we hope will find applications to future research in this area

Concurrent Knowledge-Extraction in the Public-Key Model

Knowledge extraction is a fundamental notion, modelling machine possession of values (witnesses) in a computational complexity sense. The notion provides an essential tool for cryptographic protocol design and analysis, enabling one to argue about the internal state of protocol players without ever looking at this supposedly secret state. However, when transactions are concurrent (e.g., over the Internet) with players possessing public-keys (as is common in cryptography), assuring that entities ``know'' what they claim to know, where adversaries may be well coordinated across different transactions, turns out to be much more subtle and in need of re-examination. Here, we investigate how to formally treat knowledge possession by parties (with registered public-keys) interacting over the Internet. Stated more technically, we look into the relative power of the notion of ``concurrent knowledge-extraction'' (CKE) in the concurrent zero-knowledge (CZK) bare public-key (BPK) model.Comment: 38 pages, 4 figure