854 research outputs found
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.
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 -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
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
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
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