338 research outputs found
Increasing the power of the verifier in Quantum Zero Knowledge
In quantum zero knowledge, the assumption was made that the verifier is only
using unitary operations. Under this assumption, many nice properties have been
shown about quantum zero knowledge, including the fact that Honest-Verifier
Quantum Statistical Zero Knowledge (HVQSZK) is equal to Cheating-Verifier
Quantum Statistical Zero Knowledge (QSZK) (see [Wat02,Wat06]).
In this paper, we study what happens when we allow an honest verifier to flip
some coins in addition to using unitary operations. Flipping a coin is a
non-unitary operation but doesn't seem at first to enhance the cheating
possibilities of the verifier since a classical honest verifier can flip coins.
In this setting, we show an unexpected result: any classical Interactive Proof
has an Honest-Verifier Quantum Statistical Zero Knowledge proof with coins.
Note that in the classical case, honest verifier SZK is no more powerful than
SZK and hence it is not believed to contain even NP. On the other hand, in the
case of cheating verifiers, we show that Quantum Statistical Zero Knowledge
where the verifier applies any non-unitary operation is equal to Quantum
Zero-Knowledge where the verifier uses only unitaries.
One can think of our results in two complementary ways. If we would like to
use the honest verifier model as a means to study the general model by taking
advantage of their equivalence, then it is imperative to use the unitary
definition without coins, since with the general one this equivalence is most
probably not true. On the other hand, if we would like to use quantum zero
knowledge protocols in a cryptographic scenario where the honest-but-curious
model is sufficient, then adding the unitary constraint severely decreases the
power of quantum zero knowledge protocols.Comment: 17 pages, 0 figures, to appear in FSTTCS'0
Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model
We consider a type of zero-knowledge protocols that are of interest for their
practical applications within networks like the Internet: efficient
zero-knowledge arguments of knowledge that remain secure against concurrent
man-in-the-middle attacks. In an effort to reduce the setup assumptions
required for efficient zero-knowledge arguments of knowledge that remain secure
against concurrent man-in-the-middle attacks, we consider a model, which we
call the Authenticated Public-Key (APK) model. The APK model seems to
significantly reduce the setup assumptions made by the CRS model (as no trusted
party or honest execution of a centralized algorithm are required), and can be
seen as a slightly stronger variation of the Bare Public-Key (BPK) model from
\cite{CGGM,MR}, and a weaker variation of the registered public-key model used
in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK
model. Our main result is a constant-round concurrent non-malleable
zero-knowledge argument of knowledge for any polynomial-time relation
(associated to a language in ), under the (minimal) assumption of
the existence of a one-way function family. Furthermore,We show time-efficient
instantiations of our protocol based on known number-theoretic assumptions. We
also note a negative result with respect to further reducing the setup
assumptions of our protocol to those in the (unauthenticated) BPK model, by
showing that concurrently non-malleable zero-knowledge arguments of knowledge
in the BPK model are only possible for trivial languages
Zero-Knowledge Proofs of Proximity
Interactive proofs of proximity (IPPs) are interactive proofs in which the verifier runs in time sub-linear in the input length. Since the verifier cannot even read the entire input, following the property testing literature, we only require that the verifier reject inputs that are far from the language (and, as usual, accept inputs that are in the language).
In this work, we initiate the study of zero-knowledge proofs of proximity (ZKPP). A ZKPP convinces a sub-linear time verifier that the input is close to the language (similarly to an IPP) while simultaneously guaranteeing a natural zero-knowledge property. Specifically, the verifier learns nothing beyond (1) the fact that the input is in the language, and (2) what it could additionally infer by reading a few bits of the input.
Our main focus is the setting of statistical zero-knowledge where we show that the following hold unconditionally (where N denotes the input length):
- Statistical ZKPPs can be sub-exponentially more efficient than property testers (or even non-interactive IPPs): We show a natural property which has a statistical ZKPP with a polylog(N) time verifier, but requires Omega(sqrt(N)) queries (and hence also runtime) for every property tester.
- Statistical ZKPPs can be sub-exponentially less efficient than IPPs: We show a property which has an IPP with a polylog(N) time verifier, but cannot have a statistical ZKPP with even an N^(o(1)) time verifier.
- Statistical ZKPPs for some graph-based properties such as promise versions of expansion and bipartiteness, in the bounded degree graph model, with polylog(N) time verifiers exist.
Lastly, we also consider the computational setting where we show that:
- Assuming the existence of one-way functions, every language computable either in (logspace uniform) NC or in SC, has a computational ZKPP with a (roughly) sqrt(N) time verifier.
- Assuming the existence of collision-resistant hash functions, every language in NP has a statistical zero-knowledge argument of proximity with a polylog(N) time verifier
Non-Locality in Interactive Proofs
In multi-prover interactive proofs (MIPs), the verifier is usually
non-adaptive. This stems from an implicit problem which we call
``contamination'' by the verifier. We make explicit the verifier contamination
problem, and identify a solution by constructing a generalization of the MIP
model. This new model quantifies non-locality as a new dimension in the
characterization of MIPs. A new property of zero-knowledge emerges naturally as
a result by also quantifying the non-locality of the simulator.Comment: 32 pages, 14 figures. Submitted to Crypto 2019, Feb 2019. Report
arXiv:1804.02724 merged here in the update proces
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
Efficient UC Commitment Extension with Homomorphism for Free (and Applications)
Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values.
In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment. We obtain amortized linear computational complexity in the length of the input messages and rate 1.
Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters.
While the previously best constructions use UC oblivious transfer as the main building block, our constructions only require extractable commitments and PRGs, achieving better concrete efficiency and offering new insights into the sufficient conditions for obtaining homomorphic UC commitments.
Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic.
These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments.
Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge
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