23,888 research outputs found
Round Optimal Black-Box “Commit-and-Prove”
Motivatedbytheoreticalandpracticalconsiderations,anim- portant line of research is to design secure computation protocols that only make black-box use of cryptography. An important component in nearly all the black-box secure computation constructions is a black- box commit-and-prove protocol. A commit-and-prove protocol allows a prover to commit to a value and prove a statement about this value while guaranteeing that the committed value remains hidden. A black- box commit-and-prove protocol implements this functionality while only making black-box use of cryptography.
In this paper, we build several tools that enable constructions of round- optimal, black-box commit and prove protocols. In particular, assuming injective one-way functions, we design the first round-optimal, black- box commit-and-prove arguments of knowledge satisfying strong privacy against malicious verifiers, namely:
– Zero-knowledge in four rounds and,
– Witness indistinguishability in three rounds.
Prior to our work, the best known black-box protocols achieving commit- and-prove required more rounds.
We additionally ensure that our protocols can be used, if needed, in the delayed-input setting, where the statement to be proven is decided only towards the end of the interaction. We also observe simple applications of our protocols towards achieving black-box four-round constructions of extractable and equivocal commitments.
We believe that our protocols will provide a useful tool enabling several new constructions and easy round-efficient conversions from non-black- box to black-box protocols in the future
Round-optimal Black-box Commit-and-prove with Succinct Communication
We give a four-round black-box construction of a commit-and-prove protocol with succinct communication. Our construction is WI and has constant soundness error, and it can be upgraded into a one that is ZK and has negligible soundness error by relying on a round-preserving transformation of Khurana et al. (TCC 2018). Our construction is obtained by combining the MPC-in-the-head technique of Ishai et al. (SICOMP 2009) with the two-round succinct argument of Kalai et al. (STOC 2014), and the main technical novelty lies in the analysis of the soundness---we show that, although the succinct argument of Kalai et al. does not necessarily provide soundness for NP statements, it can be used in the MPC-in-the-head technique for proving the consistency of committed MPC views. Our construction is based on sub-exponentially hard collision-resistant hash functions, two-round PIRs, and two-round OTs
Composable Security in the Tamper Proof Hardware Model under Minimal Complexity
We put forth a new formulation of tamper-proof hardware in the Global Universal Composable (GUC) framework introduced by Canetti
et al. in TCC 2007. Almost all of the previous works rely on the formulation by Katz in Eurocrypt 2007 and this formulation does not fully capture tokens in a concurrent setting. We address these shortcomings by relying on the GUC framework where we make the following
contributions:
(1) We construct secure Two-Party Computation (2PC) protocols for general functionalities with optimal round complexity and
computational assumptions using stateless tokens. More precisely, we show how to realize arbitrary functionalities with GUC
security in two rounds under the minimal assumption of One-Way Functions (OWFs). Moreover, our construction relies on the
underlying function in a black-box way. As a corollary, we obtain feasibility of Multi-Party Computation (MPC) with GUC-security
under the minimal assumption of OWFs.
As an independent contribution, we identify an issue with a claim in a previous work by Goyal, Ishai, Sahai, Venkatesan and Wadia
in TCC 2010 regarding the feasibility of UC-secure computation with stateless tokens assuming collision-resistant hash-functions
(and the extension based only on one-way functions).
(2) We then construct a 3-round MPC protocol to securely realize arbitrary functionalities with GUC-security starting from any
semi-honest secure MPC protocol. For this construction, we require the so-called one-many commit-and-prove primitive introduced in
the original work of Canetti, Lindell, Ostrovsky and Sahai in STOC 2002 that is round-efficient and black-box in the underlying
commitment.
Using specially designed ``input-delayed\u27\u27 protocols we realize this primitive (with a 3-round protocol in our framework) using
stateless tokens and one-way functions (where the underlying one-way function is used in a black-box way)
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
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
On the Efficiency of Classical and Quantum Secure Function Evaluation
We provide bounds on the efficiency of secure one-sided output two-party
computation of arbitrary finite functions from trusted distributed randomness
in the statistical case. From these results we derive bounds on the efficiency
of protocols that use different variants of OT as a black-box. When applied to
implementations of OT, these bounds generalize most known results to the
statistical case. Our results hold in particular for transformations between a
finite number of primitives and for any error. In the second part we study the
efficiency of quantum protocols implementing OT. While most classical lower
bounds for perfectly secure reductions of OT to distributed randomness still
hold in the quantum setting, we present a statistically secure protocol that
violates these bounds by an arbitrarily large factor. We then prove a weaker
lower bound that does hold in the statistical quantum setting and implies that
even quantum protocols cannot extend OT. Finally, we present two lower bounds
for reductions of OT to commitments and a protocol based on string commitments
that is optimal with respect to both of these bounds
Improved Black-Box Constructions of Composable Secure Computation
We close the gap between black-box and non-black-box constructions of secure multiparty computation in the plain model under the assumption of semi-honest oblivious transfer. The notion of protocol composition we target is security, or more precisely, security with super-polynomial helpers. In this notion, both the simulator and the adversary are given access to an oracle called an that can perform some predefined super-polynomial time task. Angel-based security maintains the attractive properties of the universal composition framework while providing meaningful security guarantees in complex environments without having to trust anyone.
Angel-based security can be achieved using non-black-box constructions in rounds where is the round-complexity of the semi-honest oblivious transfer. However, currently, the best known constructions under the same assumption require rounds. If is a constant, the gap between non-black-box and black-box constructions can be a multiplicative factor . We close this gap by presenting a -round black-box construction. We achieve this result by constructing constant-round 1-1 CCA-secure commitments assuming only black-box access to one-way functions
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