581 research outputs found
Instantaneous Decentralized Poker
We present efficient protocols for amortized secure multiparty computation
with penalties and secure cash distribution, of which poker is a prime example.
Our protocols have an initial phase where the parties interact with a
cryptocurrency network, that then enables them to interact only among
themselves over the course of playing many poker games in which money changes
hands.
The high efficiency of our protocols is achieved by harnessing the power of
stateful contracts. Compared to the limited expressive power of Bitcoin
scripts, stateful contracts enable richer forms of interaction between standard
secure computation and a cryptocurrency.
We formalize the stateful contract model and the security notions that our
protocols accomplish, and provide proofs using the simulation paradigm.
Moreover, we provide a reference implementation in Ethereum/Solidity for the
stateful contracts that our protocols are based on.
We also adopt our off-chain cash distribution protocols to the special case
of stateful duplex micropayment channels, which are of independent interest. In
comparison to Bitcoin based payment channels, our duplex channel implementation
is more efficient and has additional features
New Protocols for Secure Equality Test and Comparison
Protocols for securely comparing private values are among the most fundamental building blocks of multiparty computation. Introduced by Yao under the name millionaire\u27s problem, they have found numerous applications in a variety of privacy-preserving protocols; however, due to their inherent non-arithmetic structure, existing construction often remain an important bottleneck in large-scale secure protocols.
In this work, we introduce new protocols for securely computing the greater-than and the equality predicate between two parties. Our protocols rely solely on the existence of oblivious transfer, and are UC-secure against passive adversaries. Furthermore, our protocols are well suited for use in large-scale secure computation protocols, where secure comparisons (SC) and equality tests (ET) are commonly used as basic routines: they perform particularly well in an amortized setting, and can be preprocessed efficiently (they enjoy an extremely efficient, information-theoretic online phase). We perform a detailed comparison of our protocols to the state of the art, showing that they improve over the most practical existing solutions regarding both communication and computation, while matching the asymptotic efficiency of the best theoretical constructions
Communication Complexity and Secure Function Evaluation
We suggest two new methodologies for the design of efficient secure
protocols, that differ with respect to their underlying computational models.
In one methodology we utilize the communication complexity tree (or branching
for f and transform it into a secure protocol. In other words, "any function f
that can be computed using communication complexity c can be can be computed
securely using communication complexity that is polynomial in c and a security
parameter". The second methodology uses the circuit computing f, enhanced with
look-up tables as its underlying computational model. It is possible to
simulate any RAM machine in this model with polylogarithmic blowup. Hence it is
possible to start with a computation of f on a RAM machine and transform it
into a secure protocol.
We show many applications of these new methodologies resulting in protocols
efficient either in communication or in computation. In particular, we
exemplify a protocol for the "millionaires problem", where two participants
want to compare their values but reveal no other information. Our protocol is
more efficient than previously known ones in either communication or
computation
On the Power of Many One-Bit Provers
We study the class of languages, denoted by \MIP[k, 1-\epsilon, s], which
have -prover games where each prover just sends a \emph{single} bit, with
completeness and soundness error . For the case that
(i.e., for the case of interactive proofs), Goldreich, Vadhan and Wigderson
({\em Computational Complexity'02}) demonstrate that \SZK exactly
characterizes languages having 1-bit proof systems with"non-trivial" soundness
(i.e., ). We demonstrate that for the case that
, 1-bit -prover games exhibit a significantly richer structure:
+ (Folklore) When , \MIP[k, 1-\epsilon, s]
= \BPP;
+ When , \MIP[k,
1-\epsilon, s] = \SZK;
+ When , \AM \subseteq \MIP[k, 1-\epsilon,
s];
+ For and sufficiently large , \MIP[k, 1-\epsilon, s]
\subseteq \EXP;
+ For , \MIP[k, 1, 1-\epsilon, s] = \NEXP.
As such, 1-bit -prover games yield a natural "quantitative" approach to
relating complexity classes such as \BPP,\SZK,\AM, \EXP, and \NEXP.
We leave open the question of whether a more fine-grained hierarchy (between
\AM and \NEXP) can be established for the case when
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