519 research outputs found
NP-hardness of hypercube 2-segmentation
The hypercube 2-segmentation problem is a certain biclustering problem that
was previously claimed to be NP-hard, but for which there does not appear to be
a publicly available proof of NP-hardness. This manuscript provides such a
proof
Trusted-HB: a low-cost version of HB+ secure against Man-in-The-Middle attacks
Since the introduction at Crypto'05 by Juels and Weis of the protocol HB+, a
lightweight protocol secure against active attacks but only in a detection
based-model, many works have tried to enhance its security. We propose here a
new approach to achieve resistance against Man-in-The-Middle attacks. Our
requirements - in terms of extra communications and hardware - are surprisingly
low.Comment: submitted to IEEE Transactions on Information Theor
Entanglement-Resistant Two-Prover Interactive Proof Systems and Non-Adaptive Private Information Retrieval Systems
We show that, for any language in NP, there is an entanglement-resistant
constant-bit two-prover interactive proof system with a constant completeness
vs. soundness gap. The previously proposed classical two-prover constant-bit
interactive proof systems are known not to be entanglement-resistant. This is
currently the strongest expressive power of any known constant-bit answer
multi-prover interactive proof system that achieves a constant gap. Our result
is based on an "oracularizing" property of certain private information
retrieval systems, which may be of independent interest.Comment: 8 page
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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