1,579 research outputs found
Compact Zero-Knowledge Proofs of Small Hamming Weight
We introduce a new technique that allows to give a zero-knowledge proof that a committed vector has Hamming weight bounded by a given constant. The proof has unconditional soundness and is very compact: It has size independent of the length of the committed string, and for large fields, it has size corresponding to a constant number of commitments. We show five applications of the technique that play on a common theme, namely that our proof allows us to get malicious security at small overhead compared to semi-honest security: 1) actively secure k-out-of-n OT from black-box use of 1-out-of-2 OT, 2) separable accountable ring signatures, 3) more efficient preprocessing for the TinyTable secure two-party computation protocol, 4) mixing with public verifiability, and 5) PIR with security against a malicious client
Approximating solution structure of the Weighted Sentence Alignment problem
We study the complexity of approximating solution structure of the bijective
weighted sentence alignment problem of DeNero and Klein (2008). In particular,
we consider the complexity of finding an alignment that has a significant
overlap with an optimal alignment. We discuss ways of representing the solution
for the general weighted sentence alignment as well as phrases-to-words
alignment problem, and show that computing a string which agrees with the
optimal sentence partition on more than half (plus an arbitrarily small
polynomial fraction) positions for the phrases-to-words alignment is NP-hard.
For the general weighted sentence alignment we obtain such bound from the
agreement on a little over 2/3 of the bits. Additionally, we generalize the
Hamming distance approximation of a solution structure to approximating it with
respect to the edit distance metric, obtaining similar lower bounds
Communication Complexity of Permutation-Invariant Functions
Motivated by the quest for a broader understanding of communication
complexity of simple functions, we introduce the class of
"permutation-invariant" functions. A partial function is permutation-invariant if for every bijection
and every , it is the case that . Most of the commonly studied functions
in communication complexity are permutation-invariant. For such functions, we
present a simple complexity measure (computable in time polynomial in given
an implicit description of ) that describes their communication complexity
up to polynomial factors and up to an additive error that is logarithmic in the
input size. This gives a coarse taxonomy of the communication complexity of
simple functions. Our work highlights the role of the well-known lower bounds
of functions such as 'Set-Disjointness' and 'Indexing', while complementing
them with the relatively lesser-known upper bounds for 'Gap-Inner-Product'
(from the sketching literature) and 'Sparse-Gap-Inner-Product' (from the recent
work of Canonne et al. [ITCS 2015]). We also present consequences to the study
of communication complexity with imperfectly shared randomness where we show
that for total permutation-invariant functions, imperfectly shared randomness
results in only a polynomial blow-up in communication complexity after an
additive overhead
The problem with the SURF scheme
There is a serious problem with one of the assumptions made in the security
proof of the SURF scheme. This problem turns out to be easy in the regime of
parameters needed for the SURF scheme to work.
We give afterwards the old version of the paper for the reader's convenience.Comment: Warning : we found a serious problem in the security proof of the
SURF scheme. We explain this problem here and give the old version of the
paper afterward
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