155,696 research outputs found
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
Fast evaluation of union-intersection expressions
We show how to represent sets in a linear space data structure such that
expressions involving unions and intersections of sets can be computed in a
worst-case efficient way. This problem has applications in e.g. information
retrieval and database systems. We mainly consider the RAM model of
computation, and sets of machine words, but also state our results in the I/O
model. On a RAM with word size , a special case of our result is that the
intersection of (preprocessed) sets, containing elements in total, can
be computed in expected time , where is the
number of elements in the intersection. If the first of the two terms
dominates, this is a factor faster than the standard solution of
merging sorted lists. We show a cell probe lower bound of time , meaning that our upper bound is nearly
optimal for small . Our algorithm uses a novel combination of approximate
set representations and word-level parallelism
A privacy-preserving fuzzy interest matching protocol for friends finding in social networks
Nowadays, it is very popular to make friends, share photographs, and exchange news throughout social networks. Social networks widely expand the area of people’s social connections and make communication much smoother than ever before. In a social network, there are many social groups established based on common interests among persons, such as learning group, family group, and reading group. People often describe their profiles when registering as a user in a social network. Then social networks can organize these users into groups of friends according to their profiles. However, an important issue must be considered, namely many users’ sensitive profiles could have been leaked out during this process. Therefore, it is reasonable to design a privacy-preserving friends-finding protocol in social network. Toward this goal, we design a fuzzy interest matching protocol based on private set intersection. Concretely, two candidate users can first organize their profiles into sets, then use Bloom filters to generate new data structures, and finally find the intersection sets to decide whether being friends or not in the social network. The protocol is shown to be secure in the malicious model and can be useful for practical purposes.Peer ReviewedPostprint (author's final draft
EsPRESSo: Efficient Privacy-Preserving Evaluation of Sample Set Similarity
Electronic information is increasingly often shared among entities without
complete mutual trust. To address related security and privacy issues, a few
cryptographic techniques have emerged that support privacy-preserving
information sharing and retrieval. One interesting open problem in this context
involves two parties that need to assess the similarity of their datasets, but
are reluctant to disclose their actual content. This paper presents an
efficient and provably-secure construction supporting the privacy-preserving
evaluation of sample set similarity, where similarity is measured as the
Jaccard index. We present two protocols: the first securely computes the
(Jaccard) similarity of two sets, and the second approximates it, using MinHash
techniques, with lower complexities. We show that our novel protocols are
attractive in many compelling applications, including document/multimedia
similarity, biometric authentication, and genetic tests. In the process, we
demonstrate that our constructions are appreciably more efficient than prior
work.Comment: A preliminary version of this paper was published in the Proceedings
of the 7th ESORICS International Workshop on Digital Privacy Management (DPM
2012). This is the full version, appearing in the Journal of Computer
Securit
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