2,947 research outputs found
Constructions of Batch Codes via Finite Geometry
A primitive -batch code encodes a string of length into string
of length , such that each multiset of symbols from has mutually
disjoint recovering sets from . We develop new explicit and random coding
constructions of linear primitive batch codes based on finite geometry. In some
parameter regimes, our proposed codes have lower redundancy than previously
known batch codes.Comment: 7 pages, 1 figure, 1 tabl
Combinatorial structures for anonymous database search
This thesis treats a protocol for anonymous database search (or if one prefer, a protocol for user-private information retrieval), that is based on the use of combinatorial configurations. The protocol is called P2P UPIR. It is proved that the (v,k,1)-balanced incomplete block designs (BIBD) and in particular the finite projective planes are optimal configurations for this protocol. The notion of n-anonymity is applied to the configurations for P2P UPIR protocol and the transversal designs are proved to be n-anonymous configurations for P2P UPIR, with respect to the neighborhood points of the points of the configuration. It is proved that to the configurable tuples one can associate a numerical semigroup. This theorem implies results on existence of combinatorial configurations. The proofs are constructive and can be used as algorithms for finding combinatorial configurations. It is also proved that to the triangle-free configurable tuples one can associate a numerical semigroup. This implies results on existence of triangle-free combinatorial configurations
Derandomized Construction of Combinatorial Batch Codes
Combinatorial Batch Codes (CBCs), replication-based variant of Batch Codes
introduced by Ishai et al. in STOC 2004, abstracts the following data
distribution problem: data items are to be replicated among servers in
such a way that any of the data items can be retrieved by reading at
most one item from each server with the total amount of storage over
servers restricted to . Given parameters and , where and
are constants, one of the challenging problems is to construct -uniform CBCs
(CBCs where each data item is replicated among exactly servers) which
maximizes the value of . In this work, we present explicit construction of
-uniform CBCs with data items. The
construction has the property that the servers are almost regular, i.e., number
of data items stored in each server is in the range . The
construction is obtained through better analysis and derandomization of the
randomized construction presented by Ishai et al. Analysis reveals almost
regularity of the servers, an aspect that so far has not been addressed in the
literature. The derandomization leads to explicit construction for a wide range
of values of (for given and ) where no other explicit construction
with similar parameters, i.e., with , is
known. Finally, we discuss possibility of parallel derandomization of the
construction
Roadmap on optical security
Postprint (author's final draft
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