28,686 research outputs found
Robust Private Information Retrieval on Coded Data
We consider the problem of designing PIR scheme on coded data when certain
nodes are unresponsive. We provide the construction of -robust PIR schemes
that can tolerate up to unresponsive nodes. These schemes are adaptive
and universally optimal in the sense of achieving (asymptotically) optimal
download cost for any number of unresponsive nodes up to
Private Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in
which a user is able to compute a function on a distributed dataset without
revealing the identity of that function to the servers. In this paper it is
shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon
codes, enables private computation in many cases of interest. In particular, we
present a scheme that enables private computation of polynomials of any degree
on Lagrange encoded data, while being robust to Byzantine and straggling
servers, and to servers colluding to attempt to deduce the identities of the
functions to be evaluated. Moreover, incorporating ideas from the well-known
Shamir secret sharing scheme allows the data itself to be concealed from the
servers as well. Our results extend private computation to high degree
polynomials and to data-privacy, and reveal a tight connection between private
computation and coded computation.Comment: To appear in Transactions on Information Forensics and Securit
Private Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers that store the dataset. In this paper it is shown that Lagrange encoding, a recently suggested powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers that collude in attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to non-linear polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation
Private Polynomial Computation from Lagrange Encoding
Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers that store the dataset. In this paper it is shown that Lagrange encoding, a recently suggested powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers that collude in attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to non-linear polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation
Private Information Retrieval Schemes for Coded Data with Arbitrary Collusion Patterns
In Private Information Retrieval (PIR), one wants to download a file from a
database without revealing to the database which file is being downloaded. Much
attention has been paid to the case of the database being encoded across
several servers, subsets of which can collude to attempt to deduce the
requested file. With the goal of studying the achievable PIR rates in realistic
scenarios, we generalize results for coded data from the case of all subsets of
servers of size colluding, to arbitrary subsets of the servers. We
investigate the effectiveness of previous strategies in this new scenario, and
present new results in the case where the servers are partitioned into disjoint
colluding groups.Comment: Updated with a corrected statement of Theorem
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