Oliver W. Gnilke

Private Information Retrieval from Coded Databases with Colluding Servers

We present a general framework for Private Information Retrieval (PIR) from arbitrary coded databases, that allows one to adjust the rate of the scheme according to the suspected number of colluding servers. If the storage code is a generalized Reed-Solomon code of length n and dimension k, we design PIR schemes which simultaneously protect against t colluding servers and provide PIR rate 1-(k+t-1)/n, for all t between 1 and n-k. This interpolates between the previously studied cases of t=1 and k=1 and asymptotically achieves the known capacity bounds in both of these cases, as the size of the database grows.

Private information retrieval schemes for codec 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 t 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.

Well-rounded lattices for reliability and security in Rayleigh fading SISO channels

For many wiretap channel models asymptotically optimal coding schemes are known, but less effort has been put into actual realizations of wiretap codes for practical parameters. Bounds on the mutual information and error probability when using coset coding on a Rayleigh fading channel were recently established by Oggier and Belfiore, and the results in this paper build on their work. However, instead of using their ultimate inverse norm sum approximation, a more precise expression for the eavesdroppers probability of correct decision is used in order to determine a general class of good coset codes. The code constructions are based on well-rounded lattices arising from simple geometric criteria. In addition to new coset codes and simulation results, novel number-theoretic results on well-rounded ideal lattices are presented.

Robust Private Information Retrieval from Coded Systems with Byzantine and Colluding Servers

A private information retrieval (PIR) scheme on coded storage systems with colluding, byzantine, and non-responsive servers is presented. Furthermore, the scheme can also be used for symmetric PIR in the same setting. An explicit scheme using an <tex>

Private Information Retrieval from MDS Coded Data in Distributed Storage Systems

[n, k]

t-Private Information Retrieval Schemes Using Transitive Codes

</tex> generalized Reed-Solomon storage code is designed, protecting against t-collusion and handling up to <tex>

Mosaics of combinatorial designs

b

Well-rounded lattices for coset coding in MIMO wiretap channels

</tex> byzantine and <tex>

Analysis of Some Well-Rounded Lattices in Wiretap Channels

r

Private Information Retrieval from Coded Storage Systems with Colluding, Byzantine, and Unresponsive Servers.

</tex> non-responsive servers, when <tex>