A Private Information Retrieval (PIR) protocol enables a user to retrieve a data item from a database while hiding the identity of the item being retrieved. In a $t$-private, $k$-server PIR protocol the database is replicated among $k$ servers, and the user's privacy is protected from any collusion of up ... more >>>

We prove exponential lower bounds on the length of 2-query locally decodable codes. Goldreich et al. recently proved such bounds for the special case of linear locally decodable codes. Our proof shows that a 2-query locally decodable code can be decoded with only 1 quantum query, and then proves an ... more >>>

We show that any 1-round 2-server Private Information Retrieval Protocol where the answers are 1-bit long must ask questions that are at least $n-2$ bits long, which is nearly equal to the known $n-1$ upper bound. This improves upon the approximately $0.25n$ lower bound of Kerenidis and de Wolf while ... more >>>

A t-private private information retrieval (PIR) scheme allows a user to retrieve the i-th bit of an n-bit string x replicated among k servers, while any coalition of up to t servers learns no information about i. We present a new geometric approach to PIR, and obtain (1) A t-private ... more >>>

A two server private information retrieval (PIR) scheme allows a user U to retrieve the i-th bit of an n-bit string x replicated between two servers while each server individually learns no information about i. The main parameter of interest in a PIR scheme is its communication complexity, namely the ... more >>>

A q-query Locally Decodable Code (LDC) encodes an n-bit message x as an N-bit codeword C(x), such that one can probabilistically recover any bit x_i of the message by querying only q bits of the codeword C(x), even after some constant fraction of codeword bits has been corrupted. We give ... more >>>

In cryptography, there has been tremendous success in building primitives out of homomorphic semantically-secure encryption schemes, using homomorphic properties in a black-box way. A few notable examples of such primitives include items like private information retrieval schemes and collision-resistant hash functions. In this paper, we illustrate a general methodology for ... more >>>

Locally Decodable Codes (LDC) allow one to decode any particular symbol of the input message by making a constant number of queries to a codeword, even if a constant fraction of the codeword is damaged. In recent work ~\cite{Yekhanin08} Yekhanin constructs a $3$-query LDC with sub-exponential length of size $\exp(\exp(O(\frac{\log ... more >>>