Secure communication : CDS, PIR, PSM

Abstract

Private Information Retrieval is the problem of querying two servers to nd a value in a database, while keeping the index private. We extend this problem to Generalized Wildcard PIR, where we instead query an aggregate of the entries whose indices match a pattern, called a generalized wildcard, which species what values each segment of the indices may take. We give a construction for this variant with similar communication to that of the best PIR protocols known. We study information theoretic models in cryptography, namely Private Information Retrieval, Conditional Disclosure of Secrets, and Private Simultaneous Messages. We give extensions of PIR and CDS in the area of generalized wildcards, and give constructions for those extensions. We discuss directions towards more ecient protocols, and raise open questions.