Proofs of storage from homomorphic identification protocols

Proofs of storage (PoS) are interactive protocols allowing a client to verify that a server faithfully stores a file. Previous work has shown that proofs of storage can be constructed from any homomorphic linear authenticator (HLA). The latter, roughly speaking, are signature/message authentication schemes where 'tags' on multiple messages can be homomorphically combined to yield a 'tag' on any linear combination of these messages. We provide a framework for building public-key HLAs from any identification protocol satisfying certain homomorphic properties. We then show how to turn any public-key HLA into a publicly-verifiable PoS with communication complexity independent of the file length and supporting an unbounded number of verifications. We illustrate the use of our transformations by applying them to a variant of an identification protocol by Shoup, thus obtaining the first unbounded-use PoS based on factoring (in the random oracle model).