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Homomorphic linear authentication schemes from ε-ASU2 functions for proofs of retrievability

Liu S., Chem K.

Control and Cybernetics

2012

Vol. 41, no. 2

335-351

Proof of Retrievability (POR) refers to interactive auditing protocols executed between a storage server and clients, so that clients can be convinced that their data is available at the storage server, ready to be retrieved when needed. In an interactive POR protocol, clients initiate challenges to the server, and the server feedbacks responses to clients with the help of the stored data. Retrievability means that it should be possible for a client to extract his/her data from the server's valid responses. An essential step leading to retrievability is the server's unforgeability of valid responses, i.e, any server coming up with valid responses to a client's challenges is actually storing the client's data with overwhelming probability. Unforgeability can be achieved with authentication schemes like MAC, Digital Signature, etc. With Homomorphic Linear Authentication (HLA) schemes, the server�' several responses can be aggregated into one, hence reducing the communication complexity. In this paper, we explore some new constructions of ε-almost strong universal hashing functions (ε-ASU2), which are used to build homomorphic linear authenticator schemes in POR to provide unforgeability. We show the HLA scheme involved in Shacham and Waters' POR scheme (see Shacham and Waters, 2008) is just an employment of a class ε-ASU2 functions. Using another class of ε-ASU2 for authentication in POR results in a new HLA scheme, which enjoys unforgability, the same shortest responses as the SW scheme, but reduces the local storage from O(n+s) to O(n) for information soundness, and from O(s) to O(1) for knowledge-soundness.