Homomorphic Linear Authentication Schemes for Proofs of Retrievability

In a proof of retrievability (POR) system, interactive POR protocols are 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 input of the stored data. Retrievability means that it should be possible for a client to extract the his/her data from the server's valid responses. An essential step-stone leading to retrievability is server's unforgeability of valid responses, i.e, any server coming up 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 schemes, the authenticators can be aggregated into one tag for the challenges, hence reducing the communication complexity. In this paper, we explore some new homomorphic linear authenticator schemes in POR to provide unforgeability. Compared with the recent work of Shacham and Waters, our scheme enjoys the same shortest responses, but reduces the local storage from O(s) to O(1).

Homomorphic signatures for network coding

Network coding has been shown to optimally use bandwidth in a network, maximizing information flow but the scheme is very inherently vulnerable to pollution attacks by malicious nodes in the network. A node injecting garbage can quickly affect many receivers. The pollution of network packets spreads quickly since the output of (even an) honest node is corrupted if at least one of the incoming packets is corrupted. An attacker can easily corrupt a packet even if it is encrypted by either forging the signature or by producing a collision under the hash function. This will give an attacker access to the packets and the ability to corrupt them. Denis Charles, Kamal Jain and Kristin Lauter designed a new homomorphic encryption signature scheme for use with network coding to prevent pollution attacks.[1] The homomorphic property of the signatures allows nodes to sign any linear combination of the incoming packets without contacting the signing authority. In this scheme it is computationally infeasible for a node to sign a linear combination of the packets without disclosing what linear combination was used in the generation of the packet. Furthermore, we can prove that the signature scheme is secure under well known cryptographic assumptions of the hardness of the discrete logarithm problem and the computational Elliptic curve Diffie–Hellman.

more reference;
https://en.wikipediawiki/Homomorphi...ork_coding

Reference: http://studentbank.in/report-coding-for-...z4EklIOixA