Random Linear Network Coding with Probabilistic Polynomial-Time Wiretap Adversary

Abstract

Linear network coding can achieve the network capacity in the single source multicast case. For the single source multicast network with wiretap adversary, the paper of Cai and Yeung constructs an information-secure linear coding which tightly achieves the transmitting rate upper bound , where is the capacity of the network and is the maximum number of edges the adversary can wiretap. The current paper considers the cryptographic security for the messages in the random linear network coding setting. The indistinguishability under chosen-message-attack (or CMA-Security) from probabilistic polynomial-time (PPT) wiretap adversary is defined. With a pseudorandom generator against linear cryptanalysis, an end-to-end protocol is constructed for multicast network using random linear network coding. When the adversary wiretap less than edges, the protocol is CMA-Secure and attains transmitting rate approaching the network’s capacity from below, asymptotically in the expanding ratio (i.e., length of output string/length of input string) of the pseudorandom generator. Compared with secret-key based scheme, no secret is needed by the receiver nodes, which means the key managing issues for dynamic networks would never come up.