TESLA-Based Homomorphic MAC for Authentication in P2P System for Live Streaming with Network Coding Recently, the peer-to-peer (P2P) live streaming system has benefited from the advent of network coding. However, it was demonstrated that malicious nodes could significantly reduce the network throughput by launching pollution attacks or entropy attacks. In this paper, we propose an efficient symmetric-key based authentication scheme for P2P live streaming system with network coding, to provide in-network detection against pollution attacks and entropy attacks simultaneously. Since the nature of P2P live streaming requires that the detection scheme has high computation efficiency and small communication overheads, we firstly propose a homomorphic message authentication code (MAC), called as PMAC, which has small key size and low computation overhead. Then, the proposed PMAC and the delayed key disclosure technique are employed to make sure that the peers could not only detect the corrupted blocks, but also upload blocks in accordance with random linear network coding. Furthermore, the performance evaluation demonstrates that the proposed scheme has both low communication and computation overheads.