Network coding is a class of routing algorithms offering increased throughput and improved robustness to random failures. With traditional routing, intermediate nodes in the network may only forward unmodified packets. With network coding, instead, intermediate nodes are allowed to forward linear combinations of received packets. Original data can be reconstructed after collecting sufficiently many linear combinations. Current file sharing systems offer either low overhead and high bandwidth with no privacy, or acceptable privacy at very low speed. Thanks to network coding, a general-purpose P2P network can obtain a privacy/performance tradeoff that may be considered reasonable in most real-world scenarios. In this paper we present an integrity strategy for network coding-based P2P anonymous systems, specifically designed to preserve the anonymity of peers. Our approach is significantly easier to implement than current solutions when anonymity is required. We implement the cryptographic algorithms on which our method is based and provide performance figures. We also define verification strategies which use batching for improved performances together with an efficiency analysis.