In this paper we consider large distributed systems in which objects are shared among several users. Our focus is on peer-to-peer (P2P) systems and, specifically, we present an adaptive algorithm for file fragments allocation on multiple servers belonging to a P2P network, derived from the adaptive data replication (ADR) algorithm by Wolf-son and Jajodia. While the ADR algorithm handles replicas of files, our algorithm handles (replicated) fragments of files. Moreover, while the ADR algorithm does not take into account any security issue, we also make some critical considerations about security of the system and show how a replicated-fragmentation scheme is convenient for sharing information in P2P networks, for achieving both high performance and security. The performance of the algorithm is evaluated in terms of transmission cost of packets, i.e. in terms of network utilization of the system, in contrast of the number of packets exchanged by peers, and the transmission cost is analyzed theoretically.