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Checking data possession in networked information systems such as those related to critical infrastructures (power facilities, airports, data vaults, defense systems, etc.) is a matter of crucial importance. Remote data possession checking protocols permit to check that a remote server can access an uncorrupted file in such a way that the verifier does not need to know beforehand the entire file that is being verified. Unfortunately, current protocols only allow a limited number of successive verifications or are impractical from the computational point of view. In this paper, we present a new remote data possession checking protocol such that: 1) it allows an unlimited number of file integrity verifications; 2) its maximum running time can be chosen at set-up time and traded off against storage at the verifier.