We give a formal model for systems that store data in entangled form. We propose a new notion of entanglement, called all-or-nothing integrity (AONI) that binds the users' data in a way that makes it hard to corrupt the data of any one user without corrupting the data of all users. AONI can be a useful defense against negligent or dishonest storage providers who might otherwise be tempted to discard documents belonging to users without much clout. We show that, if all users use the standard recovery algorithm, we can implement AONI using a MAC, but, if some of the users adopt the adversary's non-standard recovery algorithm, AONI can no longer be achieved. However, even for the latter scenario, we describe a simple entangling mechanism that provides AONI for a restricted cloass of destructive adversaries.
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