In this paper we consider the problem of securely outsourcing computation on private data. We present a protocol for securely distributing the computation of the data structures used by current implementations of the Certified Information Access primitive. To this aim, we introduce the concept of a Verifiable Deterministic Envelope - that may be of independent interest - and we provide practical implementations, based on standard cryptographic assumptions. We also discuss a prototype implementation of our proposal based on the PUB-WCL framework developed at the University of Paderborn for sharing computation across a network.