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This paper revisits the important problem of sending a message “into the future” in such a way that no communication is needed between the server and other entities. This problem was recently re-investigated by Blake and Chan who showed a scalable non-interactive solution without considering a formal security model. We fill this gap by introducing a new stringent model tailored to the non-interactive setting. We then propose a new construction fitting our model and we show that it is more efficient than the recent non-interactive proposal (for which we also give a security proof in our model). We then explain how to provide our scheme and the one of Blake and Chan with an additional security property that strengthens the anonymity of receivers.