The problem of software integrity is traditionally addressed as the static verification of the code before the execution, often by checking the code signature. However, there are no well-defined solutions to the run-time verification of code integrity when the code is executed remotely, which is refer to as run-time remote entrusting. In this paper we present the research challenges involved in run-time remote entrusting and how we intend solve this problem. Specifically, we address the problem of ensuring that a given piece of code executes on an remote untrusted machine and that its functionalities have not been tampered with both before execution and during run-time.