By Vincenzo Ancona; E Ballico; Alessandro Silva; Centro internazionale per la ricerca matematica (Trento, Italy)

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A secure encryption channel now passes the form of non-interference deﬁned in Equation 17 instantiated with these abstractions and equivalences. Indeed the information ﬂow seems to have been quite accurately encoded: Low can determine the length of a High message transmitted over c but not its contents. It does, however, fail to take account of the fact that Low could detect when identical cipher-texts have been transmitted. Presumably if we really are dealing with a one-time-pad this is not relevant: the occurence of identical cipher-texts is ﬁrstly extremely unlikely and secondly signiﬁes nothing.

The essential idea is to stipulate that whatever observations Low may make of the system the space of possible High level inputs consistent with those observations is unchanged. Intuitively this is rather appealing and appears to address the encryption problem: whatever ciphertext Low observes he cannot reduce the space of plaintexts compatible with this ciphertext. We need to partition the High level events into inputs and outputs. We then restrict the high-level processes in the deﬁnition to ones with an alphabet drawn Mathematical Models of Computer Security 45 only from High inputs and we use this in the deﬁnition of Equation 17.

In fact a far more elegant and insightful proof is possible when one observes that the unwinding rules actually bear a striking resemblance to the notion of bi-simulation, allowing us to borrow some results from the process algebra literature. First we need to introduce a few ideas from the operation style of process semantics. 10 Operational Semantics An operational semantics is typically presented in the form of transition rules. µ Thus P −→ P indicates that the process term P can make a transition labelled µ to the process term P .