One protocol (called the primary protocol) is independent of other protocols (jointly called the secondary protocol) if the question whether the primary protocol achieves a security goal never depends on whether the secondary protocol is in use. In this paper, we use multiprotocol strand spaces to prove that two cryptographic protocols are independent if they use encryption in non-overlapping ways. This theorem (Proposition 7.2) applies even if the protocols share public key certificates and secret key tickets. We use the method of authentication tests to study penetrator paths, namely sequences of penetrator actions connecting regular nodes (message transmissions or receptions) in the two protocols. Of special interest are inbound linking paths, which lead from a message transmission in the secondary protocol to a message reception in the primary protocol. We show that bundles can be modified to remove all inbound linking paths, if encryption does not overlap in the two protocols. The resulting bundle does not depend on any activity of the secondary protocol. We illustrate this method using the Neuman-Stubblebine protocol as an example.
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