Security protocol analysis aims to find logical flaws in protocols which lead to failures
even while using perfect cryptographic mechanisms. One of the important problems is to
check if a given protocol preserves secrecy. Generally security protocols turn out to be
infinite state systems, the two main sources of unboundedness being the agents' ability
to communicate arbitrarily long messages and the ability to generate unbounded amount of
new data. It has been shown that even if only one of the above two parameters are unbounded,
checking secrecy of protocols is undecidable. We prove two decidability results. We identify
a subclass of protocols for which the secrecy problem is decidable assuming bounded message
length. We identify a different subclass of protocols for which the secrecy problem is
decidable assuming boundedly many nonces.
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