What does “simulator” and “interactive” mean in a cryptographic credential system's definition of security? Definition 1 on Page 7 of “An Efficient System for Non-transferable Anonymous Credentials with Optional Anonymity Revocation” by Camenisch and Lysyanskaya, uses the term “simulator” in defining the security of a cryptographic credential system, which I'm finding a little confusing.

In particular, the sentence says:


  CSS is secure if there exists a simulator S (ideal-world adversary [defined above as a probabilistic polynomial time machine]) such that the following holds: […]


What does “simulator” in a cryptographic credential system's definition of security?
Also, what does it mean for a probabilistic machine to be "interactive"?
"simulator":

That's a definition of security in a model that is related to but weaker than the universal composability framework (thanks to Yehuda Lindell for making that clear and you can look at the paper in his comment). You could also look up the wiki link and I think there are also several question on this site.

As @Yehuda Lindell mentions in a comment, if you are not familiar with the concept of a "simulator" at all so far it is better to look at definitions of secure (multiparty) computation or the zero-knowledge property of interactive proofs.

"interactive":

Think of two probabilistic polynomial time Turing machines (Turing machine with additional random tape) who have local input and output tapes (as usual), but also additional tapes to write input to the other machine and receive input from it. Both machines after interacting halt with local outputs. 

For instance, a machine $A$ may run on local input a secret key and machine $B$ on the respective public key and a message. After interaction $B$ halts with a signature for the message and $A$ with no local output (that would be the signing procedure of a blind signature scheme, which you probably know or are familiar with when studying anonymous credentials).