I've been reading this question where a detailed description of mine is given, I've understood that a polynomial-time adversary is an adversary for which the only feasible strategy are those that take polynomial time to run; anyway, I just can't understand why do we require the adversary to be probabilistic.
In Katz' book is explained that this is natural because the honest parties are required to be probabilistic (in order to generate random keys and so on), actually this isn't very natural for me (the fact that the honest parties are probabilistic shouldn't imply we must consider adversaries to be probabilistic too).
Also, they say that this is useful because the ability to toss coins may provide additional power, and therefore if the scheme is secure against PPT adversaries, then is secure against deterministic polynomial-times adversaries.
Please, someone can explain me why is this a valid argument? Thank you very much!.