What is the meaning of probabilistic polynomial time adversary?

Question

I learned about probabilistic polynomial time adversary, but I have some doubt.

• Is probabilistic polynomial time adversary referred to those who attack in polynomial time with the form of probabilistic?

Answer 1

Yes, but note as below, the probability is not biased.

From the Lindell, Katz book;

An algorithm $A$ is said to run in polynomial time if there exists a polynomial $p(\cdot)$ such that for every input $x \in \{0,1\}^*$, the computation of $A(x)$ terminates within at most $p(|x|)$ steps.

A probabilistic algorithm is one that has the capability of "tossing coins", i.e. the algorithm has access to a random source of randomness that yields unbiased random bits that are independently equal to 1 with $1/2$ probability and to 0 with $1/2$ probability.

Probabilistic Polynomial-time adversary means; An adversary runs in probabilistic polynomial time algorithm.

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Different formulation (due to a comment of SEJPM):

• A probabilistic polynomial-time algorithm is a probabilistic algorithm that may only perform a polynomial amount of operations including at most a polynomial number of coin-flips.
• A probabilistic polynomial-time adversary is then any probabilistic polynomial-time algorithm.