Advantage (cryptography)

In cryptography, an adversary's advantage is a measure of how successfully it can attack a cryptographic algorithm, by distinguishing it from an idealized version of that type of algorithm. Note that in this context, the "adversary" is itself an algorithm and not a person. A cryptographic algorithm is considered secure if no adversary has a non-negligible advantage, subject to specified bounds on the adversary's computational resources (see concrete security). "Negligible" usually means "within O(2^−p)" where p is a security parameter associated with the algorithm. For example, p might be the number of bits in a block cipher's key.

Let F be an oracle for the function being studied, and let G be an oracle for an idealized function of that type. The adversary A is a probabilistic algorithm given F or G as input and which outputs 1 or 0. A's job is to distinguish F from G based on making queries to the oracle that it's given. We say: ${\displaystyle Adv(A)=|\Pr[A(F)=1]-\Pr[A(G)=1]|}$

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