# Doubts on Definition of Indistinguishable Encryption in the Textbook

In the classic crypto textbook "Introduction to Modern Cryptography" by Jonathan Katz and Yehuda Lindell, there is a definition for indistinguishable encryption in the presence of an eavesdropper as such that for every probabilistic polynomial time adversary A there is a negligible function negl(n) such that

$\Pr[PrivK_{A,\Pi}=1] \leq negl(n)$

where PrivK is the indistinguishability experiment and for the purpose of this question we only need to know that the experiment outcome is 1 iff the adversary makes the correct guess.

My doubts are as follows. Consider a sequence of probabilistic polynomial time adversaries $\{A_i\}_{i>=1}$ whose advantage in the indistinguishability experiment is bounded by the following sequence of negligible functions

$\Pr[PrivK_{A,\Pi}=1] \leq negl_i(n) = \frac{1}{(1+1/i)^n}$

Clearly it is necessary for the above conditions to hold for a indistinguishable encryption. But is it a correct model/condition for real-world applications? For example, in practice we typically choose a sufficiently large n and set up some encryption scheme. However, there is the always some adversary $A_i$ that wins the experiment with probability close to one. So what's wrong?

Depends on how different your algorithms are. If you can compute $A_i$ from $i$ in polynomial time, then $A'$ with $A'(n) = A_n(n)$ is a polynomial time adversary too and violates the assumption (as it has non-negligible success probability). This would make your series of $A_i$ uniform and is one usual class of adversaries to consider.