Let us introduce an integer-valued security parameter chosen by honest parties before they begin a cryptographic scheme.
Typically will correspond to the length of the key.
The security parameter is assumed to be known to the adversary.
Definition. A function is polynomially bounded if there exist constants such that for all positive integers , we have .
Definition. A function is negligible if for every positive polynomial there is an such that for all integers it holds that , i.e.,
Equivalently, function is negligible if for all constants there exists an such that for all it holds that . We usually denote a negligible function by negl or by .
Equivalently, a function is negligible if and only if for all , we have .
Definition. A private-key encryption scheme has indistinguishable encryptions in the presence of an eavesdropper, or is EAV-secure, if for all probabilistic polynomial-time adversaries there is a negligible function such that for all ,
— Feb 1, 2023
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