(A one-way function is an efficiently computable function f from a domain A to a

Question

(A one-way function is an efficiently computable function f from a domain A to a codomain B, f : A B, such that for every efficient (possibly probabilistic) algorithm Adv taking an input from B and producing an output in A, and for x A selected uniformly at random, Pr[f(Adv(f(x))) = f(x)] is negligible. Provide a precise asymptotic definition of a one-way function)

A one-way function is an efficiently computable function f from a domain A to a codomain B, f : A B, such that for every efficient (possibly probabilistic) algorithm Adv taking an input from B and producing an output in A, and for A selected uniformly at random Pr[f(Adv(f(z))) = f(x)] is negligible. Provide a precise asymptotic definition of a one-way function.

Explanation / Answer

A function can be called as an One-way function if it’s easy to compute, but hard to decode meaning which satisfies following conditions:

            Advf (I) := Pr [ I(1n , f(x)) f 1 (f(x)) ] = negl(n)

is a negligible function (in the security parameter n).

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