# 1. Prove the equivalence of Definition 3.8 and Definition 3.9 2. Let |G(s)| = ?(|s|) for some… 1 answer below »

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1. Prove the equivalence of Definition 3.8 and Definition 3.9

2. Let |G(s)| = ℓ(|s|) for some ℓ. Consider the following experiment:

The PRG indistinguishability experiment

(a) A uniform bit b ∈ {0, 1} is chosen. If b = 0 then choose a uniform r ∈ {0, 1}ℓ(n) ; if b = 1 then choose a uniform s ∈ {0, 1} n and set r := G(s).

(b) The adversary A is given r, and outputs a bit

(c) The output of the experiment is defined to be 1 if b’ = b, and 0 otherwise.

Provide a definition of a pseudorandom generator based on this experiment, and prove that your definition is equivalent to Definition 3.14. (That is, show that G satisfies your definition if and only if it satisfies Definition 3.14.)