# Construct an adversary [on hold]

Fix $$N$$, $$e$$ with $$\text{gcd}(e, \phi(N))$$ = 1, and assume there is an adversary $$A$$ running in time $$t$$ for which $$Pr[A([x^e \mod N]) = x] = 0.01$$, where the probability is taken over uniform choice of $$x ∈ Z_N^*$$ .

Show that it is possible to construct an adversary $$A'$$ for which $$Pr[A'(x^e \mod N) = x] = 0.99$$ for all $$x$$. The running time t' of $$A'$$ should be polynomial in t and $$|N|$$ (the number of bits it takes to write down $$N$$).

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## put on hold as off-topic by Maeher, fkraiem, Squeamish Ossifrage, Mikero, AleksanderRasJun 13 at 7:39

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• – Mikero Jun 12 at 15:18