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DP-1 DP-O Problem 5.1, 15 points. Consider the following decisional problem DP. Let G be a cyclic group of prime order m and let g,q be generators of G. Consider the experiments associated with an adversary A: Experiment Exp6,99 ??(A) | Experiment Exp6.0.7(A) x + Zm. x $ Zm; y $ Zm X + g; Y + que X + g? ; Y + 9% d+ A(9,q, X, Y) d+ A(g, q, X, Y) Return d Return d Adva, gal DP DP-1 DP-O The DP-advantage of A is defined as q(A) Pr [Exp6.04 (A) = 1] - Pr [Exp6.9.7(A) = 1] . The DP problem is said to be hard in G if the DP-advantage of any efficient adversary with reasonable resources is small. Show that DP is equivalent to DDH. You don't have to do the reductions. Think of a simpler justification. DP-1 DP-O Problem 5.1, 15 points. Consider the following decisional problem DP. Let G be a cyclic group of prime order m and let g,q be generators of G. Consider the experiments associated with an adversary A: Experiment Exp6,99 ??(A) | Experiment Exp6.0.7(A) x + Zm. x $ Zm; y $ Zm X + g; Y + que X + g? ; Y + 9% d+ A(9,q, X, Y) d+ A(g, q, X, Y) Return d Return d Adva, gal DP DP-1 DP-O The DP-advantage of A is defined as q(A) Pr [Exp6.04 (A) = 1] - Pr [Exp6.9.7(A) = 1] . The DP problem is said to be hard in G if the DP-advantage of any efficient adversary with reasonable resources is small. Show that DP is equivalent to DDH. You don't have to do the reductions. Think of a simpler justification

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