€ For M = 365 and 15 ≤ q ≤ 30, compare the exact value of e given by the formula in the statement of Theorem 5.4 with th

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For M 365 And 15 Q 30 Compare The Exact Value Of E Given By The Formula In The Statement Of Theorem 5 4 With Th 1 (172.21 KiB) Viewed 40 times

€ For M = 365 and 15 ≤ q ≤ 30, compare the exact value of e given by the formula in the statement of Theorem 5.4 with the estimate for e derived after the proof of that theorem. For each q, include an error estimate between the two calculations. Please submit your answer in chart/table format, with the following layout: Q Theorem Estimate Reminder: The constant, e = 2.71828... (Euler's number), that appears in the estimate formula is the base of the natural logarithm. Do not confuse e with € (epsilon). Actual (Theorem 5.4) Recall, the following formula calculates the success probability for the FIND-COLLISION(h, Q) algorithm. Error € = 1- - (M¹) (M²).. .(M-Q+¹) (1) But Pr[success] = 1- Pr[failure] This implies that the probability of failure is given by: Q-1 (¹ – ž) (¹ – ²³ ) · · · (¹ – ¹¹) – II (¹ = - II (¹ - 1) (2) M i=1 Estimation -Q(Q-1) €1-e 2M 3