Answered: Implement the modular exponentiation…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Implement the modular exponentiation (a.k.a. fast exponentiation) function mod_exp (b, n, m) to compute bn (mod m) more efficiently. (Hint: to read n bit-by-bit, use / and % operations repeatedly) a) Test your function for b = 3, n = 231 – 2, m = 231 – 1. b) Report the result and the time (in seconds) it takes to find the result. Q3. [30 pts] Modify your is_prime function to use the mod_exp (b, n, m) instead of the standard power operation (b**n % m). Rename it as is_prime2. Modify the mersenne (p) function to use is_prime2, and call it mersenne2. a) Use the modified function mersenne2 to print all the Mersenne primes Mp for p between 2 and 31 if possible, (with k = 3 in the is_prime function). Compare the results with the ones found in Q1. b) Gradually increase the range of p to find more Mersenne primes (say up to p = 101 if possible). What is the largest Mersenne prime you can achieve here? c) Extend the work in part (b) and find the maximum Mersenne prime you can get from this experiment in a reasonable amount of time (Say within two minutes). **** answer only 3 i put 2 because 3 is from 2 . answer in plaintext descibable .

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