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Entered Answer Preview Result Message 4 4 correct 147 147 correct 1 incorrect 0, 1, 2, 3 0,1,2,3 25% correct Your first number is incorrect Your third number is incorrect Your fourth number is incorrect 2 3 3 correct correct At least one of the answers above is NOT correct. (1 point) The Miller-Rabin primality test is based around the following observation. If p is prime and x² = 1 mod p then x = ±1 mod p. Note that x = -1 mod p and x = p - 1 mod p mean the same thing. We will use the Miller-Rabin test to test n = 2353 for primality. To do this we will closely examine an-1 mod n for various integers a. First we divide out all of the 2's from n - 1. We can write n - 1 = 2ur where u = 4 is maximal, and r = 147 Now we randomly select some a Є Zn, such as a = 1441. Initially we compute a = 1 mod n. If this number is 1 then the test is inconclusive and another a is selected (up until the number of a's determined by the security level). Otherwise we compute the list of values a²r, a½r, ..., 4r r α a2r. Note a² 2" an-1. Please enter this list for n = 2353 and a = 1441 in comma separated format. 0,1,2,3 When the list is computed one of a few things could happen. 1) The value 1 never occurs on the list. 2) The value −1 = p-1 mod p occurs on the list, immediately followed by 1. 3) The value 1 occurs in the list, but *not* preceded by -1. Which one of these possibilities holds in our case (enter the number)? 2 What conclusion should we draw from what we have done? 1) n is prime. 2) n is composite. 3) The test is inconclusive. 3

Entered Answer Preview Result Message 4 4 correct 147 147 correct 1 incorrect 0, 1, 2, 3 0,1,2,3 25% correct Your first number is incorrect Your third number is incorrect Your fourth number is incorrect 2 3 3 correct correct At least one of the answers above is NOT correct. (1 point) The Miller-Rabin primality test is based around the following observation. If p is prime and x² = 1 mod p then x = ±1 mod p. Note that x = -1 mod p and x = p - 1 mod p mean the same thing. We will use the Miller-Rabin test to test n = 2353 for primality. To do this we will closely examine an-1 mod n for various integers a. First we divide out all of the 2's from n - 1. We can write n - 1 = 2ur where u = 4 is maximal, and r = 147 Now we randomly select some a Є Zn, such as a = 1441. Initially we compute a = 1 mod n. If this number is 1 then the test is inconclusive and another a is selected (up until the number of a's determined by the security level). Otherwise we compute the list of values a²r, a½r, ..., 4r r α a2r. Note a² 2" an-1. Please enter this list for n = 2353 and a = 1441 in comma separated format. 0,1,2,3 When the list is computed one of a few things could happen. 1) The value 1 never occurs on the list. 2) The value −1 = p-1 mod p occurs on the list, immediately followed by 1. 3) The value 1 occurs in the list, but *not* preceded by -1. Which one of these possibilities holds in our case (enter the number)? 2 What conclusion should we draw from what we have done? 1) n is prime. 2) n is composite. 3) The test is inconclusive. 3

Database System Concepts
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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Entered Answer Preview Result Message 4 4 correct 147 147 correct 1 incorrect 0, 1, 2, 3 0,1,2,3 25% correct Your first number is incorrect Your third number is incorrect Your fourth number is incorrect 2 3 3 correct correct At least one of the answers above is NOT correct. (1 point) The Miller-Rabin primality test is based around the following observation. If p is prime and x² = 1 mod p then x = ±1 mod p. Note that x = -1 mod p and x = p - 1 mod p mean the same thing. We will use the Miller-Rabin test to test n = 2353 for primality. To do this we will closely examine an-1 mod n for various integers a. First we divide out all of the 2's from n - 1. We can write n - 1 = 2ur where u = 4 is maximal, and r = 147 Now we randomly select some a Є Zn, such as a = 1441. Initially we compute a = 1 mod n. If this number is 1 then the test is inconclusive and another a is selected (up until the number of a's determined by the security level). Otherwise we compute the list of values a²r, a½r, ..., 4r r α a2r. Note a² 2" an-1. Please enter this list for n = 2353 and a = 1441 in comma separated format. 0,1,2,3 When the list is computed one of a few things could happen. 1) The value 1 never occurs on the list. 2) The value −1 = p-1 mod p occurs on the list, immediately followed by 1. 3) The value 1 occurs in the list, but *not* preceded by -1. Which one of these possibilities holds in our case (enter the number)? 2 What conclusion should we draw from what we have done? 1) n is prime. 2) n is composite. 3) The test is inconclusive. 3
Transcribed Image Text:Entered Answer Preview Result Message 4 4 correct 147 147 correct 1 incorrect 0, 1, 2, 3 0,1,2,3 25% correct Your first number is incorrect Your third number is incorrect Your fourth number is incorrect 2 3 3 correct correct At least one of the answers above is NOT correct. (1 point) The Miller-Rabin primality test is based around the following observation. If p is prime and x² = 1 mod p then x = ±1 mod p. Note that x = -1 mod p and x = p - 1 mod p mean the same thing. We will use the Miller-Rabin test to test n = 2353 for primality. To do this we will closely examine an-1 mod n for various integers a. First we divide out all of the 2's from n - 1. We can write n - 1 = 2ur where u = 4 is maximal, and r = 147 Now we randomly select some a Є Zn, such as a = 1441. Initially we compute a = 1 mod n. If this number is 1 then the test is inconclusive and another a is selected (up until the number of a's determined by the security level). Otherwise we compute the list of values a²r, a½r, ..., 4r r α a2r. Note a² 2" an-1. Please enter this list for n = 2353 and a = 1441 in comma separated format. 0,1,2,3 When the list is computed one of a few things could happen. 1) The value 1 never occurs on the list. 2) The value −1 = p-1 mod p occurs on the list, immediately followed by 1. 3) The value 1 occurs in the list, but *not* preceded by -1. Which one of these possibilities holds in our case (enter the number)? 2 What conclusion should we draw from what we have done? 1) n is prime. 2) n is composite. 3) The test is inconclusive. 3
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