Entered Answer Preview Result Message 4 4 correct 147 147 correct 1576 1576 incorrect 0, 1, 2, 3, 4, 5 0, 1, 2, 3, 4, 5 17% correct Your first number is incorrect Your third number is incorrect Your fourth number is incorrect Your fifth number is incorrect Your sixth number is incorrect 2 2 correct 3 3 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 We can write n − 1 = 2ur where u = 4 is maximal, and r = 147 = 1. Now we randomly select some a Є Zn, such as a = 1441. Initially we compute ar = 1576 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, a 4r, ..., ..., a²r. Note a 2ª n-1 a Please enter this list for n = 2353 and a = 1441 in comma separated format. 0,1,2,3,4,5 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