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Quick warning, there is a typo in 2.A where it says "choose the exponent a=7" it is meant to say choose the BASE a=7 Exercise 2: The following exercises are on prime numbers. a) Use the Miller-Rabin Primality Test to test whether n = 1105 is a prime. Choose the exponent a = 7. b) Eve is given a large composite number n = px q. She attempts a brute force approach to finding a factor of n by testing whether p divides n for p = 2,3, 5, 7,... until she finds a factor pln. Prove that Eve has to test at most d= 26/2+1 bln 2

Quick warning, there is a typo in 2.A where it says "choose the exponent a=7" it is meant to say choose the BASE a=7 Exercise 2: The following exercises are on prime numbers. a) Use the Miller-Rabin Primality Test to test whether n = 1105 is a prime. Choose the exponent a = 7. b) Eve is given a large composite number n = px q. She attempts a brute force approach to finding a factor of n by testing whether p divides n for p = 2,3, 5, 7,... until she finds a factor pln. Prove that Eve has to test at most d= 26/2+1 bln 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Quick warning, there is a typo in 2.A where it says "choose the exponent a=7" it is meant to say choose the BASE a=7 Exercise 2: The following exercises are on prime numbers. a) Use the Miller-Rabin Primality Test to test whether n = 1105 is a prime. Choose the exponent a = 7. b) Eve is given a large composite number n = p x q. She attempts a brute force approach to finding a factor of n by testing whether p divides n for p = 2, 3, 5, 7, . until she finds a factor p|n. Prove that Eve has to test at most 26/2+1 bln 2 factors until she finds p|n, where b = log2(n) is the approximate number of bits in n.
Transcribed Image Text:Quick warning, there is a typo in 2.A where it says "choose the exponent a=7" it is meant to say choose the BASE a=7 Exercise 2: The following exercises are on prime numbers. a) Use the Miller-Rabin Primality Test to test whether n = 1105 is a prime. Choose the exponent a = 7. b) Eve is given a large composite number n = p x q. She attempts a brute force approach to finding a factor of n by testing whether p divides n for p = 2, 3, 5, 7, . until she finds a factor p|n. Prove that Eve has to test at most 26/2+1 bln 2 factors until she finds p|n, where b = log2(n) is the approximate number of bits in n.
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