math135-a9-2011 - Assignment 9 Questions 1(a Given n = pq p...

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Assignment 9 – Questions 1. (a) Given n = pq , p > q , and φ ( n ) = ( p - 1)( q - 1) prove that p + q = n - φ ( n ) + 1 and p - q = p ( p + q ) 2 - 4 n. (b) The integer n = 71531 is the product of two primes p and q , and the Euler phi function φ ( n ) = ( p - 1)( q - 1) = 70992. Determine the prime factors p and q . 2. Use Fermat’s Little Theorem and the Square and Multiply Algorithm to prove that the integer 2479 is not prime (without testing each prime p 2479 to see if is a factor). 3. (a) In an RSA scheme, the public key (
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