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MAT135-Assignment9

# MAT135-Assignment9 - p ≤ √ 3599 to see if is a...

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MATH 135, Fall 2010 Assignment #9 Due at 4:00pm on Tuesday, November 23 Problem 1 . Suppose that p and q are prime numbers with p > q . Suppose also that n = pq and φ ( n ) = ( p - 1)( q - 1). (a) Prove that p + q = n - φ ( n ) + 1 and p - q = p ( p + q ) 2 - 4 n . (b) If n = 1 281 783 203 and φ ( n ) = 1 281 711 600, determine p and q . Problem 2 . Use Fermat’s Little Theorem and the Square and Multiply Algorithm to show that the integer 3599 is not prime, without testing each prime
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Unformatted text preview: p ≤ √ 3599 to see if is a factor. (Hint: compute 2 3598 (mod 3599)). Problem 3 . (a) Let p = 53, q = 61, e = 241 and n = pq . Encrypt the message 1047 using the RSA public key ( e,n ). (b) Let p = 53, q = 61, e = 2641 and n = pq . Decrypt the cyphertext c = 2818 which was encoded from a 2-letter message using the RSA public key ( e,n ). 1...
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