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# HW3 - HW#3 Public Key Cryptography CS 392/6813 Computer...

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HW #3: Public Key Cryptography CS 392/6813: Computer Security Fall 2009 [100pts] DUE 10/12/2009 at Midnight Problem 1 [10*3=30pts] 1) We discussed how to use the Euclidian algorithm to compute the GCD of two numbers. Use this algorithm to compute the following values. Show all of the steps involved. a. The GCD of 56 and 225. b. The GCD of 52 and 876. 2) We also discussed the use of the Extended Euclidian algorithm to calculate modular inverses. Use this algorithm to compute the following values. Show all of the steps involved. a. 957895 -1 (mod 122939945) b. 13 -1 (mod 31) 3) Let n be a product of two large primes p and q (i.e., n = pq). Assume that x, y, and g are relatively prime to n. a. If x y (mod n), is g x g y (mod n)? Show why or why not. b. If x y (mod Φ (n)) instead, is g x g y (mod n)? Show why or why not. Problem 3 [30pts] Download the RSA code found at http://www.funet.fi/pub/crypt/cryptography/asymmetric/rsa/rsaref2.tar.gz Review the RSA key generation, encryption, and decryption functions and the sample code, then perform the following: 1)

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