Consider the following simplified version of the RSA algorithm for public cryptography: (i) Bob's public key...
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Consider the following simplified version of the RSA algorithm for public cryptography: (i) Bob's public key is a pair (n, e), where n is a prime number and e is a positive integer that is smaller than n and is relatively prime with n-1 (ii) Bob's private key is d = e 'mod (n-1). (iii) Alice encrypts a message m(0 <m < n 1) by calculating c = m"mod n, and sends the ciphertext c to Bob. (iv) Bob decrypts the ciphertext c by calculating mod n. Suppose n = 251 and e= 137. (a) Calculate d using the extended GCD algorithm. Show the computa- tional steps. (b) Suppose m = 200. Calculate c = m"mod n using repeated squaring. Show the computational steps. (c) Is the system secure? Explain why or why not. Consider the following simplified version of the RSA algorithm for public cryptography: (i) Bob's public key is a pair (n, e), where n is a prime number and e is a positive integer that is smaller than n and is relatively prime with n-1 (ii) Bob's private key is d = e 'mod (n-1). (iii) Alice encrypts a message m(0 <m < n 1) by calculating c = m"mod n, and sends the ciphertext c to Bob. (iv) Bob decrypts the ciphertext c by calculating mod n. Suppose n = 251 and e= 137. (a) Calculate d using the extended GCD algorithm. Show the computa- tional steps. (b) Suppose m = 200. Calculate c = m"mod n using repeated squaring. Show the computational steps. (c) Is the system secure? Explain why or why not.
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a Calculated using the extended GCD algorithm The extended GCD algorithm is a method for finding the greatest common divisor gcd of two integersas well as the modular inverses of the two integers with ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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