lec42a - Announcements Assignment 4 due by noon Friday...

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Announcements Assignment 4 due by noon Friday Final Exam Thursday April 29, 7:00-9:00. CSE A101 Cumulative, emphasis on part III Pick up graded work by May 28.

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Lecture 42 Solution space trees and backtracking 21.1
Hard Problems Some problems are hard to solve. No polynomial time algorithm is known. E.g., NP-hard problems such as machine scheduling, bin packing, 0/1 knapsack. Is this necessarily bad? Data encryption relies on difficult to solve problems.

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Cryptography decryption algorithm encryption algorithm message message Transmission Channel encryption key decryption key
Public Key Cryptosystem (RSA) A public encryption method that relies on a public encryption algorithm, a public decryption algorithm, and a public encryption key. Using the public key and encryption algorithm, everyone can encrypt a message. The decryption key is known only to authorized parties. Asymmetric method. Encryption and decryption keys are different; one is not easily computed from the other.

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Public Key Cryptosystem (RSA) p and q are two prime numbers. n = pq m = (p-1)(q-1) a is such that 1 < a < m and gcd(m,a) = 1 . b is such that (ab) mod m = 1 . a is computed by generating random positive integers and testing gcd(m,a) = 1 using the extended Euclid’s gcd algorithm. The extended Euclid’s gcd algorithm also computes b when gcd(m,a) = 1 .
RSA Encryption And Decryption Message M < n . Encryption key = (a,n) . Decryption key = (b,n) . Encrypt => E = M a mod n . Decrypt => M = E b mod n .

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Breaking RSA Factor n and determine p and q , n = pq . Now determine m = (p-1)(q-1) . Now use Euclid’s extended gcd algorithm to compute gcd(m,a) . b is obtained as a byproduct. The decryption key (b,n) has been determined!
Security Of RSA Relies on the fact that prime factorization is computationally very hard. Let

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This note was uploaded on 01/18/2012 for the course COP 3530 taught by Professor Davis during the Fall '08 term at University of Florida.

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lec42a - Announcements Assignment 4 due by noon Friday...

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