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Unformatted text preview: CS 312: Algorithm Analysis Lecture #4: Primality Testing, GCD This work is licensed under a Creative Commons AttributionShare Alike 3.0 Unported License. Slides by: Eric Ringger, with contributions from Mike Jones, Eric Mercer, Sean Warnick Announcements HW #2 Due Now Homework: Be sure to show your work Project #1 Today well work through the rest of the math Early: this Friday, 1/13 Holiday: Monday, 1/16 Due: next Wednesday, 1/18 Practice Key points: Represent exponent in binary Break up the problem into factors (one per binary digit) Use the substitution rule Practice Two key points: Represent exponent in binary Use the substitution rule Objectives Part 1: Introduce Fermats Little Theorem Understand and analyze the Fermat primality tester Part 2: Discuss GCD and Multiplicative Inverses, modulo N Prepare to Introduce Public Key Cryptography This adds up to a lot of ideas! Part 1: Primality Testing Fermats Little Theorem If p is prime, then a p1 1 (mod p ) for any a such that 1 a < p Examples: p = 3, a = 2 p = 7, a = 4 How do you wish you could use this theorem? Fermats Little Theorem If p is prime, then a p1 1 mod p for any a such that 1 a < p Examples: p = 3, a = 2 p = 7, a = 4 Logic Review a b (a implies b) Which is equivalent to the above statement? b a ~a ~b ~b ~a Logic Review a b (a implies b) Which is equivalent to the above statement?...
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 Winter '08
 Jones,M

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