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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 we’ll 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 Fermat’s 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 Fermat’s 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? Fermat’s 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
 Prime number, Greatest common divisor, multiplicative inverses, Primality

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