lec-06 - CSE565: Computer Security Lecture 6 Number Theory...

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1 9/17/09 UB Fall 2009 CSE565: S. Upadhyaya Lec 6.1 CSE565: Computer Security Lecture 6 Number Theory Concepts Shambhu Upadhyaya Computer Science & Eng. University at Buffalo Buffalo, New York 14260 9/17/09 UB Fall 2009 CSE565: S. Upadhyaya Lec 6.2 Acknowledgments Material is drawn from Lawrie Brown’s slides
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2 9/17/09 UB Fall 2009 CSE565: S. Upadhyaya Lec 6.3 Prime Numbers Prime numbers only have divisors of 1 and self they cannot be written as a product of other numbers note: 1 is prime, but is generally not of interest E.g., 2,3,5,7 are prime, 4,6,8,9,10 are not Prime numbers are central to number theory List of prime number less than 200 is: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 9/17/09 UB Fall 2009 CSE565: S. Upadhyaya Lec 6.4 Prime Factorization To factor a number n is to write it as a product of other numbers: n=a × b × c Note that factoring a number is relatively hard compared to multiplying the factors together to generate the number The prime factorization of a number n is when it is written as a product of primes E.g., 91=7×13 ; 3600=2 4 ×3 2 ×5 2
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3 9/17/09 UB Fall 2009 CSE565: S. Upadhyaya
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lec-06 - CSE565: Computer Security Lecture 6 Number Theory...

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