Modular Arithmetic and Primality

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2 binary numbers of arbitrary length n Note that doubling and dividing by two are just a left shift or right shift in binary 1 1 0 * 1 0 1 1 1 0 0 0 0 1 1 0 Complexity - Can we do better CS 312 - Complexity Examples - Arithmetic and RSA 8
x y 15 11 At each step double x and half y. Then add up versions of x where y is odd. CS 312 - Complexity Examples - Arithmetic and RSA 9
Page 1 and 2: Addition Multiplication Bigger Ex
Page 3 and 4: Addition of two numbers of length n
Page 5 and 6: Addition of two numbers of length n
Page 7: Isn’t addition in a computer just
Page 11 and 12: ⎧⎧ 2(x⋅ ⎣⎣y/2⎦⎦) if y
Page 13 and 14: x y y binary # of x’s 15 8 0 1 30
Page 15 and 16: function multiply(x,y) Input: Two n
Page 17 and 18: Is multiplication O(n 2 ) - Could w
Page 19 and 20: Assume we start with numbers Mod N
Page 21 and 22: There is a faster algorithm - Rathe
Page 23 and 24: ⎧⎧ (x ⎣⎣y/2⎦⎦ ) 2 if y
Page 25 and 26: x y y binary power of x z return va
Page 27 and 28: function modexp (x, y, N) //Iterati
Page 29 and 30: function primality(N) Input: Positi
Page 31 and 32: How often does a composite number c
Page 33 and 34: Primality testing is efficient! - O

Modular Arithmetic and Primality

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