Modular Arithmetic and Primality
Modular Arithmetic and Primality
Modular Arithmetic and Primality
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function modexp (x, y, N) //Iterative version<br />
Input: Two n-bit integers x <strong>and</strong> N, an integer exponent y (arbitrarily large)<br />
Output: x y mod N<br />
if y = 0: return 1<br />
i = y; r = 1; z = x mod N<br />
while i > 0<br />
if i is odd: r = r z mod N<br />
z = z 2 mod N<br />
i = floor(i/2)<br />
return r<br />
– Same big-O complexity<br />
– Iteration can save overhead of calling stack (optimizing compilers)<br />
– Some feel that recursion is more elegant<br />
– Either way is reasonable<br />
CS 312 - Complexity Examples - <strong>Arithmetic</strong> <strong>and</strong> RSA 27
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