Modular Arithmetic and Primality
Modular Arithmetic and Primality
Modular Arithmetic and Primality
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There is a faster algorithm<br />
– Rather than multiply, square x each time <strong>and</strong> multiply the powers<br />
corresponding to 1’s in the binary representation of y.<br />
– x mod N -> x 2 mod N -> x 4 mod N -> x 8 mod N -> x log(y) mod N<br />
– Thus there are only log 2 (y) multiplications<br />
– Then take the product of the appropriate powers<br />
– x 21 : change the 21 to binary: 10101 2<br />
– x 10101 = x 10000 · x 100 · x 1 (binary) = x 16 · x 4 · x 1 = x 21<br />
CS 312 - Complexity Examples - <strong>Arithmetic</strong> <strong>and</strong> RSA 21
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