PPT Slide

Numbers can get too big when encrypting and decrypting (bigger than the biggest number in type long). We need a way to keep integers small. Use arithmetic modulo m, in which all integers are kept in the range 0..m-1.

For any integer i,

mod(i,m), or i mod m ,

is the integer that satisfies

i = q*m+r and 0<=r < m (for some q)

6 mod 5 = 1 1 mod 5 = 1 -4 mod 5 = 1

5 mod 5 = 0 0 mod 5 = 0 -5 mod 5 = 0

4 mod 5 = 4 -1 mod 5 = 4

3 mod 5 = 3 -2 mod 5 = 3

2 mod 5 = 2 -3 mod 5 = 2

To calculate (i mod m):

If i >=0: Use i%m (remainder when i is divided by m)

If iɘ: Use (i%m) + m

See method mod in class Crypto for an analysis.

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