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Update: Your solution is cool but \$max is not guaranteed to be a power of 2. In fact, it almost certainly isn't.

I just scribbled this on a piece of paper, I think I heard something about it to do with the RSA encryption algorithm once...

```\$result = (\$prime_number * \$input + \$seed) % \$max;

Example for \$max = 10, \$prime_number = 7 and \$seed = 5..

```shuffle(5,10,0) == (7 * 0 + 5) % 10 == 5 % 10 == 5
shuffle(5,10,1) == (7 * 1 + 5) % 10 == 12 % 10 == 2
shuffle(5,10,2) == (7 * 2 + 5) % 10 == 19 % 10 == 9
shuffle(5,10,3) == (7 * 3 + 5) % 10 == 26 % 10 == 6
shuffle(5,10,4) == (7 * 4 + 5) % 10 == 33 % 10 == 3
shuffle(5,10,5) == (7 * 5 + 5) % 10 == 40 % 10 == 0
shuffle(5,10,6) == (7 * 6 + 5) % 10 == 47 % 10 == 7
shuffle(5,10,7) == (7 * 7 + 5) % 10 == 54 % 10 == 4
shuffle(5,10,8) == (7 * 8 + 5) % 10 == 61 % 10 == 1
shuffle(5,10,9) == (7 * 9 + 5) % 10 == 68 % 10 == 8

So that works for 7 and 10. Does it work for any \$max and any \$prime_number? If not what conditions will it work for? I am no good with proofs.

-Andrew.

Andrew Tomazos  |  andrew@tomazos.com  |  www.tomazos.com

In reply to Re^2: Random 1-1 mapping by tomazos
in thread Random 1-1 mapping by tomazos

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