Reordering numbers

I have numbers in range 1-62 I want to be able to "crypt" them, so that it's hard to guess they are generated in some order.

So, it should be some mapping, for example开发者_如何学JAVA

1->35 2->19 3->61 ...

so that I have 1 to 1 mapping, 100% reversible.

I can hardcode mapping, but I would prefer math solution to that, some kind of formula which takes number as argument, and produces number in range 1-62, and does NOT generate duplicates. Is there any chance this formula exists?

Just for history, validation script:

<?
  $test = array();

  $val = 37;
  for($i=0;$i<62;$i++)
  {
    if($test[($i*$val)%62])
    {
      print("Collision: $i ".$test[($i*$val)%62]."<br/>");
    }
    $test[($i*$val)%62] = $i;
    print("$i => ".(($i*$val)%62)."<br/>");
  }

?>

Update:

Here are IDs generated thanks to these answers:

qpOLHk
NMb84H
aI740D
x5urn0
UsROKn
hPeb7K
EcByu7
1zYVRu
oWlieR
LjIFBe
8G52YB
v3splY
SqPMIl
fNc95I
Cazws5
ZxWTPs
mUjgcP
JhGDzc
6E30Wz

Sweeeeeet :-)

You could put the numbers 1 to 62 in an array and shuffle the array (for example using the Fisher-Yates shuffle). The index of the array is then mapped to the content of that cell (but be careful of the off-by-one error if you use 0-indexed arrays).

To make it deterministic use a particular seed for the random number generator.

Edit: A less computationally expensive (and also easier to guess) mapping is to multiply by some constant and then calculate the result modulo 62:

result = (input * 37) % 62

The number 37 is just an example. You can use any number that is coprime to 62 - that is any odd number apart from 31.

Along the lines of Mark Byers's comment. Find the inverse of x mod n (e.g., n=62).

Let x be your input integer in the interval [1, n]. Use the extended Euclidean algorithm to find y and t such that xy + nt = 1 mod n. Then y = x^{-1} mod n.

Take a look at this comment on the str_rot13() manual page.

Use RSA. It's quite easy to implement (well, depends on the language) and here's a worked example.