math - One-to-one integer mapping function

Question

We are using MySQL and developing an application where we'd like the ID sequence not to be publicly visible... the IDs are hardly top secret and there is no significant issue if someone indeed was able to decode them.

So, a hash is of course the obvious solution, we are currently using MD5... 32bit integers go in, and we trim the MD5 to 64bits and then store that. However, we have no idea how likely collisions are when you trim like this (especially since all numbers come from autoincrement or the current time). We currently check for collisions, but since we may be inserting 100.000 rows at once the performance is terrible (can't bulk insert).

But in the end, we really don't need the security offered by the hashes and they consume unnecessary space and also require an additional index... so, is there any simple and good enough function/algorithm out there that guarantees one-to-one mapping for any number without obvious visual patterns for sequential numbers?

EDIT: I'm using PHP which does not support integer arithmetic by default, but after looking around I found that it could be cheaply replicated with bitwise operators. Code for 32bit integer multiplication can be found here: http://pastebin.com/np28xhQF

Answer 1

You could simply XOR with 0xDEADBEEF, if that's good enough.

Alternatively multiply by an odd number mod 2^32. For the inverse mapping just multiply by the multiplicative inverse

Example: n = 2345678901; multiplicative inverse (mod 2^32): 2313902621 For the mapping just multiply by 2345678901 (mod 2^32):

1 --> 2345678901 2 --> 396390506

For the inverse mapping, multiply by 2313902621.