Question

I have a table with an auto-increment 32-bit integer primary key in a database, which will produce numbers ranging 1-4294967295.

I would like to keep the convenience of an auto-generated primary key, while having my numbers on the front-end of an application look like randomly generated.

Is there a mathematical function which would allow a two-way, one-to-one transformation between an integer and another?

For example a function would take a number, and translate it to another:

1 => 1538645623
2 => 2043145593
3 =>  393439399

And another function the way back:

1538645623 => 1
2043145593 => 2
 393439399 => 3

I’m not necessarily looking for an implementation here, but rather a hint on what I suppose, must be a well-known mathematical problem somewhere 🙂

Answer 1

Mathematically this is almost exactly the same problem as cryptography.

You: I want to go from an id(string of bits) to another number (string of bits) and back again in a non-obvious way.
Cryptography: I want to go from plaintext (string of bits) to another string of bits and back again (reversible) in a non-obvious way.

So for a simple solution, can I suggest just plugging in whatever cryptography algorithm is most convenient in your language, and encrypt and decrypt your id?

If you wanted to be a bit cleverer you can do what is called “salting” in addition to cryptography. Take your id as a 32 bit (or whatever) number. Concatenate it with a random 32 bit number. Encrypt the result. To reverse, just decrypt, and throw away the random part.

Of course, if someone was seriously attacking this, this might be vulnerable to known plaintext/differential cryptanalysis attacks as you have a very small known plaintext space, but it sounds like you aren’t trying to defend against serious attacks.