Question

I need an algorithm that can do a one-to-one mapping (ie. no collision) of a 32-bit signed integer onto another 32-bit signed integer.

My real concern is enough entropy so that the output of the function appears to be random. Basically I am looking for a cipher similar to XOR Cipher but that can generate more arbitrary-looking outputs. Security is not my real concern, although obscurity is.

Edit for clarification purpose:

1. The algorithm must be symmetric, so that I can reverse the operation without a keypair.
2. The algorithm must be bijective, every 32-bit input number must generate a 32-bit unique number.
3. The output of the function must be obscure enough, adding only one to the input should result big effect on the output.

Example expected result:

F(100) = 98456

F(101) = -758

F(102) = 10875498

F(103) = 986541

F(104) = 945451245

F(105) = -488554

Just like MD5, changing one thing may change lots of things.

I am looking for a mathematical function, so manually mapping integers is not a solution for me. For those who are asking, algorithm speed is not very important.

Answer 1

Use any 32-bit block cipher! By definition, a block cipher maps every possible input value in its range to a unique output value, in a reversible fashion, and by design, it’s difficult to determine what any given value will map to without the key. Simply pick a key, keep it secret if security or obscurity is important, and use the cipher as your transformation.

For an extension of this idea to non-power-of-2 ranges, see my post on Secure Permutations with Block Ciphers.

Addressing your specific concerns:

1. The algorithm is indeed symmetric. I’m not sure what you mean by “reverse the operation without a keypair”. If you don’t want to use a key, hardcode a randomly generated one and consider it part of the algorithm.
2. Yup – by definition, a block cipher is bijective.
3. Yup. It wouldn’t be a good cipher if that were not the case.