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How can you inexpensively two-way encrypt a 32 bit int, such that every number maps to some other int in that space and back in a way that’s difficult to predict?
And doesn’t require pre-storing 4.29 billion ints in a mapping table, of course.
What you want is a 32-bit block cipher. Unfortunately, most block ciphers are 64-bits or more due to the weaknesses of a short block size. If you can handle the encrypted int being twice as large as the input, then you can just use Blowfish, TDES, or some other nicely vetted 64-bit block cipher.
If you really need 32 bits and don’t mind the decreased security then its easy enough to trim a Feistel network cipher like Blowfish down to any block length that’s a multiple of 2 and less than the starting cipher. For Blowfish, just split your input number evenly between the two half blocks, and trim the output of the F function and the P-values down to 1/2 your target block size. This can all be done after keying the algorithm as usual.