Obscure / encrypt an order number as another numbe

Question

Client has an simple increasing order number (1, 2, 3...). He wants end-users to receive an 8- or 9- digit (digits only -- no characters) "random" number. Obviously, this "random" number actually has to be unique and reversible (it's really an encryption of the actualOrderNumber).

My first thought was to just shuffle some bits. When I showed the client a sample sequence, he complained that subsequent obfuscOrderNumbers were increasing until they hit a "shuffle" point (point where the lower-order bits came into play). He wants the obfuscOrderNumbers to be as random-seeming as possible.

My next thought was to deterministically seed a linear congruential pseudo-random-number generator and then take the actualOrderNumber th value. But in that case, I need to worry about collisions -- the client wants an algorithm that is guaranteed not to collide in at least 10^7 cycles.

My third thought was "eh, just encrypt the darn thing," but if I use a stock encryption library, I'd have to post-process it to get the 8-or-9 digits only requirement.

My fourth thought was to interpret the bits of actualOrderNumber as a Gray-coded integer and return that.

My fifth though was: "I am probably overthinking this. I bet someone on StackOverflow can do this in a couple lines of code."

Answer 1

In 9 digit number, the first digit is a random index between 0 and 7 (or 1-8). Put another random digit at that position. The rest is the "real order number:

• Orig order: 100
• Random index: 5
• Random digit: 4 (guaranteed, rolled a dice :) )

• Result: 500040100

• Orig Nr: 101

• Random index: 2
• Random digit 6
• Result: 200001061

You can decide that the 5th (or any other) digit is the index.

Or, if you can live with real order numbers of 6 digits, then you can introduce "secondary" index as well. And you can reverse the order of the digits in the "real" order nr.