Generating non-repeating random numbers in Python

Question

Ok this is one of those trickier than it sounds questions so I\'m turning to stack overflow because I can\'t think of a good answer. Here is what I want: I need Python to ge

Answer 1

You could use Format-Preserving Encryption to encrypt a counter. Your counter just goes from 0 upwards, and the encryption uses a key of your choice to turn it into a seemingly random value of whatever radix and width you want.

Block ciphers normally have a fixed block size of e.g. 64 or 128 bits. But Format-Preserving Encryption allows you to take a standard cipher like AES and make a smaller-width cipher, of whatever radix and width you want (e.g. radix 10, width 9 for the parameters of the question), with an algorithm which is still cryptographically robust.

It is guaranteed to never have collisions (because cryptographic algorithms create a 1:1 mapping). It is also reversible (a 2-way mapping), so you can take the resulting number and get back to the counter value you started with.

AES-FFX is one proposed standard method to achieve this.

I've experimented with some basic Python code for AES-FFX--see Python code here (but note that it doesn't fully comply with the AES-FFX specification). It can e.g. encrypt a counter to a random-looking 7-digit decimal number. E.g.:

0000000   0731134
0000001   6161064
0000002   8899846
0000003   9575678
0000004   3030773
0000005   2748859
0000006   5127539
0000007   1372978
0000008   3830458
0000009   7628602
0000010   6643859
0000011   2563651
0000012   9522955
0000013   9286113
0000014   5543492
0000015   3230955
...       ...

For another example in Python, using another non-AES-FFX (I think) method, see this blog post "How to Generate an Account Number" which does FPE using a Feistel cipher. It generates numbers from 0 to 2^32-1.