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    <p>From my response to <a href="https://stackoverflow.com/questions/158716/how-do-you-efficiently-generate-a-list-of-k-non-repeating-integers-between-0-an#161552">another question</a>:</p> <blockquote> <p>It is actually possible to do this in space proportional to the number of elements selected, rather than the size of the set you're selecting from, regardless of what proportion of the total set you're selecting. You do this by generating a random permutation, then selecting from it like this:</p> <p>Pick a block cipher, such as <a href="http://en.wikipedia.org/wiki/Tiny_Encryption_Algorithm" rel="nofollow noreferrer">TEA</a> or XTEA. Use <a href="http://isthe.com/chongo/tech/comp/fnv/#xor-fold" rel="nofollow noreferrer">XOR folding</a> to reduce the block size to the smallest power of two larger than the set you're selecting from. Use the random seed as the key to the cipher. To generate an element n in the permutation, encrypt n with the cipher. If the output number is not in your set, encrypt that. Repeat until the number is inside the set. On average you will have to do less than two encryptions per generated number. This has the added benefit that if your seed is cryptographically secure, so is your entire permutation.</p> <p>I wrote about this in much more detail <a href="http://blog.notdot.net/archives/37-Damn-Cool-Algorithms,-Part-2-Secure-permutations-with-block-ciphers.html" rel="nofollow noreferrer">here</a>.</p> </blockquote> <p>Of course, there's no guarantee that every permutation can be generated (and depending on your block size and key size, that may not even be possible), but the permutations you can get are highly random (if they weren't, it wouldn't be a good cipher), and you can have as many of them as you want.</p>
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    1. POIterating shuffled [0..n) without arrays
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    1. USNick Johnson
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    1. COThis doesn't seem practical for small sets, and if I don't care about security can it be simplified (eg, use same structure?) Also do I need to go In = Dec(Xn), In+1 = In + 1, Xn+1 = Enc(In+1), Or can I do Xn+1 = Enc(Xn) ?
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      1. USProcedural Throwback
    2. COI doubt it can be simplified much. Ciphers just provide very good mixing, ensuring that every key value maps to a distinct permutation. If you're doing this with small sets, why not just shuffle an array? You can re-encrypt instead of using a counter, but there's no guarantee you won't get a cycle.
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    3. COThis doesn't iterate through the elements of a specific permutation. Iterating through a random one is possible in space of n bits, but you still need a random source of n log n bits.
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