I wrote

> Write a block cipher that enciphers 0, 1, ..., n.  Pick a random key.  
> Encipher 0, 1, ..., n.  The cipher will have tables but hopefully much 
> smaller than n in length.

For there to be a possibility that any of the possible permutations will be 
generated, the cipher will have to accept a key of at least log2(n!) bits and 
its possible internal states after the key is applied must take at least 
log2(n!) bits to describe.  Whether uniformly distributed keys will produce 
uniformly distributed permutations is harder to guarantee.

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