Shuffle sequential numbers without a buffer

I am looking for a shuffle algorithm to shuffle a set of sequential numbers without buffering. Another way to state this is that I’m looking for a random sequence of unique numbers that have a given period.

Your typical Fisher–Yates shuffle needs to have each element all of the elements it is going to shuffle, so that isn’t going to work.

A Linear-Feedback Shift Register (LFSR) does what I want, but only works for periods that are powers-of-two less two. Here is an example of using a 4-bit LFSR to shuffle the numbers 1-14:

1	2	3	4	5	6	7	8	9	10	11	12	13	14
8	12	14	7	4	10	5	11	6	3	2	1	9	13

The first two is the input, and the second row the output. What’s nice is that the state is very small—just the current index. You can start of any index and get a difference set of numbers (starting at 1 yields: 8, 12, 14; starting at 9: 6, 3, 2), although the sequence is always the same (5 is always followed by 11). If I want a different sequence, I can pick a different generator polynomial.

The limitations to the LFSR are that the periods are always power-of-two less two (the min and max are always the same, thus unshuffled) and there not enough enough generator polynomials to allow every possible random sequence.

A block cipher algorithm would work. Every key produces a uniquely shuffled set of numbers. However all block ciphers (that I know about) have power-of-two block sizes, and usually a fixed or limited number of block sizes. A block cipher with a arbitrary non-binary block size would be perfect if such a thing exists.

There are a couple of projects I have that could benefit from such an algorithm. One is for small embedded micros that need to produce a shuffled sequence of numbers with a period larger than the memory they have available (think Arduino Uno needing to shuffle 1 to 100,000).

Does such an algorithm exist? If not, what things might I search for to help me develop such an algorithm? Or is this simply not possible?