You could try an
LFSR<http://en.wikipedia.org/wiki/Linear_feedback_shift_register>,
it only needs as much extra ram as your key is long plus one bit :P It';s
not cryptographically secure at alll though, but it's very suitable for
Digital Signatures. In fact, CRC is an LFSR with an extra input block and no
streaming output.

The algorithm for a 15-bit two-tap CRC of "x^15+x^1+1" is:
New = (Old<<1) + (Old<0> XOR Old<14>)

Here's a list with valid tap bits. It's hard to come by on the internet, I
had to brute-force them all! (on pentium assembly, still took me hours!)
2 bits: 1, 0
3 bits: 2, 0
4 bits: 3, 0
5 bits: 4, 1
6 bits: 5, 0
7 bits: 6, 0
9 bits: 8, 3
10 bits: 9, 2
11 bits: 10, 1
15 bits: 14, 0
17 bits: 16, 2
18 bits: 17, 6
20 bits: 19, 2
21 bits: 20, 1
22 bits: 21, 0
23 bits: 22, 4
35 bits: 24, 2
38 bits: 27, 2
29 bits: 28, 1
31 bits: 30, 2
(note that some bit lengths have no valid two-tap LFSR's)

Mark
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