For making things like IP fragmentation ids and other similar protocol elements unpredictable, it would be useful to have what I'll call a cryptographic ergodic sequence generator -- that is, a generator that will produce a sequence of n bit numbers such that there are no repeats until you pass the 2^nth number in the sequence (that is, the sequence is a permutation of all 2^n bit numbers) and such that it is very difficult to predict what the next number in the sequence might be beyond the fact that it will not be one of the numbers seen earlier in the sequence. It is also rather important that the generator be computationally inexpensive.
The characteristic you ask for is exactly that of an n-bit block cipher in Counter Mode. For example, that's exactly why we developed Skip32, which is on our web page; we needed an unpredictable but non-repeating 32 bit nonce.
If you aren't prepared to accept the cost of a (scaled down) block cipher, then you'll have to restate your requirements.
Greg.
Greg Rose INTERNET: [EMAIL PROTECTED] Qualcomm Australia VOICE: +61-2-9817 4188 FAX: +61-2-9817 5199 Level 3, 230 Victoria Road, http://people.qualcomm.com/ggr/ Gladesville NSW 2111 232B EC8F 44C6 C853 D68F E107 E6BF CD2F 1081 A37C
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