Thinking about the pooling issue a bit more, I have a suggestion for how to refine it:
A key danger already identified by the Riecoin creators in using 4-chains as the PoW for pooled mining is the possibility of creating a miner tailored to finding 4 chains.
This isn't theoretical - I've played with a proof-of-concept, and it's both easy and gives a share advantage over a "correct" miner. I've also run into it on the other side, where by too-aggressively screening out all six candidates, I created mining code that almost never generated a pool share unless it also found a block.
I don't think it's possible to avoid all bias in this, but a few possibilities make it easier to make a more-correct pooled miner. The first suggestion also has the advantage of providing a form of variable-difficulty pooled mining that is independently controllable from the Riecoin difficulty itself:
(a) Minimum divisor requirement for *all* numbers:
Accept PoW only if:
(a) The first four numbers are (MR) prime; and
(b) None of the six numbers has a divisor <= N for N=some reasonable size prime.
As an example, the optimized miner jh00 released sieves all six possibilities up to 50,000 (
https://github.com/jh000/xptMiner/blob/master/xptMiner/riecoinMiner.cpp ). A minimum PoW of 50,000 would then exclude any share that has more of a bias towards four-chains than the default ypool miner.
(b) Generator polynomial matches only
The pattern of primes chosen for Riecoin (p, p+4, p+6, p+10, p+12, p+16) can only occur at certain values. The simplest polynomial for these is n*210 + 7 and n*210 + 97. Any miner searching at locations *other* than these is clearly doing something weird, because no valid 6-chain can occur at other locations. Any non-matching share should be rejected.
-Dave
Another way around the bias towards 4-tuples, is that the pool should accept any sextuplet of the required form as long as at least ANY 4 of the numbers are prime (instead of the first 4). This way, if you bias towards the first 4 you loose the other combinations. If you bias towards all the combinations, you are at the same time biasing towards the full sextuplets. This would discourage searching for shares instead of actually searching for blocks.
In order to optimize both the miner and the server side checking, I would require only the first p to be prime, as long as at least 3 of the other 5 numbers (p+4, p+6, p+10, p+12, p+16) are prime too.
