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
