Hi Filippo,

If a malicious miner, M broadcasts {m1, m2 ... mn} at a regular interval, *and* 
also broadcasts {m1*, mn*} where mn* is  bitcoin block then M will cheat all 
other miners of their reward. You correctly identified this attack. The problem 
stems from the fact that I wanted to use the bitcoin block as the sentinel to 
mark the shares from the DAG that need to be rewarded. There's a few approaches 
we can take here, but I think the best one is that the hub broadcasts a 
"sentinel" to mark out the point in logical time up to which shares will be 
rewarded.

m1* <-------------------- mn*<--------+
                                      |
m1 <----m2 <---m3 <-------------------+
^        ^      ^                     |
|        |      |                     |
|        |      +-----------+         |
|        |                  |         |
|        +--------+         |    SENTINEL
+-----+           |         |         |
      |           |         |         |
      a1  <------ a2 <-----a3  <------+


In the above diagram, when hub receives mn*, the bitcoin block to be rewarded, 
the hub has also received {m1...m3, a1...a3} and therefore rewards all those 
shares and broadcasts this logical time to the p2p by sending a sentinel 
announcement.

This solution will also scale to the multiple hubs construction, as each hub 
will define their own sentinel and the miners working with each hub can 
independently verify their shares are being correctly rewarded. The solution 
also handles the case where M is not referencing any other shares.

The above alternative, might also answer your question about why we need to 
build a DAG. With a DAG we can capture logical time. Without a DAG, the above 
solution will require the hub to announce the hash of shares from each miner 
that have been rewarded.

I really appreciate you taking the time to go through the proposal and pointing 
out the attack. I hope the above solution addresses your concerns.

Thanks and best regards
pool2win
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