Since there was a discussion recently in the general forum about GLBSE + anonymous networks, I had another idea how to do share trading in a bitcoin style block chain:
1) Build a "share chain" similar to the p2pool one with blocks on average every 10 (or rather 30...) seconds.
2) Every 2nd block is a special block (by protocol design): It contains (PGP signed) the header of the block before and has difficulty 1. This adds a point of centralization, as only the PGP key(s) of the exchange would be allowed/accepted to sign this block's content. Future blocks of course then have to build upon this block. Difficulty 1 is enough for this, as it is a forced block anyways and a small FPGA machine or so in a corner of the room would be enough for the exchange to maintain + operate as mining equipment (they can output a new diff1 block in a few seconds).
3) Conflicting orders can be decided by attaching transaction fees to your orders - or just firing up a miner and crunching that block yourself with your order in it instead of the other guy's. This might provide additional income for miners.
1) Ensures that transactions get into blocks reasonably fast
2) Ensures that after you see the signed block, you can be sure that your transaction is in the major chain. Also it means the system can't be reversed as soon as a new key block is released.
3) I'm not 100% sure about this one, but there's definitely a need to decide between conflicting orders - and "first in - first included" might not always work or be the most sustainable solution, considering that in New York there are whole buildings bought just because they are closer to sea cables and might save a few microseconds to get data faster for algo-trading. This is CRAZY and unsustainable, especially for a global stock exchange (currently someone based closer to e.g. GLBSE would have better pings = better trades. This is just unfair imho.)
Did I overlook some major issue? Please post some feedback!