Let us say I face an attack that will work against 1 round of Darksend but will fail against 2 rounds of Darksend. This could be the Sybil example I quoted above. If the attacker has also partially compromised the masternode network, then I need a sequence of 2 un-compromised Darksend rounds for protection from this attack. In this example sequence 1 will not work
1) Honest Malicious Honest Malicious Honest Malicious
but sequence 2 will work
2) Malicious Honest Honest Malicious Malicious Honest
because of the bold part. So it is the probability of the sequence of n honest masternodes in the chain that matters, and this is much lower than the probability of a single honest masternode in the chain.
OK I've considered this and I'm not sure it's a fair representation of how Darksend works.
1 round of Darksend with blinding uses 20 random masternodes. With more than 1 round, round 2 uses a different set of 20 masternodes and so on, resulting in the astronomical probabilities.
Your example is showing 6 MNs and 50% of them are malicious, but we were talking about 15% of the network being compromised. Therefore only 3 of 20 nodes are likely to be malicious and your sequence doesn't work.
Forgive me if I've misunderstood your example.
Also, I'm not sure we have the full picture on masternode blinding here. See vague description from Evan below.
Masternode BlindingRecently a paper by 3 researches at Saarland University came out describing a new technique, while there are some serious problems with the approach they take, the concept of blinding the users they use is novel. In CoinShuffle, each output is sent to the next peer in a circle, one at a time. The new peer adds an output, shuffles and then sends the list again. We can do this and actually improve upon it.
To implement blinding, each user would connect to one completely random masternode and say "Send masternode X this output/value for mix N" and pass a single output. That output would be passed to the leading masternode. It would take access to all masternodes used to know who did what, which is as solid as M rounds mathematically (M = number of outputs). This is great because all users can submit all inputs at once. So it's super fast compared to CoinShuffle and even more secure.
