With at least one dishonest mirror, the probability of discovering an inconsistency is 1 - (1 / 2^(k-1)), where k is the number of disjoint consistency checks. This is the probability that each individual consistency check succeeds.
This assumes that mirrors are selected at random, which is almost never the case.
A client is never subject to attack as long as they use one honest mirror. They are only subject to denial of service if they discover the inconsistency. Maybe. It could depend on client policy. For instance, if the client has 5 low quality mirrors and 1 defects, they might ignore the defector and carry on.
A client that uses a single dishonest mirror might be subject to an attack if the canonical source of information colludes with the dishonest mirror. That extends to the case where all mirrors and the canonical source collude.
This analysis only applies if a client chooses a mirror at random from a set of k mirrors that contains a single dishonest mirror. I am not sure how many deployments would use that sort of random sampling.
In the end, I'd suggest that this concentrate on what happens AFTER a client has selected a set of mirrors. And note that there are different policies that clients can implement.
I think that this is potentially misleading:
This assumes that mirrors are selected at random, which is almost never the case.
A client is never subject to attack as long as they use one honest mirror. They are only subject to denial of service if they discover the inconsistency. Maybe. It could depend on client policy. For instance, if the client has 5 low quality mirrors and 1 defects, they might ignore the defector and carry on.
A client that uses a single dishonest mirror might be subject to an attack if the canonical source of information colludes with the dishonest mirror. That extends to the case where all mirrors and the canonical source collude.
This analysis only applies if a client chooses a mirror at random from a set of k mirrors that contains a single dishonest mirror. I am not sure how many deployments would use that sort of random sampling.
In the end, I'd suggest that this concentrate on what happens AFTER a client has selected a set of mirrors. And note that there are different policies that clients can implement.