Show that byzantine agreement can be reached for three generals, with one of them faulty, if the generals digitally sign their messages.

Question

What will be an ideal response?

Answer 1

Any lieutenant can verify the signature on any message. No lieutenant can forge another signature. The correct lieutenants sign what they each received and send it to one another.

A correct lieutenant decides x if it receives messages [x](signed commander) and either [[x](signed commander)](signed lieutenant) or a message that either has a spoiled lieutenant signature or a spoiled commander signature.
Otherwise, it decides on a default course of action (retreat, say).

A correct lieutenant either sees the proper commander’s signature on two different courses of action (in which case both correct lieutenants decide ‘retreat’); or, it sees one good signature direct from the commander and one improper commander signature (in which case it decides on whatever the commander signed to do); or it sees no good commander signature (in which case both correct lieutenants decide ‘retreat’).
In the middle case, either the commander sent an improperly signed statement to the other lieutenant, or the other lieutenant is faulty and is pretending that it received an improper signature. In the former case, both correct lieutenants will do whatever the (albeit faulty) commander told one of them to do in a signed message. In the latter case, the correct lieutenant does what the correct commander told it to do.