Cryptography, in particular threshold cryptography, plays an important role in those protocols. An important prerequisite for such a service is Byzantine agreement. We have designed a new protocol for Byzantine agreement that works in a completely asynchronous network and makes use of cryptography, specifically of threshold signatures and coin-tossing protocols. Christian Cachin, Klaus Kursawe, and Victor Shoup. Another important primitive for these protocols are efficient threshold-cryptography protocols.
Pratical threshold signatures.
Springer-Verlag, May 2000. This work describes how to build reliable broadcast protocols in an asynchronous network with Byzantine failures. It presents a new formal model based on modern cryptography, and a new protocol for atomic broadcast based on multi-valued Byzantine agreement, among other things. Christian Cachin, Klaus Kursawe, Frank Petzold, and Victor Shoup. Secure and Efficient Asynchronous Broadcast Protocols.