Byzantine Agreement Using Partial Authentication

Three decades ago, Pease

et al.

introduced the problem of

Byzantine Agreement

[PSL 80] where nodes need to maintain a consistent view of the world in spite of the challenge posed by Byzantine faults. Subsequently, it is well known that Byzantine agreement over a completely connected synchronous network of

n

nodes tolerating up to

t

faults is (efficiently) possible if and only if

t

 < 

n

/3. Pease

et al.

further empowered the nodes with the ability to authenticate themselves and their messages and proved that agreement in this new model (popularly known as authenticated Byzantine agreement (ABA)) is possible if and only if

t

 < 

n

. (which is a huge improvement over the bound of

t

 < 

n

/3 in the absence of authentication for the same functionality).

To understand the utility, potential and limitations of using authentication in distributed protocols for agreement, Gupta

et al.

[GGBS10] studied ABA in new light. They generalize the existing models and thus, attempt to give a unified theory of agreements over the authenticated and non-authenticated domains. In this paper we extend their results to synchronous (undirected) networks and give a complete characterization of agreement protocols.

As a corollary, we show that agreement can be

strictly

easier than all-pair point-to-point communication. It is well known that in a synchronous network over

n

nodes of which up to any

t

are corrupted by a Byzantine adversary, BA is possible only if all pair point-to-point reliable communication is possible [Dol82, DDWY93]. Thus, a folklore in the area is that maintaining

global

consistency (agreement) is at least as hard as the problem of all pair

point-to-point

communication. Equivalently, it is widely believed that protocols for BA over incomplete networks exist only if it is possible to simulate an overlay-ed complete network. Surprisingly, we show that the folklore is not always true. Thus, it seems that agreement protocols may be more fundamental to distributed computing than reliable communication.