Towards a Theory of Consistency Primitives

Abstract

One of the classical results in the theory of distributed systems is the theorem by Lamport, Shostak, and Pease stating that among n parties, any t of which may be cheaters, one of the parties (the sender) can consistently broadcast a value to the other parties if and only if t≤ n/3. This is achieved by use of a protocol among the players, using bilateral channels.

The purpose of this paper is to look at various generalizations of this result and to propose a new concept, called consistency specification, a very general type of consistency guarantee a protocol among n parties P ₁,..., P _n can provide. A consistency specification specifies, for every possible set H⊆{P ₁,..., P _n } of honest players and for every choice of their inputs, a certain security guarantee, i.e., a consistency condition on their outputs. This models that security can degrade smoothly with an increasing number of cheaters rather than abruptly when a certain threshold is exceeded, as is the case in the previous literature.