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Towards a Theory of Consistency Primitives

Ueli Maurer

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 $t\leq n/3$. 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 $P_1\pp P_n$ can provide. A consistency specification specifies, for every possible set $H\subseteq\{P_1\pp P_n\}$ 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.