Byzantine-Tolerant Set-Constrained Delivery Broadcast

Set-Constrained Delivery Broadcast (SCD-broadcast), recently introduced at ICDCN 2018, is a high-level communication abstraction that captures ordering properties not between individual messages but between sets of messages. More precisely, it allows processes to broadcast messages and deliver sets of messages, under the constraint that if a process delivers a set containing a message m before a set containing a message m', then no other process delivers first a set containing m' and later a set containing m. It has been shown that SCD-broadcast and read/write registers are computationally equivalent, and an algorithm implementing SCD-broadcast is known in the context of asynchronous message passing systems prone to crash failures. This paper introduces a Byzantine-tolerant SCD-broadcast algorithm, which we call BSCD-broadcast. Our proposed algorithm assumes an underlying basic Byzantine-tolerant reliable broadcast abstraction. We first introduce an intermediary communication primitive, Byzantine FIFO broadcast (BFIFO-broadcast), which we then use as a primitive in our final BSCD-broadcast algorithm. Unlike the original SCD-broadcast algorithm that is tolerant to up to t<n/2 crashing processes, and unlike the underlying Byzantine reliable broadcast primitive that is tolerant to up to t<n/3 Byzantine processes, our BSCD-broadcast algorithm is tolerant to up to t<n/4 Byzantine processes. As an illustration of the high abstraction power provided by the BSCD-broadcast primitive, we show that it can be used to implement a Byzantine-tolerant read/write snapshot object in an extremely simple way.