Towards Optimal Parallel Broadcast Under a Dishonest Majority
摘要
The parallel broadcast (PBC) problem generalizes the classic Byzantine broadcast problem to the setting where all n nodes broadcast a message and deliver O(n) messages. PBC arises naturally in many settings including multi-party computation. The state-of-the-art PBC protocol, TrustedPBC, is due to Tsimos, Loss, and Papamanthou (CRYPTO 2022), which is secure under an adaptive adversary assuming $$f < (1 - \epsilon )n$$ , where f is the number of Byzantine failures and $$\epsilon \in (0,1)$$ . TrustedPBC focuses on single-bit inputs and achieves $$\tilde{O}(n^2 \kappa ^4)$$ communication and $$O(\kappa \log n)$$ rounds. In this work, we propose three PBC protocols for L-bit messages, for any size L, that significantly improve TrustedPBC. First, we propose a new extension protocol that uses a $$\kappa $$ -bit PBC as a black box and achieves i) communication complexity of $$O(L n^2 + n^3\kappa +\mathcal{P}(\kappa ))$$ , where $$\mathcal{P}(\kappa )$$ is the communication complexity of the $$\kappa $$ -bit PBC, and ii) round complexity same as the $$\kappa $$ -bit PBC. By comparison, the state-of-the-art extension protocol for regular broadcast (Nayak et al., DISC 2020) incurs O(n) additional rounds of communication. Next, we propose a protocol that is secure against a static adversary, for $$\kappa $$ -bit messages with $$O(n^2 \kappa ^{1+K} + n\kappa ^3 + \kappa ^4)$$ communication and $$O(\kappa )$$ round complexity, where K is an arbitrarily small constant such that $$0