Breaking the

Byzantine agreement (BA), the task of n parties to agree on one of their input bits in the face of malicious agents, is a powerful primitive that lies at the core of a vast range of distributed protocols. Interestingly, in BA protocols with the best overall communication, the demands of the parties are highly unbalanced : the amortized cost is O ~ ( 1 ) bits per party, but some parties must send Ω ( n ) bits. In best known balanced protocols, the overall communication is sub-optimal, with each party communicating O ~ ( n ) . In this work, we ask whether asymmetry is inherent for optimizing total communication. In particular, is BA possible where each party communicates only O ~ ( 1 ) bits? Our contributions in this line are as follows: We define a cryptographic primitive— succinctly reconstructed distributed signatures (SRDS)—that suffices for constructing O ~ ( 1 ) balanced BA. We provide two constructions of SRDS from different cryptographic and public-key infrastructure (PKI) assumptions. The SRDS-based BA follows a paradigm of boosting from “almost-everywhere” agreement to full agreement, and does so in a single round. Complementarily, we prove that PKI setup and cryptographic assumptions are necessary for such protocols in which every party sends o ( n ) messages. We further explore connections between a natural approach toward attaining SRDS and average-case succinct non-interactive argument systems (SNARGs) for a particular type of NP-Complete problems (generalizing Subset-Sum and Subset-Product).