Breaking the O(√n) -Bit Barrier: Byzantine Agreement with Polylog Bits Per Party

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). Our results provide new approaches forward, as well as limitations and barriers, toward minimizing per-party communication of BA. In particular, we construct the first two BA protocols with O~ (1) balanced communication, offering a trade-off between setup and cryptographic assumptions and answering an open question presented by King and Saia (DISC’09).