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 protocols with the best overall communication, the demands of the parties are highly unbalanced: the amortized cost is $tilde O(1)$ bits per party, but some parties must send $Omega(n)$ bits. In best known balanced protocols, the overall communication is sub-optimal, with each party communicating $tilde O(sqrt{n})$.

In this work, we ask whether asymmetry is inherent for optimizing total communication. In particular, is BA possible where each party communicates only $tilde O(1)$ bits? Our contributions in this line are as follows:

1) We define a cryptographic primitive—succinctly reconstructed distributed signatures (SRDS)—that suffices for constructing $tilde O(1)$ balanced BA. We provide two constructions of SRDS from different cryptographic and Public-Key Infrastructure (PKI) assumptions.

2) 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.

3) 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, towards minimizing per-party communication of BA. In particular, we construct the first two BA protocols with $tilde O(1)$ balanced communication, offering a tradeoff between setup and cryptographic assumptions, and answering an open question presented by King and Saia (DISC’09).

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