Communication-Efficient Byzantine Agreement without Erasures
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Byzantine agreement (BA) is one of the most fundamental building blocks in distributed systems. A long-standing open problem is whether BA protocols with subquadratic communication complexity are possible in the presence of an adaptive attacker. A breakthrough result by King and Saia (JACM'11) showed how to overcome the quadradtic "barrier", assuming erasures---that is, honest player can untraceably erase memory contents---achieving a communication complexity of n^1.5 while tolerating a constant fraction of corrupt nodes. Another very recent result by Micali (ITCS'17) also considers the erasure model and shows how to achieve close-to-optimal communication complexity O(n · n), and handling f<(1-ϵ)n/3 corrupted players, but this time using cryptographic assumptions (the existence of unique signatures and a "random oracle") and relying on a public key infrastructure (PKI). Both of these results are in the synchronous model of computation. In this work, we present the first subquadratic protocols in the presence of a fully adaptive attacker without erasures. We rely on the existence of an honestly generated PKI. We have: (1) an expected O(1)-round BA protocol with O(n · n) communication complexity in the synchronous model of communication, tolerating f<(1-ϵ) n/2 adaptive corruptions; (2) a BA protocol with O(n · n) communication complexity in the partially-synchronous model of communication, tolerating f<(1-ϵ) n/3 adaptive corruptions. In the partially-synchronous model, the corruption bound f<n/3 is known to be tight, whereas in the synchronous model, the f< n/2 bound is the best known among expected O(1)-round protocols even for protocols with large communication complexity.
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