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OciorCOOL: Faster Byzantine Agreement and Reliable Broadcast

Jinyuan Chen

TL;DR

In this work, it is shown that COOL can be optimized by reducing one communication round, and an optimal reliable broadcast protocol is designed that requires only six communication rounds.

Abstract

COOL (Chen'21) is an error-free and deterministic Byzantine agreement protocol that achieves consensus on an $\ell$-bit message with a communication complexity of $O(\max\{n\ell, n t \log t \})$ bits in four phases, given $n\geq 3t + 1$, for a network of $n$ nodes, where up to $t$ nodes may be dishonest. In this work we show that COOL can be optimized by reducing one communication round. The new protocol is called OciorCOOL. Additionally, building on OciorCOOL, we design an optimal reliable broadcast protocol that requires only six communication rounds.

OciorCOOL: Faster Byzantine Agreement and Reliable Broadcast

TL;DR

In this work, it is shown that COOL can be optimized by reducing one communication round, and an optimal reliable broadcast protocol is designed that requires only six communication rounds.

Abstract

COOL (Chen'21) is an error-free and deterministic Byzantine agreement protocol that achieves consensus on an -bit message with a communication complexity of bits in four phases, given , for a network of nodes, where up to nodes may be dishonest. In this work we show that COOL can be optimized by reducing one communication round. The new protocol is called OciorCOOL. Additionally, building on OciorCOOL, we design an optimal reliable broadcast protocol that requires only six communication rounds.
Paper Structure (20 sections, 23 theorems, 51 equations, 2 tables, 3 algorithms)

This paper contains 20 sections, 23 theorems, 51 equations, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Primitives
  3. $\text{OciorCOOL}$
  4. Overview of $\text{OciorCOOL}$
  5. Phases 1 and 2
  6. Phase 3
  7. Analysis of $\text{OciorCOOL}$
  8. Some lemmas
  9. Analysis for Case 1
  10. Analysis for Case 2
  11. $\text{OciorRBC}$
  12. Overview of $\text{OciorRBC}$
  13. Initial phase
  14. Phase 1
  15. Phase 2
  16. ...and 5 more sections

Key Result

Theorem 1

Given $n\geq 3t+1$, if all honest nodes receive their inputs, then every honest node eventually outputs a message and terminates in $\text{OciorCOOL}$.

Theorems & Definitions (46)

  • Definition 1: Byzantine agreement
  • Definition 2: Reliable broadcast Bracha:87
  • Definition 3: Distributed multicast
  • Definition 4: $\text{Unique agreement}$
  • Theorem 1: Termination
  • proof
  • Theorem 2: Validity
  • proof
  • Theorem 3: Consistency
  • proof
  • ...and 36 more