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Slim-ABC: An Optimized Atomic Broadcast Protocol

Nasit S Sony, Xianzhong Ding, Mukesh Singhal

TL;DR

While Slim-ABC reduces the number of accepted requests, it significantly mitigates resource wastage, making it more efficient and robust, and provides a rigorous security analysis, demonstrating that Slim-ABC satisfies the agreement, validity, and totality properties of the asynchronous common subset protocol.

Abstract

The Byzantine Agreement (BA) problem is a fundamental challenge in distributed systems, focusing on achieving reaching an agreement among parties, some of which may behave maliciously. With the rise of cryptocurrencies, there has been significant interest in developing atomic broadcast protocols, which facilitate agreement on a subset of parties' requests. However, these protocols often come with high communication complexity ($O(ln^2 + λn^3 \log n)$, where $l$ is the bit length of the input, $n$ is the number of parties, and $λ$ represents the security parameter bit length). This can lead to inefficiency, especially when the requests across parties exhibit little variation, resulting in unnecessary resource consumption. In this paper, we introduce Slim-ABC, a novel atomic broadcast protocol that eliminates the $O(ln^2 + λn^3 \log n)$ term associated with traditional atomic broadcast protocols. While Slim-ABC reduces the number of accepted requests, it significantly mitigates resource wastage, making it more efficient. The protocol leverages the asynchronous common subset and provable-broadcast mechanisms to achieve a communication complexity of $O(ln^2 + λn^2)$. Despite the trade-off in accepted requests, Slim-ABC maintains robust security by allowing only a fraction ($f+1$) of parties to broadcast requests. We present an extensive efficiency analysis of Slim-ABC, evaluating its performance across key metrics such as message complexity, communication complexity, and time complexity. Additionally, we provide a rigorous security analysis, demonstrating that Slim-ABC satisfies the \textit{agreement}, \textit{validity}, and \textit{totality} properties of the asynchronous common subset protocol.

Slim-ABC: An Optimized Atomic Broadcast Protocol

TL;DR

While Slim-ABC reduces the number of accepted requests, it significantly mitigates resource wastage, making it more efficient and robust, and provides a rigorous security analysis, demonstrating that Slim-ABC satisfies the agreement, validity, and totality properties of the asynchronous common subset protocol.

Abstract

The Byzantine Agreement (BA) problem is a fundamental challenge in distributed systems, focusing on achieving reaching an agreement among parties, some of which may behave maliciously. With the rise of cryptocurrencies, there has been significant interest in developing atomic broadcast protocols, which facilitate agreement on a subset of parties' requests. However, these protocols often come with high communication complexity (, where is the bit length of the input, is the number of parties, and represents the security parameter bit length). This can lead to inefficiency, especially when the requests across parties exhibit little variation, resulting in unnecessary resource consumption. In this paper, we introduce Slim-ABC, a novel atomic broadcast protocol that eliminates the term associated with traditional atomic broadcast protocols. While Slim-ABC reduces the number of accepted requests, it significantly mitigates resource wastage, making it more efficient. The protocol leverages the asynchronous common subset and provable-broadcast mechanisms to achieve a communication complexity of . Despite the trade-off in accepted requests, Slim-ABC maintains robust security by allowing only a fraction () of parties to broadcast requests. We present an extensive efficiency analysis of Slim-ABC, evaluating its performance across key metrics such as message complexity, communication complexity, and time complexity. Additionally, we provide a rigorous security analysis, demonstrating that Slim-ABC satisfies the \textit{agreement}, \textit{validity}, and \textit{totality} properties of the asynchronous common subset protocol.
Paper Structure (42 sections, 3 theorems, 6 figures, 2 tables, 9 algorithms)

This paper contains 42 sections, 3 theorems, 6 figures, 2 tables, 9 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Definitions and Assumptions
  4. Provable-Broadcast
  5. Cryptographic Abstractions
  6. $(1, \kappa, \epsilon)$- Committee Selection
  7. System Model
  8. Computation
  9. Communications
  10. Design Goal
  11. Atomic Broadcast
  12. Asynchronous Common Subset (ACS)
  13. Design of Slim-ABC
  14. Slim-ABC Overview
  15. Committee selection protocol.
  16. ...and 27 more sections

Key Result

Lemma 4.1

In the $propose$ step of the protocol, one or more provable-broadcast proof reaches more than one party.

Figures (6)

  • Figure 1: An overview of Slim-ABC.
  • Figure 2: pPB illustration. Here the parties $p_1$ and $p_2$ are the committee members. They first broadcast a message of the form $(ID, r1)$ to every party. When a party receives the message, adds the sign-share $CShare(r1)$ on the message and returns to the sender. A committee member wait for the sign-shares and combines the sign-share to get a threshold-signature ($ts$).
  • Figure 3: Propose-Suggest illustration. Here the committee members $p_1$ and $p_2$ get their proofs $(ts1, ts2)$ and broadcast that as a proposal to every party. When a party receives a proposal with proof, the party broadcasts the the proposal as a suggestion to every parties (second to third column). A party waits for $2f+1$ suggestions before concluding the steps.
  • Figure :
  • Figure :
  • ...and 1 more figures

Theorems & Definitions (9)

  • definition 2.1: Validated Asynchronous Common Subset (VACS)
  • Lemma 4.1
  • proof
  • Lemma 4.2
  • proof
  • Theorem 4.3
  • proof
  • definition A.1: Verfiability
  • proof