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TRAIL: Cross-Shard Validation for Cryptocurrency Byzantine Shard Protection

Mitch Jacovetty, Joseph Oglio, Mikhail Nesterenko, Gokarna Sharma

TL;DR

TRAIL addresses shard-failure resilience in sharded blockchains by introducing a coin-specific trail of shards that validate cross-shard transactions. It combines internal shard PBFT with a cross-shard PBFT across the trail, ensuring safety (ownership continuity) and liveness (request satisfaction) under Byzantine faults, including up to $F$ faulty shards. The work provides correctness proofs via a SimpleTRAIL reduction, analyzes message complexity, and describes practical extensions such as coin splitting/merging and dynamic shard management. Experimental evaluation in a simulator demonstrates improved security with modest overhead and favorable scalability, establishing TRAIL as a viable approach to robust sharded cryptocurrency.

Abstract

We present TRAIL: an algorithm that uses a novel consensus procedure to tolerate failed or malicious shards within a blockchain-based cryptocurrency. Our algorithm takes a new approach of selecting validator shards for each transaction from those that previously held the assets being transferred. This approach ensures the algorithm's robustness and efficiency. TRAIL is presented using PBFT for internal shard transaction processing and a modified version of PBFT for external cross-shard validation. We describe TRAIL, prove it correct, analyze its message complexity, and evaluate its performance. We propose various TRAIL optimizations: we describe how it can be adapted to other Byzantine-tolerant consensus algorithms, how a complete system may be built on the basis of it, and how TRAIL can be applied to existing and future sharded blockchains.

TRAIL: Cross-Shard Validation for Cryptocurrency Byzantine Shard Protection

TL;DR

TRAIL addresses shard-failure resilience in sharded blockchains by introducing a coin-specific trail of shards that validate cross-shard transactions. It combines internal shard PBFT with a cross-shard PBFT across the trail, ensuring safety (ownership continuity) and liveness (request satisfaction) under Byzantine faults, including up to faulty shards. The work provides correctness proofs via a SimpleTRAIL reduction, analyzes message complexity, and describes practical extensions such as coin splitting/merging and dynamic shard management. Experimental evaluation in a simulator demonstrates improved security with modest overhead and favorable scalability, establishing TRAIL as a viable approach to robust sharded cryptocurrency.

Abstract

We present TRAIL: an algorithm that uses a novel consensus procedure to tolerate failed or malicious shards within a blockchain-based cryptocurrency. Our algorithm takes a new approach of selecting validator shards for each transaction from those that previously held the assets being transferred. This approach ensures the algorithm's robustness and efficiency. TRAIL is presented using PBFT for internal shard transaction processing and a modified version of PBFT for external cross-shard validation. We describe TRAIL, prove it correct, analyze its message complexity, and evaluate its performance. We propose various TRAIL optimizations: we describe how it can be adapted to other Byzantine-tolerant consensus algorithms, how a complete system may be built on the basis of it, and how TRAIL can be applied to existing and future sharded blockchains.
Paper Structure (8 sections, 3 theorems, 10 figures, 1 algorithm)

This paper contains 8 sections, 3 theorems, 10 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Network Model, Problem Statement, PBFT
  3. TRAIL Description
  4. TRAIL Correctness and Efficiency
  5. TRAIL Algorithmic Extensions and Implementation Considerations
  6. Performance Evaluation and Security Analysis
  7. Related Work and Its Application to TRAIL
  8. Future Work

Key Result

Lemma 1

SimpleTRAIL solves the Currency Transmission Problem with at most $F$ Byzantine shards.

Figures (10)

  • Figure 1: Trail membership modification under consequent transactions. The first transaction moves a coin from a wallet in shard $S4$ to a wallet in shard $S5$. The second moves the same coin from $S5$ to $S6$.
  • Figure 2: Message transmission in TRAIL's normal operation. The coin trail contains shards: $S1, S2, S3$ and $S4$. The coin is located in a wallet stored by shard $S4$. A client sends a transaction requesting to move the coin from the wallet of this source shard $S4$ to a wallet of shard $S5$. First, the source shard runs internal PBFT; then, it runs the phases of external shard PBFT. After committing, the trail shards notify the client and the target shard.
  • Figure 3: Transactions approved over time without TRAIL shard validation. The network approves both honest and malicious transactions.
  • Figure 4: Transactions approved over time with TRAIL shard validation. The network approves honest transactions only.
  • Figure 5: Transactions approved over time in TRAIL with shard validation and wallet recovery from the failed shards. Correct shards detect the failure and submit additional transactions moving coins from the failed shards.
  • ...and 5 more figures

Theorems & Definitions (6)

  • Definition 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1