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$\mathsf{CRATE}$: Cross-Rollup Atomic Transaction Execution

Ioannis Kaklamanis, Fan Zhang

TL;DR

CRATE addresses the lack of cross-rollup composability by enabling atomic, serializable cross-rollup transactions across distinct L1s. It extends a trigger-action framework with session tracking, chain and DAG CRT models, and a two-phase commit between Validator Smart Contracts on separate L1s, powered by an off-chain XEVM executor. The work provides formal definitions of CRTs and proves CRATE’s security, complemented by a full prototype with gas benchmarks and a cross-rollup flash loan application. Practically, CRATE achieves end-to-end finality in $4$ L1 rounds and demonstrates feasible gas costs, illustrating secure cross-rollup finance primitives without reliance on trusted intermediaries.

Abstract

Blockchains have revolutionized decentralized applications, with composability enabling atomic, trustless interactions across smart contracts. However, layer 2 (L2) scalability solutions like rollups introduce fragmentation and hinder composability. Current cross-chain protocols, including atomic swaps, bridges, and shared sequencers, lack the necessary coordination mechanisms or rely on trust assumptions, and are thus not sufficient to support full cross-rollup composability. This paper presents $\mathsf{CRATE}$, a secure protocol for cross-rollup composability that ensures all-or-nothing and serializable execution of cross-rollup transactions (CRTs). $\mathsf{CRATE}$ supports rollups on distinct layer 1 (L1) chains, achieves finality in 4 rounds on L1, and only relies on the underlying L1s and the liveness of L2s. We introduce two formal models for CRTs, define atomicity within them, and formally prove the security of $\mathsf{CRATE}$. We also provide an implementation of $\mathsf{CRATE}$ along with a cross-rollup flash loan application; our experiments demonstrate that $\mathsf{CRATE}$ is practical in terms of gas usage on L1.

$\mathsf{CRATE}$: Cross-Rollup Atomic Transaction Execution

TL;DR

CRATE addresses the lack of cross-rollup composability by enabling atomic, serializable cross-rollup transactions across distinct L1s. It extends a trigger-action framework with session tracking, chain and DAG CRT models, and a two-phase commit between Validator Smart Contracts on separate L1s, powered by an off-chain XEVM executor. The work provides formal definitions of CRTs and proves CRATE’s security, complemented by a full prototype with gas benchmarks and a cross-rollup flash loan application. Practically, CRATE achieves end-to-end finality in L1 rounds and demonstrates feasible gas costs, illustrating secure cross-rollup finance primitives without reliance on trusted intermediaries.

Abstract

Blockchains have revolutionized decentralized applications, with composability enabling atomic, trustless interactions across smart contracts. However, layer 2 (L2) scalability solutions like rollups introduce fragmentation and hinder composability. Current cross-chain protocols, including atomic swaps, bridges, and shared sequencers, lack the necessary coordination mechanisms or rely on trust assumptions, and are thus not sufficient to support full cross-rollup composability. This paper presents , a secure protocol for cross-rollup composability that ensures all-or-nothing and serializable execution of cross-rollup transactions (CRTs). supports rollups on distinct layer 1 (L1) chains, achieves finality in 4 rounds on L1, and only relies on the underlying L1s and the liveness of L2s. We introduce two formal models for CRTs, define atomicity within them, and formally prove the security of . We also provide an implementation of along with a cross-rollup flash loan application; our experiments demonstrate that is practical in terms of gas usage on L1.

Paper Structure

This paper contains 31 sections, 6 theorems, 2 equations, 4 figures, 6 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Technical Overview
  4. Problem Statement
  5. Building Block: Trigger-Action Paradigm
  6. Technical Challenges and Our Solutions
  7. Our Solutions
  8. Overview of CRATE
  9. Formal Foundations
  10. Safety
  11. Liveness and Efficiency
  12. CRATE: Off-Chain Execution -- XEVM
  13. General System Contract
  14. Executor Specification
  15. CRATE: 2PC Protocol
  16. ...and 16 more sections

Key Result

Lemma 1

Let $\mathsf{crt_{chain}} = [a_i]_{i \in [n]}$ and $\{\mathsf{rol}_{b}, h_{\mathsf{ST_{b}}}, h_{\mathsf{ST_{b}'}}, \mathsf{batch}_{b}\}_{b \in \{1,2\}}$ be as in def:forward-atom-chain-crt, when using the original SVS$\mathsf{GSC}$ contract for off-chain execution. For $b \in \{1,2\}$, let $\{\maths

Figures (4)

  • Figure 1: SVS shared-val-seq-23 trigger-action paradigm. Here "$\mathsf{CALL}(f)$" denotes that the (smart contract) function $f$ will be executed.
  • Figure 2: Serializability attack on SVS shared-val-seq-23. A malicious Executor (shown on the right in red) can execute $a_3$ before $a_1'$, flipping the order of steps (2,3) with steps (6,7). Since $a_1'$ only modifies $\mathsf{trigTree}_1$ and $\mathsf{GSC}_1.\mathsf{action}(a_3)$ only modifies $\mathsf{actTree}_1$, the two $\mathsf{GSC}$ contracts result in the same state as in the honest execution (shown in the middle), thus passing the consistency check.
  • Figure 3: $CRATE$ Overview
  • Figure 4: L1 gas usage increase incurred by the MPT-based (red) and SNARK-based (green) implementation of the $CRATE$ 2PC protocol, compared to the observed gas usage range of a vanilla zk-rollup (Zksync).

Theorems & Definitions (20)

  • Remark 1: VSM Communication via Bridges
  • Remark 2: Setup
  • Remark 3
  • Definition 1: CRT Atomicity
  • Definition 2: Efficiency
  • Claim 1
  • proof
  • Lemma 1
  • proof : Proof of \ref{['lem:svs-gsc-all-or-none-exec']}
  • Lemma 2
  • ...and 10 more