Polar Coded Merkle Tree: Mitigating Data Availability Attacks in Blockchain Systems Using Informed Polar Code Design

TL;DR

This paper introduces Polar Coded Merkle Tree (PCMT), a novel coding scheme designed to improve data availability attack mitigation in blockchains by offering better detection, lower fraud proof size, and tractable guarantees for large blocks.

Contribution

The paper proposes a new Polar Coded Merkle Tree with specialized design algorithms, addressing decoding complexity and fraud proof size issues of prior codes in large block size blockchain applications.

Findings

PCMT outperforms LDPC codes in DA detection probability and communication cost.

PCMT has lower coding fraud proof size than LDPC and 2D-RS codes.

PCMT provides tractable code guarantees at large code lengths.

Abstract

Data availability (DA) attack is a well-known problem in certain blockchains where users accept an invalid block with unavailable portions. Previous works have used LDPC and 2-D Reed Solomon (2DRS) codes with Merkle trees to mitigate DA attacks. These codes perform well across various metrics such as DA detection probability and communication cost. However, these codes are difficult to apply to blockchains with large blocks due to large decoding complexity and coding fraud proof size (2D-RS codes), and intractable code guarantees for large code lengths (LDPC codes). In this paper, we focus on large block size applications and address the above challenges by proposing the novel Polar Coded Merkle Tree (PCMT): a Merkle tree encoded using the encoding graph of polar codes. We provide a specialized polar code design algorithm called Sampling Efficient Freezing and an algorithm to prune the polar encoding graph. We demonstrate that the PCMT built using the above techniques results in a better DA detection probability and communication cost compared to LDPC codes, has a lower coding fraud proof size compared to LDPC and 2D-RS codes, provides tractable code guarantees at large code lengths (similar to 2D-RS codes), and has comparable decoding complexity to 2D-RS and LDPC codes.