Concentrated Stopping Set Design for Coded Merkle Tree: Improving Security Against Data Availability Attacks in Blockchain Systems

TL;DR

This paper introduces a specialized LDPC code design, using the EC-PEG algorithm, to improve detection of data availability attacks in blockchain light nodes by concentrating stopping sets.

Contribution

It presents a deterministic LDPC code construction that concentrates stopping sets, enhancing security against DA attacks in Coded Merkle Trees.

Findings

Higher probability of detecting DA attacks.

Effective at short code lengths.

Improved security through stopping set concentration.

Abstract

In certain blockchain systems, light nodes are clients that download only a small portion of the block. Light nodes are vulnerable to data availability (DA) attacks where a malicious node hides an invalid portion of the block from the light nodes. Recently, a technique based on erasure codes called Coded Merkle Tree (CMT) was proposed by Yu et al. that enables light nodes to detect a DA attack with high probability. The CMT is constructed using LDPC codes for fast decoding but can fail to detect a DA attack if a malicious node hides a small stopping set of the code. To combat this, Yu et al. used well-studied techniques to design random LDPC codes with high minimum stopping set size. Although effective, these codes are not necessarily optimal for this application. In this paper, we demonstrate a more specialized LDPC code design to improve the security against DA attacks. We achieve this goal by providing a deterministic LDPC code construction that focuses on concentrating stopping sets to a small group of variable nodes rather than only eliminating stopping sets. We design these codes by modifying the Progressive Edge Growth algorithm into a technique called the entropy-constrained PEG (EC-PEG) algorithm. This new method demonstrates a higher probability of detecting DA attacks and allows for good codes at short lengths.