A data availability attack on a blockchain protocol based on LDPC codes

TL;DR: It is shown that the sparse nature of LDPC matrices and the use of the so-called peeling decoder make the SPAR protocol less secure than expected, owing to a new possible attack strategy that can be followed by malicious nodes.

Abstract: In a blockchain Data Availability Attack (DAA), a malicious node publishes a block header but withholds part of the block, which contains invalid transactions. Honest full nodes, which can download and store the full blockchain, are aware that some data are not available but they have no formal way to prove it to light nodes, i.e., nodes that have limited resources and are not able to access the whole blockchain data. A common solution to counter these attacks exploits linear error correcting codes to encode the block content. A recent protocol, called SPAR, employs coded Merkle trees and low-density parity-check (LDPC) codes to counter DAAs. We show that the sparse nature of LDPC matrices and the use of the so-called peeling decoder make the protocol less secure than expected, owing to a new possible attack strategy that can be followed by malicious nodes.