Analysis of a blockchain protocol based on LDPC codes

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 codes to counter DAAs. In this paper, we show that the protocol is less secure than claimed, owing to a redefinition of the adversarial success probability. As a consequence we show that, for some realistic choices of the parameters, the total amount of data downloaded by light nodes is larger than that obtainable with competitor solutions.