Light nodes are clients in blockchain systems that only store a small portion of the blockchain ledger. In certain blockchains, light nodes are vulnerable to a data availability (DA) attack where a malicious node makes the light nodes accept an invalid block by hiding the invalid portion of the block from the nodes in the system. Recently, a technique based on LDPC codes called Coded Merkle Tree was proposed by Yu et al. that enables light nodes to detect a DA attack by randomly requesting/sampling portions of the block from the malicious node. However, light nodes fail to detect a DA attack with high probability if a malicious node hides a small stopping set of the LDPC code. In this paper, we demonstrate that a suitable co-design of specialized LDPC codes and the light node sampling strategy leads to a high probability of detection of DA attacks. We consider different adversary models based on their computational capabilities of finding stopping sets. For the different adversary models, we provide new specialized LDPC code constructions and coupled light node sampling strategies and demonstrate that they lead to a higher probability of detection of DA attacks compared to approaches proposed in earlier literature.
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