Light nodes in blockchains improve the scalability of the system by storing 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 (CMT) 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. To mitigate this problem, Yu et al. used random LDPC codes that achieve large minimum stopping set size with high probability. Although effective, these codes are not necessarily optimal for this application, especially at short code lengths, which are relevant for low latency systems, IoT blockchains, etc.. In this paper, we focus on short code lengths and demonstrate that a suitable co-design of specialized LDPC codes and the light node sampling strategy can improve the probability of detection of DA attacks. We consider different adversary models based on their computational capabilities of finding stopping sets in LDPC codes. For a weak adversary model, we devise a new LDPC code construction termed as the entropy-constrained PEG (EC-PEG) algorithm which concentrates stopping sets to a small group of variable nodes. We demonstrate that the EC-PEG algorithm coupled with a greedy sampling strategy improves the probability of detection of DA attacks. For stronger adversary models, we provide a co-design of a sampling strategy called linear-programming-sampling (LP-sampling) and an LDPC code construction called linear-programming-constrained PEG (LC-PEG) algorithm. The new co-design demonstrates a higher probability of detection of DA attacks compared to approaches in earlier literature.

中文翻译：

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克服区块链系统中的数据可用性攻击：编码默克尔树的短代码长度 LDPC 代码设计

区块链中的轻节点通过存储一小部分区块链账本来提高系统的可扩展性。在某些区块链中，轻节点容易受到数据可用性（DA）攻击，其中恶意节点通过向系统中的节点隐藏块的无效部分来使轻节点接受无效块。最近，Yu 提出了一种基于 LDPC 码的技术，称为 Coded Merkle Tree (CMT)。等。这使轻节点能够通过从恶意节点随机请求/采样块的部分来检测 DA 攻击。但是，如果恶意节点隐藏了一小部分 LDPC 代码停止集，轻节点很有可能无法检测到 DA 攻击。为了缓解这个问题，Yu等。使用随机 LDPC 码以高概率实现大的最小停止集大小。虽然有效，但这些代码不一定适合该应用程序，尤其是短代码长度，这与低延迟系统、物联网区块链等相关。在本文中，我们关注短代码长度并证明合适的协同设计专门的 LDPC 码和轻节点采样策略可以提高 DA 攻击的检测概率。我们根据它们在 LDPC 码中找到停止集的计算能力来考虑不同的对手模型。对于弱对手模型，我们设计了一种新的 LDPC 码结构，称为熵约束PEG (EC-PEG) 算法将停止集集中到一小组变量节点。我们证明了 EC-PEG 算法与贪婪采样策略相结合提高了 DA 攻击的检测概率。对于更强大的对手模型，我们提供了一种抽样策略的协同设计，称为线性规划采样(LP-sampling) 和称为 LDPC 码结构线性规划约束PEG (LC-PEG) 算法。与早期文献中的方法相比，新的协同设计展示了更高的 DA 攻击检测概率。