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Data availability (DA) attack is a well-known problem in certain blockchainswhere users accept an invalid block with unavailable portions. Previous workshave used LDPC and 2-D Reed Solomon (2DRS) codes with Merkle trees to mitigateDA attacks. These codes perform well across various metrics such as DAdetection probability and communication cost. However, these codes aredifficult to apply to blockchains with large blocks due to large decodingcomplexity and coding fraud proof size (2D-RS codes), and intractable codeguarantees for large code lengths (LDPC codes). In this paper, we focus onlarge block size applications and address the above challenges by proposing thenovel Polar Coded Merkle Tree (PCMT): a Merkle tree encoded using the encodinggraph of polar codes. We provide a specialized polar code design algorithmcalled Sampling Efficient Freezing and an algorithm to prune the polar encodinggraph. We demonstrate that the PCMT built using the above techniques results ina better DA detection probability and communication cost compared to LDPCcodes, has a lower coding fraud proof size compared to LDPC and 2D-RS codes,provides tractable code guarantees at large code lengths (similar to 2D-RScodes), and has comparable decoding complexity to 2D-RS and LDPC codes.

Polar Coded Merkle Tree: Mitigating Data Availability Attacks in Blockchain Systems Using Informed Polar Code Design