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The concept of verifiable delay functions has received attention from researchers since it was first proposed in 2018. The applications of verifiable delay are also widespread in blockchain research, such as: computational timestamping, public random beacons, resource-efficient blockchains, and proofs of data replication. This paper introduces the concept of verifiable delay functions and systematically summarizes the types of verifiable delay functions. Firstly, the description and characteristics of verifiable delay functions are given, and weak verifiable delay functions, incremental verifiable delay functions, decodable verifiable delay functions, and trapdoor verifiable delay functions are introduced respectively. The construction of verifiable delay functions generally relies on two security assumptions: algebraic assumption or structural assumption. Then, the security assumptions of two different verifiable delay functions are described based on cryptography theory. Secondly, a post-quantum verifiable delay function based on super-singular isogeny is introduced. Finally, the paper summarizes the blockchain-related applications of verifiable delay functions.

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Blockchain, with its characteristics of non-tamperability and decentralization, has had a profound impact on various fields of society and has set off a boom in the research and application of blockchain technology. However, blockchain technology faces the problem of data availability attacks during its application, which greatly limits the scope and domain of blockchain applications. One of the most advantageous researches to address this problem is the scalable data availability solution that integrates coding theory design into the Merkle tree promise. Based on this scheme, this paper combines a zero-knowledge accumulator with higher efficiency and security with local repair coding, and proposes a data availability scheme with strong dataset privacy protection. The scheme first encodes the data block information on the blockchain to ensure tamper-proof data, and then uses a zero-knowledge accumulator to store the encoded data block information. Its main purpose is to use zero-knowledge property to protect the accumulation set information stored in the accumulator from being leaked and to ensure that no other information about the accumulation set is revealed during the data transmission. It fundamentally reduces the possibility of attackers generating fraudulent information by imitating block data and further resists data availability attacks.

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