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.
Keywords: algebraic assumption; blockchain; structural assumption; verifiable delay function.