We construct a verifiable delay function (VDF). A VDF is a function whose evaluation requires running a given number of sequential steps, yet the result can be efficiently verified. They have applications in decentralised systems, such as the generation of trustworthy public randomness in a trustless environment, or resource-efficient blockchains. To construct our VDF, we actually build a trapdoor VDF. A trapdoor VDF is essentially a VDF which can be evaluated efficiently by parties who know a secret (the trapdoor). By setting up this scheme in a way that the trapdoor is unknown (not even by the party running the setup, so that there is no need for a trusted setup environment), we obtain a simple VDF. Our construction is based on groups of unknown order such as an RSA group, or the class group of an imaginary quadratic field. The output of our construction is very short (the result and the proof of correctness are each a single element of the group), and the verification of correctness is very efficient.

Additional Metadata
Persistent URL dx.doi.org/10.1007/978-3-030-17659-4_13
Series Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence
Conference Advances in Cryptology - EUROCRYPT
Wesolowski, B.P.C. (2019). Efficient verifiable delay functions. In Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence. doi:10.1007/978-3-030-17659-4_13