Verifiable Delay Functions using Elliptic Curves

A verifiable delay function (VDF) is a function that takes a pre-determined time to compute, even on parallel processors, and once computed, its output can be quickly verified by anyone. We are working on a number of novel constructions of VDFs, uVDFs (Unique VDFs), and cVDFs (Continuous VDFs) from point multiplication on elliptic curves, along with an implementation study. Previous work has generally been theoretical, with no efficient constructions. Further, using elliptic curves for such a purpose is not obvious:  In most cryptographic applications of elliptic curves, knowing the order of the group of points or the order of some points on the elliptic curve is required. Schoof’s algorithm is a well-known way to solve this problem for elliptic curves; we have found a way to avoid this issue.

We are building modified versions of Wesolowski’s and Pietrzak’s schemes, and run detailed simulations, analyzing Evaluation, Proof Generation, Verification Time, and, critically, the proof size. Our preliminary tests indicate that our modified versions of Wesolowski-based VDFs, uVDFs, and cVDFs are more suitable for decentralized clock applications.

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