# Verifiable Delay Functions

@article{Boneh2018VerifiableDF,
title={Verifiable Delay Functions},
author={Dan Boneh and Joseph Bonneau and Benedikt B{\"u}nz and Ben Fisch},
journal={IACR Cryptol. ePrint Arch.},
year={2018},
volume={2018},
pages={601}
}
• Published 19 August 2018
• Computer Science, Mathematics
• IACR Cryptol. ePrint Arch.
We study the problem of building a verifiable delay function (VDF). A $$\text {VDF}$$requires a specified number of sequential steps to evaluate, yet produces a unique output that can be efficiently and publicly verified. $$\text {VDF}$$s have many applications in decentralized systems, including public randomness beacons, leader election in consensus protocols, and proofs of replication. We formalize the requirements for $$\text {VDF}$$s and present new candidate constructions that are the…
251 Citations
Delay Function with Fixed Effort Verification
This paper proposes a verifiable delay function that requires fixed effort during verification and this effort to verify is independent of the security parameter of the scheme.
Two Sequential Squaring Verifiable Delay Function
This paper proposes a verifiable delay function that requires only 2modulo squaring for verification, so the sequential effort required for verification is independent of the security parameter.
How Hard Are Verifiable Delay Functions?
This paper shows that the class of all the VDFs, VDF * IP, is constructed from an EXP-complete language and reduced to the derived VDF, which means if VDF ⊆ PSPACE = IP then EXP ⊬ = IP which has no proof yet.
Nakamoto Consensus with Verifiable Delay Puzzle
• Computer Science, Mathematics
ArXiv
• 2019
This paper summarizes the work-in-progress on a new consensus protocol based on verifiable delay function, which resembles the hashing puzzle used in the PoW mechanism but can only be solved sequentially and shows that VDP can be combined with the Nakamoto consensus in a proof-of-stake/proof- of-delay hybrid protocol.
A Survey of Two Verifiable Delay Functions
• Computer Science
IACR Cryptol. ePrint Arch.
• 2018
This short note briefly surveys and compares two recent beautiful Verifiable Delay Functions (VDFs), one due to Pietrzak and the other due to Wesolowski, and provides a new computational proof of security for one of them.
RandRunner: Distributed Randomness from Trapdoor VDFs with Strong Uniqueness
• Computer Science, Mathematics
IACR Cryptol. ePrint Arch.
• 2020
This design allows RandRunner to tolerate adversarial or failed leaders while guaranteeing safety and liveness of the protocol despite possible periods of asynchrony, and avoids the necessity of a BFT consensus protocol and its accompanying high complexity and communication overhead.
Efficient verifiable delay functions
• B. Wesolowski
• Computer Science, Mathematics
IACR Cryptol. ePrint Arch.
• 2018
This work constructs a verifiable delay function (VDF) based on groups of unknown order such as an RSA group, or the class group of an imaginary quadratic field, which is very short, and the verification of correctness is very efficient.
Efficient Verifiable Delay Functions
This work constructs a verifiable delay function (VDF) based on groups of unknown order such as an RSA group or the class group of an imaginary quadratic field, and the output of the construction is very short, the verification of correctness is very efficient.
Efficient Verifiable Delay Functions (extended version)
This work constructs a verifiable delay function (VDF) based on groups of unknown order such as an RSA group, or the class group of an imaginary quadratic field, which is very short, and the verification of correctness is very efficient.
Simple Verifiable Delay Functions
A statistically sound public-coin protocol to prove that a tuple (N,x,T,y) satisfies y=x2T (mod N) where the prover doesn’t know the factorization of N and its running time is dominated by solving the puzzle, that is, compute x2T, which is conjectured to require T sequential squarings.

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This work constructs a verifiable delay function (VDF) based on groups of unknown order such as an RSA group, or the class group of an imaginary quadratic field, which is very short, and the verification of correctness is very efficient.
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