VDF research

Hello! This page keeps track of public material (papers, videos, explainers) relevant to VDFs and groups of unknown order. It is maintained by the VDF Alliance, a collaborative effort to design and implement production-grade VDFs in software and in hardware.

To make changes to this page please submit a pull request to the Github repo. Also feel free to reach out to vdf@ethereum.org.

hidden order group VDFs

2021—Rotem Simple and Efficient Batch Verification Techniques for Verifiable Delay Functions

2021—Block, Holmgren, Rosen, Rothblum, Soni Time- and Space-Efficient Arguments from Groups of Unknown Order

2020—Belabas, Keinjung, Sanso, Wesolowski A note on the low order assumption in class group of an imaginary quadratic number fields

2020—Lombardi, Vaikuntanathan Fiat-Shamir for Repeated Squaring with Applications to PPAD-Hardness and VDFs

2020—Attias, Vigneri, Dimitrov Implementation Study of Two Verifiable Delay Functions

2019—Döttling, Garg, Malavolta, Vasudevan Tight Verifiable Delay Functions

2019—Ephraim, Freitag, Komargodski, Pass Continuous Verifiable Delay Functions

2018—Boneh, Bünz, Fisch A Survey of Two Verifiable Delay Functions

2018—Pietrzak Simple Verifiable Delay Functions

2018—Wesolowski Efficient Verifiable Delay Functions

other VDFs

2021—Loe, Medley, O’Connell, Quaglia A Practical Verifiable Delay Function and Delay Encryption Scheme

2021—Chavez-Saab, Henríquez, Tibouchi Verifiable Isogeny Walks: Towards an Isogeny-based Postquantum VDF

2020—Jaques, Montgomery, Roy Time-release Cryptography from Minimal Circuit Assumptions

2020—Rotem, Segev, Shahaf Generic-Group Delay Functions Require Hidden-Order Groups

2019—Mahmoody, Smith, Wu A Note on the (Im)possibility of Verifiable Delay Functions in the Random Oracle Model

2019—Shani A note on isogeny-based hybrid verifiable delay functions

2019—De Feo, Masson, Petit, Sanso Verifiable delay functions from supersingular isogenies and pairings

2018—Boneh, Bonneau, Bünz, Fisch Verifiable Delay Functions

2015—Lenstra, Wesolowski A Random Zoo: Sloth, Unicorn, and Trx

hidden order groups

2022—Hoffmann, Hubáček, Kamath, Klein, Pietrzak Practical Statistically-Sound Proofs of Exponentiation in any Group

2021—Sreedhar, Horowitz, Torng A Fast Large-Integer Extended GCD Algorithm and Hardware Design for Verifiable Delay Functions and Modular Inversion

2021—van Baarsen, Stevens On Time-Lock Cryptographic Assumptions in Abelian Hidden-Order Groups

2020—Kirchner, Fouque Getting Rid of Linear Algebra in Number Theory Problems

2020—Zhu, Song, Tian, Wang An Efficient Accelerator of the Squaring for the Verifiable Delay Function Over a Class Group

2020—Rotem, Segev Generically Speeding-Up Repeated Squaring is Equivalent to Factoring: Sharp Thresholds for All Generic-Ring Delay Functions

2020—Katz, Loss, Xu On the Security of Time-Locked Puzzles and Timed Commitments

2020—Seres, Burcsi A Note on Low Order Assumptions in RSA groups

2020—Thakur Constructing hidden order groups using genus three Jacobians

2020—Lee The security of Groups of Unknown Order based on Jacobians of Hyperelliptic Curves

2020—Dobson, Galbraith Trustless Groups of Unknown Order with Hyperelliptic Curves

2018—Feist Generating RSA UFOs

2014—Gnos1s RSA UFO

low-latency modular multiplication

2021—San LLMonPro: Low-Latency Montgomery modular multiplication suitable for Verifiable Delay Functions

2020—Wesolowski, Williams Lower bounds for the depth of modular squaring

2020—Mert, Öztürk, Savaş Low-Latency ASIC Algorithms of Modular Squaring of Large Integers for VDF Applications

2019—Öztürk Modular Multiplication Algorithm Suitable For Low-Latency Circuit Implementations

scalable RSA MPC

2020—Omer Shlomovits (ZenGo X team) DogByte Attack: Playing Red Team for Eth2.0 VDF

2020—Omer Shlomovits (ZenGo X team) Diogenes Octopus: Playing Red Team for Eth2.0 VDF

2020—Chen, Hazay, Ishai, Kashnikov, Micciancio, Riviere, shelat, Venkitasubramaniam, Wang Diogenes: Lightweight Scalable RSA Modulus Generation with a Dishonest Majority

2020—Chen, Cohen, Doerner, Kondi, Lee, Rosefield, shelat Multiparty Generation of an RSA Modulus

non-VDF schemes

2022—Arun, Bonneau, Clark Short-lived zero-knowledge proofs and signatures

2020—Thyagarajan, Bhat, Malavolta, Döttling, Kate, Schröder Verifiable Timed Signatures Made Practical

2020—Tomescu, Xia, Newman Authenticated Dictionaries with Cross-Incremental Proof (Dis)aggregation

2020—Agrawal, Raghuraman KVaC: Key-Value Commitments for Blockchains and Beyond

2020—Ephraim, Freitag, Komargodski, Pass Non-Malleable Time-Lock Puzzles and Applications

2020—Chvojka, Jager, Slamanig, Striecks Generic Constructions of Incremental and Homomorphic Timed-Release Encryption

2020—Wahby, Boneh, Jeffrey, Poon An airdrop that preserves recipient privacy

2020—Burdges, De Feo Delay Encryption

2020—Castagnos, Catalano, Laguillaumie, Savasta, Tucker Bandwidth-efficient threshold EC-DSA

2020—Campanelli, Fiore, Greco, Kolonelos, Nizzardo Vector Commitment Techniques and Applications to Verifiable Decentralized Storage

2019—Ozdemir, Wahby, Boneh Scaling Verifiable Computation Using Efficient Set Accumulators

2019—Bünz, Fisch, Szepieniec Transparent SNARKs from DARK Compilers

2019—Malavolta, Thyagarajan Homomorphic Time-Lock Puzzles and Applications

2019—Drake Fixed-modulus timelock puzzles

2019—Landerreche, Stevens, Schaffner Non-interactive Cryptographic Timestamping based on Verifiable Delay Functions

2018—Boneh, Bünz, Fisch Batching Techniques for Accumulators with Applications to IOPs and Stateless Blockchains

2018—Lai, Malavolta Subvector Commitments with Application to Succinct Arguments

1999—Sander Efficient Accumulators without Trapdoor Extended Abstract

randomness beacons

2020—Cascudo, David, Shlomovits, Varlakov Mt. Random: Multi-Tiered Randomness Beacons

2020—Han, Yu, Lin RandChain: Decentralised Randomness Beacon from Sequential Proof-of-Work

2020—Schindler, Judmayer, Hittmeir, Stifter, Weippl RandRunner: Distributed Randomness from Trapdoor VDFs with Strong Uniqueness

2020—Baum, David, Dowsley, Nielsen, Oechsner CRAFT: Composable Randomness and Almost Fairness from Time

2018—Drake Minimal VDF Randomness Beacon

2018—Drake VDF-based RNG with Linear Lookahead

2018—Jensen, Kristensen, Michno Developing a Trustworthy Randomness Beacon for the Public

2018—Schindler, Judmayer, Stifter, Weippl HydRand: Practical Continuous Distributed Randomnesss

2017—Bünz, Goldfeder, Bonneau Proofs-of-delay and Randomness Beacons in Ethereum

2016—Darknet RANDAO: A DAO Working as RNG of Ethereum

1998—Goldschlag, Stubblebine Publicly Veriable Lotteries: Applications of Delaying Functions

VDFs and randomness explainers

2020—StarkWare, Joseph Bonneau, Justin Drake (crowdcast) Time-warping STARKs

2020—Luca De Feo (podcast) Isogenies VDFs

2019—Joseph Bonneau (podcast) Exploring VDFs

2019—Justin Drake (podcast) Randomness and Random Beacons

2019—Bruno Skvorc Two Point Oh: Randomness

2019—Maxwell Foley Qi Hardware—VDF FAQ pt. 1

2018—Arthur Breitman Better randomness

2018—Trail of Bits Introduction to Verifiable Delay Functions (VDFs)

2018—Justin Drake Minimal VDF randomness beacon

2018—Jeromy Johnson A VDF Explainer

2018—Danny Ryan VDFs are not Proof of Work

2018—Anatoly Yakovenko Proof of History: A clock for blockchain

hidden order group explainers

2020—Alan Szepieniec Jacobians of Hyperelliptic Curves

2019—Lipa Long Binary Quadratic Forms

2019—Michael Straka Class Groups for Cryptographic Accumulators

other relevant reading

2021—Thyagarajan, Gong, Bhat, Kate, Schröder OpenSquare: Decentralized Repeated Modular Squaring Service

2018—Cohen, Pietrzak Simple Proofs of Sequential Work

2013—Mahmoody, Moran, Vadhan Publicly Verifiable Proofs of Sequential Work

2001—Buchmann, Hamdy A Survey on IQ Cryptography

2000—Boneh, Naor Timed Commitments

1996—Rivest, Shamir, Wagner Time-lock Puzzles and Timed-release Crypto

VDF day #4

Feb 18, 2020 @ Stanford

Justin Drake Introduction to Stanford VDF Day 2020

Kelly Olson VDF Hardware Performance

Benedikt Bünz Better, Faster, Smaller, Safer, DARKER

Luigi Vigneri and Vassil Dimitrov VDFs in IOTA

Alex Ozdemir Wesolowski Proofs Inside a SNARK

Ryan Williams Modular Squaring Lower Bounds

Dan Cline Clockwork, VDFs for Front-Running Prevention

Bram Cohen VDFs in Chia

Riad Wahby Airdrops that Preserve Privacy

Eli Ben-Sasson STARK-based VDFs

Ilan Komargodski Continuous VDFs

Mohammad Mahmoody (Im)possibility of VDFs in the Random Oracle Model

Dankrad Feist RSA Assumption Bounties

Stanford Blockchain Conference 2020

Eli Ben-Sasson STARK-based Timelock Puzzle and VDFs

Megan Chen Scalable RSA Modulus Generation with Dishonest Majority

Simon Peffers Hardware Accelerated RSA—VDFs, Accumulators, and SNARKs

Ben Fisch Transparent SNARKs from DARK Compilers

Daniel Cline ClockWork: An Exchange Protocol for Proofs of Non Front-Running

VDF day #3

May 17, 2019 @ MIT

Ron Rivest Comments and Observations about Timelocks and VDFs

Justin Drake Blockchain VDF Ecosystem and Opportunities for Participation

Erdinç Öztürk Novel Low-Latency Modular Multiplier

Omer Paneth Alternate VDF constructions

Mariano Sorgente Proof of Space Nakamoto Consensus using Classgroup VDFs

Muthu Venkitasubramaniam RSA Multi-party Computation Protocol Overview

VDF day #2

Feb 3–4, 2019 @ Stanford

Dan Boneh Verifiable Delay Functions

Jeromy Johnson VDFs and Filecoin

Justin Drake Towards Productions VDFs

Benjamin Wesolowski A Hybrid VDF prover

Erdinç Öztürk Low Latency Modular Multiplication

Abhi Shelat Threshold Factoring from Factoring

other relevant videos

2020—Benjamin Smith Trustless groups of unknown order

2020—Jack Doerner Multiparty Generation of an RSA Modulus

2020—Lior Rotem Generic-Group Delay Functions Require Hidden-Order Groups

2020—Eli Ben-Sasson VeeDo

2020—István András Seres A Note on Low Order Assumptions in RSA Groups

2019—Benjamin Wesolowski Efficient Verifiable Delay Functions

2019—Dankrad Feist VDF Applications

2018—Ben Fisch Verifiable Delay Functions: Applications and Candidate Constructions

2017—Benedikt Bünz Proofs-of-Delay and Randomness Beacons in Ethereum

2017—Joseph Bonneau Verifiable Lotteries