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Zero-knowledge Proof (ZKP)

"We are currently experiencing a Cambrian Explosion in the field of cryptographic proofs of computational integrity (CI), a subset of which include zero knowledge proofs. While a couple of years ago there were about 1–3 new systems a year, the rate has picked up so much that today we are seeing this same amount monthly, if not weekly."

-- ELI BEN-SASSON, A Cambrian Explosion of Crypto Proofs

Since its invention in 1986, ZKP systems, more and more, become building blocks for many other important domains, such as blockchains, Anonymous Credentials (in Web3), authentication systems, etc. In the following, we will mainly elaborate on the pratical ZKPs and roughly divide them into two categories: specific purpose ZKP and general purpose ZKP, in which their differences mainly come from the ability to prove different statements.

If we compare this with Partial Homomorphic Encryption and Fully Homomorphic Encryption, specific ZKP can only prove some specific(simple) and finite statements, while general ZK (theoretically) can prove any statements.

Survey & Tutorial

  • Zero-Knowledge twenty years after its invention, also called A Short Tutorial of Zero-Knowledge
    Oded Goldreich
    Gol10, paper, Gol04 older version,homepage

  • Proofs, Arguments, and Zero-Knowledge
    Justin Thaler
    Tha23, paper

Milestones

  • The Knowledge Complexity of Interactive Proof-Systems (Invention of zero-knowledge)
    Shafi Goldwasser, Silvio Micali, and Charle Rackoff
    STOC 1985, paper, GMR85

  • On defining proofs of knowledge
    Bellare Mihir and Oded Goldreich
    CRYPTO 1992, paper, BG92

  • Algebraic methods for interactive proof systems
    Carsten Lund, Lance Fortnow, Howard Karloff, and Noam Nisan
    JACM 1992, paper, LFKN92

  • Efficient Identification and Signatures for Smart Cards
    Schnorr Claus-Peter
    CRYPTO 1989, paper, Sch89

  • Zero-knowledge from secure multiparty computation
    Yuval Ishai, Eyal Kushilevitz, Rafail Ostrovsky, and Amit Sahai
    STOC 2007, paper, IKOS07

  • Delegating computation: interactive proofs for muggles
    Shafi Goldwasser, Yael Tauman Kalai, and Guy N. Rothblum
    STOC 2008, paper, GKR08 older version, GKR08

  • Short Pairing-Based Non-Interactive Zero-Knowledge Arguments
    Groth Jens
    ASIACRYPT 2010, paper, Gro10

  • Quadratic Span Programs and Succinct NIZKs without PCPs
    Rosario Gennaro, Craig Gentry, Bryan Parno, and Mariana Raykova
    EUROCRYPT 2013, paper, GGPR13

  • On the Size of Pairing-Based Non-Interactive Arguments
    Groth Jens
    EUROCRYPT 2016, paper, Gro16

  • Bulletproofs: Short Proofs for Confidential Transactions and More
    Benedikt Bunz, Jonathan Bootle, Dan Boneh, Andrew Poelstra, Pieter Wuille, and Greg Maxwell
    S&P 2018, paper, BBB+18

  • Fast Reed-Solomon Interactive Oracle Proofs of Proximity
    Eli Ben-Sasson, Iddo Bentov, Ynon Horesh, and Michael Riabzev
    ICALP 2018, paper, BBHR18

  • Scalable Zero Knowledge with no Trusted Setup
    Eli Ben-Sasson, Iddo Bentov, Ynon Horesh, and Michael Riabzev
    CRYPTO 2019, paper, BBHR19

  • PLONK: Permutations over Lagrange-Bases for Oecumenical Noninteractive Arguments of Knowledge
    Ariel Gabizon, Zachary J. Williamson, and Oana Ciobotaru
    eprint 2019, paper, GWC19

  • Wolverine: Fast, Scalable, and Communication-Efficient Zero-Knowledge Proofs for Boolean and Arithmetic Circuits
    Chenkai Weng, Kang Yang, Jonathan Katz, and Xiao Wang
    S&P 2021, paper, WYK+21

  • Gemini: Elastic SNARKs for Diverse Environments
    Jonathan Bootle, Alessandro Chiesa, Yuncong Hu, and Michele Orrù
    EUROCRYPT 2022, paper, BCHO22

Specific ZKP

Traditional & simple relations (over logarithm)

  • Efficient Identification and Signatures for Smart Cards
    Claus-Peter Schnorr
    CRYPTO 1989, paper, Sch89

  • A Practical Zero-Knowledge Protocol Fitted to Security Microprocessor Minimizing Both Transmission and Memory
    Louis C. Guillou, and Jean-Jacques Quisquater
    EUROCRYPT 1988, paper, GQ88

  • Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols
    Ronald Cramer, Ivan Damgård, and Berry Schoenmakers
    CRYPTO 1994, paper, CDS94

  • Proof Systems for General Statements about Discrete Logarithms
    Jan Camenisch, and Markus Stadler
    ETH Zurich Report 1997, paper, CS97

  • Short Group Signatures
    Dan Boneh, Xavier Boyen, and Hovav Shacham
    CRYPTO 2004, paper, BBS04

  • Unifying Zero-Knowledge Proofs of Knowledge
    Maurer Ueli
    AFRICACRYPT 2009, paper, Mau09

  • Non-Interactive Composition of Sigma-Protocols via Share-Then-Hash
    Masayuki Abe, Miguel Ambrona, Andrej Bogdanov, Miyako Ohkubo, and Alon Rosen
    ASIACRYPT 2020, paper, AAB+20

  • Compressing Proofs of K-Out-Of-n Partial Knowledge
    Thomas Attema, Ronald Cramer, and Serge Fehr
    CRYPTO 2021, paper, ACF21

  • DAG-Sigma: A DAG-Based Sigma Protocol for Relations in CNF
    Gongxian Zeng, Junzuo Lai, Zhengan Huang, Yu Wang, and Zhiming Zheng
    ASIACRYPT 2022, paper, ZLH+22

  • Revisiting BBS Signatures
    Stefano Tessaro and Chenzhi Zhu
    EUROCRYPT 2023, paper, TZ23

Membership(Range) Proof

  • A Digital Signature Based on a Conventional Encryption Function
    Ralph C Merkle
    CRYPTO 1987, paper, Mer87

  • Statistical Zero Knowledge Protocols to Prove Modular Polynomial Relations
    Eiichiro Fujisaki, and Tatsuaki Okamoto
    CRYPTO 1997, paper, FO97

  • Efficient proofs that a committed number lies in an interval
    Fabrice Boudot
    EUROCRYPT 2000, paper, Bou00

  • Dynamic Accumulators and Application to Efficient Revocation of Anonymous Credentials
    Jan Camenisch and Anna Lysyanskaya
    CRYPTO 2002, paper, CL02

  • Accumulators from Bilinear Pairings and Applications to ID-Based Ring Signatures and Group Membership Revocation
    Nguyen Lan
    CT-RSA 2005, paper, Ngu05

  • Efficient Protocols for Set Membership and Range Proofs
    Jan Camenisch, Rafik Chaabouni, and abhi shelat
    ASIACRYPT 2008, paper, CCs08

  • An Accumulator Based on Bilinear Maps and Efficient Revocation for Anonymous Credentials
    Jan Camenisch, Markulf Kohlweiss, and Claudio Soriente
    PKC 2009, paper, CKS09

  • Bulletproofs: Short Proofs for Confidential Transactions and More
    Benedikt Bunz, Jonathan Bootle, Dan Boneh, Andrew Poelstra, Pieter Wuille, and Greg Maxwell
    S&P 2018, paper, BBB+18

  • Batching Techniques for Accumulators with Applications to IOPs and Stateless Blockchains
    Dan Boneh, Benedikt Bünz, and Ben Fisch
    CRYPTO 2019, paper, BBF19

  • Compressed $\varSigma$-Protocol Theory and Practical Application to Plug & Play Secure Algorithmics
    Thomas Attema, and Ronald Cramer
    CRYPTO 2020, paper, AC20

  • Caulk: Lookup Arguments in Sublinear Time
    Arantxa Zapico, Vitalik Buterin, Dmitry Khovratovich, Mary Maller, Anca Nitulescu, and Mark Simkin
    CCS21, paper, ZBK+21

  • Zero-Knowledge Proofs for Set Membership: Efficient, Succinct, Modular
    Daniel Benarroch, Matteo Campanelli, Dario Fiore, Kobi Gurkan, and Dimitris Kolonelos
    FC 2021, paper, BGF+21

  • Batching, Aggregation, and Zero-Knowledge Proofs in Bilinear Accumulators
    Shravan Srinivasan, Ioanna Karantaidou, Foteini Baldimtsi, and Charalampos Papamanthou
    CCS 2022, paper, SKB+22

  • Succinct Zero-Knowledge Batch Proofs for Set Accumulators
    Matteo Campanelli, Dario Fiore, Semin Han, Jihye Kim, Dimitris Kolonelos, and Hyunok Oh
    CCS 2022, paper, CFH+22

General purpose ZKP

Frameworks

  • Interactive Oracle Proofs
    Eli Ben-Sasson, Alessandro Chiesa, and Nicholas Spooner
    TCC 2016, paper, BCS16

  • Spartan: Efficient and General-Purpose ZkSNARKs Without Trusted Setup
    Srinath Setty
    CRYPTO 2020, paper, Set20

  • VOProof: Efficient ZkSNARKs from Vector Oracle Compilers
    Yuncong Zhang, Alan Szepeniec, Ren Zhang, Shi-Feng Sun, Geng Wang, and Dawu Gu
    CCS 2022, paper, ZSZ+22

with SRS(Structured Reference String), including ZKSNARK

Traditional SRS usually need trusted setup per curcuit.

  • Short Pairing-Based Non-Interactive Zero-Knowledge Arguments
    Groth Jens
    ASIACRYPT 2010, paper, Gro10

  • From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again
    Nir Bitansky, R. Canetti, A. Chiesa, and Eran Tromer
    ITCS 2012, paper, BCC+12

  • Quadratic Span Programs and Succinct NIZKs without PCPs
    Rosario Gennaro, Craig Gentry, Bryan Parno, and Mariana Raykova
    EUROCRYPT 2013, paper, GGPR13

  • Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture
    Eli Ben-Sasson, A. Chiesa, Eran Tromer, and M. Virza
    USENIX 2014, paper, BCT+14

  • On the Size of Pairing-Based Non-Interactive Arguments
    Groth Jens
    EUROCRYPT 2016, paper, Gro16

  • DIZK: A Distributed Zero Knowledge Proof System
    Howard Wu, Wenting Zheng, Alessandro Chiesa, Raluca Ada Popa, and Ion Stoica
    USENIX 2018, paper, WZC+18

  • Snarky Ceremonies
    Markulf Kohlweiss, Mary Maller, Janno Siim, and Mikhail Volkhov
    ASIACRYPT 2021, paper, KMS+21

with updatable universal SRS

Updatable universal SRS means that the same SRS by a trusted setup could be used for statements about all circuits of a certain bounded size.

  • Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updatable Structured Reference Strings
    Mary Maller, Sean Bowe, Markulf Kohlweiss, and Sarah Meiklejohn
    CCS 2019, paper, MBK+19

  • Marlin: Preprocessing ZkSNARKs with Universal and Updatable SRS
    Alessandro, Chiesa, Yuncong Hu, Mary Maller, Pratyush Mishra, Noah Vesely, and Nicholas Ward
    EUROCRYPT 2020, paper, CHM+20

  • PLONK: Permutations over Lagrange-Bases for Oecumenical Noninteractive Arguments of Knowledge
    Ariel Gabizon, Zachary J. Williamson, and Oana Ciobotaru
    eprint 2019, paper, GWC19

  • Libra: Succinct Zero-Knowledge Proofs with Optimal Prover Computation
    Tiancheng Xie, Jiaheng Zhang, Yupeng Zhang, Charalampos Papamanthou, and Dawn Song
    CRYPTO 2019, paper, XZZ+19

  • MIRAGE: Succinct Arguments for Randomized Algorithms with Applications to Universal Zk-SNARKs
    Ahmed Kosba, Dimitrios Papadopoulos, Charalampos Papamanthou, and Dawn Song
    USENIX Security 2020, paper, KPP+20

  • Lunar: A Toolbox for More Efficient Universal and Updatable ZkSNARKs and Commit-and-Prove Extensions
    Matteo Campanelli, Antonio Faonio, Dario Fiore, Anaïs Querol, and Hadrián Rodríguez
    ASIACRYPT 2021, paper, CFF+21

  • An Algebraic Framework for Universal and Updatable SNARKs
    Carla Ràfols, and Arantxa Zapico
    CRYPTO 2021, paper, RZ21

  • Counting Vampires: From Univariate Sumcheck to Updatable ZK-SNARK
    Helger Lipmaa, Janno Siim, and Michał Zając
    ASIACRYPT 2022, paper, LSZ22

  • HyperPlonk: Plonk with Linear-Time Prover and High-Degree Custom Gates
    Binyi Chen, Benedikt Bünz, Dan Boneh, and Zhenfei Zhang
    EUROCRYPT 2023, paper, CBB+23

with URS(Uniform Reference String), including ZKSTARK

Without trusted setup.

  • Ligero: Lightweight Sublinear Arguments Without a Trusted Setup
    Scott Ames, Carmit Hazay, Yuval Ishai, and Muthuramakrishnan Venkitasubramaniam
    CCS 2017, paper, AHI+17

  • Scalable Zero Knowledge with No Trusted Setup
    Eli Ben-Sasson, Iddo Bentov, Yinon Horesh, and Michael Riabzev
    CRYPTO 2019, paper, BBH+19

  • HALO: Recursive Proof Composition without a Trusted Setup
    Sean Bowe, J. Grigg, and Daira Hopwood
    eprint 2019, paper, BGH19

  • Aurora: Transparent Succinct Arguments for R1CS
    Eli Ben-Sasson, Alessandro Chiesa, Michael Riabzev, Nicholas Spooner, Madars Virza, and Nicholas P. Ward
    EUROCRYPT 2019, paper, BCR+19

  • DEEP-FRI: Sampling Outside the Box Improves Soundness
    Eli Ben-Sasson, Lior Goldberg, Swastik Kopparty, and Shubhangi Saraf
    arXiv 2019, paper, BGKS19

  • Ligero++: A New Optimized Sublinear IOP
    Rishabh Bhadauria, Zhiyong Fang, Carmit Hazay, Muthuramakrishnan Venkitasubramaniam, Tiancheng Xie, and Yupeng Zhang
    CCS 2020, paper, BFH+20

  • Fractal: Post-Quantum and Transparent Recursive Proofs from Holography
    Alessandro Chiesa, Dev Ojha, and Nicholas Spooner
    EUROCRYPT 2020, paper, COS20

  • Transparent Polynomial Delegation and Its Applications to Zero Knowledge Proof
    Jiaheng Zhang, Tiancheng Xie, Yupeng Zhang, and Dawn Song
    S&P 2020, paper, ZXZ+20

  • Sumcheck Arguments and Their Applications
    Jonathan Bootle, Alessandro Chiesa, and Katerina Sotiraki
    CRYPTO 2021, paper, BCS21

  • Doubly Efficient Interactive Proofs for General Arithmetic Circuits with Linear Prover Time
    Jiaheng Zhang, Tianyi Liu, Weijie Wang, Yinuo Zhang, Dawn Song, and Xiang Xie
    CCS 2021, paper, ZLW+21

  • RedShift: Transparent SNARKs from List Polynomial Commitments
    Assimakis A. Kattis, Konstantin Panarin, and Alexander Vlasov
    CCS 2022, paper, KPV22

  • Flashproofs: Efficient Zero-Knowledge Arguments of Range and Polynomial Evaluation with Transparent Setup
    Nan Wang, and Sid Chi-Kin Chau
    ASIACRYPT 2022, paper, WC22

  • Linear-Time Arguments with Sublinear Verification from Tensor Codes
    Jonathan Bootle, Alessandro Chiesa, and Jens Groth
    TCC 2020, paper, BCG20

  • Orion: Zero Knowledge Proof with Linear Prover Time
    Tiancheng Xie, Yupeng Zhang, and Dawn Song
    CRYPTO 2022, paper, XZS22

  • Dew: Transparent Constant-sized zkSNARKs
    Arasu Arun, Chaya Ganesh, Satya Lokam, Tushar Mopuri, and Sriram Sridhar
    PKC 2023, paper, AGL+23

DL-based

  • Efficient Zero-Knowledge Arguments for Arithmetic Circuits in the Discrete Log Setting
    Jonathan Bootle, Andrea Cerulli, Pyrros Chaidos, Jens Groth, and Christophe Petit
    EUROCRYPT 2016, paper, BCC+16

  • Doubly-Efficient ZkSNARKs Without Trusted Setup
    Riad S. Wahby, Ioanna Tzialla, Abhi Shelat, Justin Thaler, and Michael Walfish
    SP 2018, paper, WTS+18

  • Bulletproofs: Short Proofs for Confidential Transactions and More
    Benedikt Bunz, Jonathan Bootle, Dan Boneh, Andrew Poelstra, Pieter Wuille, and Greg Maxwell
    S&P 2018, paper, BBB+18

  • Non-Interactive Zero-Knowledge Proofs for Composite Statements
    Shashank Agrawal, Chaya Ganesh, and Payman Mohassel
    CRYPTO 2018, paper, AGM18

  • Shorter Non-Interactive Zero-Knowledge Arguments and ZAPs for Algebraic Languages
    Geoffroy Couteau, and Dominik Hartmann
    CRYPTO 2020, paper, CH20

  • Compressed $\varSigma$-Protocol Theory and Practical Application to Plug & Play Secure Algorithmics
    Thomas Attema, and Ronald Cramer
    CRYPTO 2020, paper, AC20

  • Compressed $\varSigma$-Protocols for Bilinear Group Arithmetic Circuits and Application to Logarithmic Transparent Threshold Signatures
    Thomas Attema, Ronald Cramer, and Matthieu Rambaud
    ASIACRYPT 2021, paper, ACR21

  • Halo Infinite: Proof-Carrying Data from Additive Polynomial Commitments
    Dan Boneh, Justin Drake, Ben Fisch, and Ariel Gabizon
    CRYPTO 2021, paper, BDF+21

  • Efficient NIZKs for Algebraic Sets
    Geoffroy Couteau, Helger Lipmaa, Roberto Parisella, and Arne Tobias Ødegaard
    ASIACRYPT 2021, paper, CLP+21

  • ECLIPSE: Enhanced Compiling Method for Pedersen-Committed ZkSNARK Engines
    Diego F. Aranha, Emil Madsen Bennedsen, Matteo Campanelli, Chaya Ganesh, Claudio Orlandi, and Akira Takahashi
    PKC 2022, paper, ABC+22

MPC-in-the-head-based

  • Zero-knowledge from secure multiparty computation
    Yuval Ishai, Eyal Kushilevitz, Rafail Ostrovsky, and Amit Sahai
    STOC 2007, paper, IKOS07

  • Zkboo: Faster zero-knowledge for boolean circuits
    Irene Giacomelli, Jesper Madsen, and Claudio Orlandi
    USENIX 2016, paper, GMO16

  • Post-quantum zero-knowledge and signatures from symmetric-key primitives
    Melissa Chase, David Derler, Steven Goldfeder, Claudio Orlandi, Sebastian Ramacher, Christian Rechberger, Daniel Slamanig, and Greg Zaverucha
    CCS 2017, paper, CDG+17

  • Ligero: Lightweight sublinear arguments without a trusted setup
    Scott Ames, Carmit Hazay, Yuval Ishai, and Muthuramakrishnan Venkitasubramaniam
    CCS 2017, paper, AHIV17

  • Improved non-interactive zero knowledge with applications to post-quantum signatures
    Jonathan Katz, Vladimir Kolesnikov, and Xiao Wang
    CCS 2018, paper, KKW18

  • Concretely-efficient zero-knowledge arguments for arithmetic circuits and their application to lattice-based cryptography
    Carsten Baum and Ariel Nof
    PKC 2020, paper, BN20

  • Limbo: Efficient zero-knowledge MPCitH-based arguments
    Cyprien de Saint Guilhem, Emmanuela Orsini, and Titouan Tanguy
    CCS 2021, paper, dOT21

VOLE-based (Commit-and-prove type)

  • Appenzeller to Brie: Efficient Zero-Knowledge Proofs for Mixed-Mode Arithmetic and Z2k
    Carsten Baum, Lennart Braun, Alexander Munch-Hansen, Benoit Razet, and Peter Scholl
    CCS 2021, paper, BBM+21

  • $\mathsf{Mac’n’Cheese}$: Zero-Knowledge Proofs for Boolean and Arithmetic Circuits with Nested Disjunctions
    Carsten Baum, Alex J. Malozemoff, Marc B. Rosen, and Peter Scholl
    CRYPTO 2021, paper, BMR+21

  • Line-Point Zero Knowledge and Its Applications
    Samuel Dittmer, Yuval Ishai, and Rafail Ostrovsky
    ITC 2021, paper, DIO21

  • Wolverine: Fast, Scalable, and Communication-Efficient Zero-Knowledge Proofs for Boolean and Arithmetic Circuits
    Chenkai Weng, Kang Yang, Jonathan Katz, and Xiao Wang
    S&P 2021, paper, WYK+21

  • QuickSilver: Efficient and Affordable Zero-Knowledge Proofs for Circuits and Polynomials over Any Field
    Kang Yang, Pratik Sarkar, Chenkai Weng, and Xiao Wang
    CCS 2021, paper, YSW+21

  • Mystique: Efficient Conversions for Zero-Knowledge Proofs with Applications to Machine Learning
    Chenkai Weng, Kang Yang, Xiang Xie, Jonathan Katz, and Xiao Wang
    USENIX 2021. paper, WYX+21

  • Improving Line-Point Zero Knowledge: Two Multiplications for the Price of One
    Samuel Dittmer, Yuval Ishai, Steve Lu, and Rafail Ostrovsky
    CCS 2022, paper, DIL+22

  • AntMan: Interactive Zero-Knowledge Proofs with Sublinear Communication
    Chenkai Weng, Kang Yang, Zhaomin Yang, Xiang Xie, and Xiao Wang
    CCS 2022, paper, WYY+22

Applications on ZKP systems

Here just list several interesting applicaitons.

  • Prio: Private, Robust, and Scalable Computation of Aggregate Statistics
    Henry Corrigan-Gibbs and Dan Boneh
    USENIX 2017, paper

  • Scaling Verifiable Computation Using Efficient Set Accumulators
    Alex Ozdemir, Riad S Wahby, Barry Whitehat, and Dan Boneh
    USENIX 2020, paper, OWW+20

  • Efficient Zero-Knowledge Proofs on Signed Data with Applications to Verifiable Computation on Data Streams
    Dario Fiore, and Ida Tucker
    CCS 2022, paper, FT22

For Machine Learning(Federated Learning)

  • Zero Knowledge Proofs for Decision Tree Predictions and Accuracy
    Jiaheng Zhang, Zhiyong Fang, Yupeng Zhang, and Dawn Song
    CCS 2020. paper, ZFZ+20

  • ZkCNN: Zero Knowledge Proofs for Convolutional Neural Network Predictions and Accuracy
    Tianyi Liu, Xiang Xie, and Yupeng Zhang
    CCS 2021, paper, LXZ21

  • Mystique: Efficient Conversions for Zero-Knowledge Proofs with Applications to Machine Learning
    Chenkai Weng, Kang Yang, Xiang Xie, Jonathan Katz, and Xiao Wang
    USENIX 2021. paper, WYX+21

For Web3(Authentication)

  • Constant-Size Dynamic k-TAA
    Man Ho Au, Willy Susilo, and Yi Mu
    SCN06, paper, ASM06

  • Anonymous Credentials Light
    Foteini Baldimtsi, and Anna Lysyanskaya
    CCS 2013, paper, BL13

  • Anonymous Attestation Using the Strong Diffie Hellman Assumption Revisited
    Jan Camenisch, Manu Drijvers, and Anja Lehmann
    Trust and Trustworthy Computing 2016, paper, CDL16

  • DECO: Liberating Web Data Using Decentralized Oracles for Threshold
    Fan Zhang, Sai Krishna Deepak Maram, Harjasleen Malvai, Steven Goldfeder, and Ari Juels
    CCS 2020, paper, ZMM+20

  • Zero-Knowledge Middleboxes
    Paul Grubbs, Arasu Arun, Ye Zhang, Joseph Bonneau, and Michael Walfish
    USENIX 2022, paper, GAZ+22

  • Zk-Creds: Flexible Anonymous Credentials from ZkSNARKs and Existing Identity Infrastructure
    Michael Rosenberg, Jacob White, Christina Garman, and Ian Miers
    S&P 2023, paper, RWG+23

For Blockchains

  • Zerocash: Decentralized Anonymous Payments from Bitcoin
    Ben Sasson, Eli, Alessandro Chiesa, Christina Garman, Matthew Green, Ian Miers, Eran Tromer, and Madars Virza
    S&P 2014, paper, BCG+14

  • ZeeStar: Private Smart Contracts by Homomorphic Encryption and Zero-Knowledge Proofs
    Samuel Steffen, Benjamin Bichsel, Roger Baumgartner, and Martin Vechev
    S&P 2022, paper, SBB+22

Signature from ZKP

  • Post-quantum zero-knowledge and signatures from symmetric-key primitives
    Melissa Chase, David Derler, Steven Goldfeder, Claudio Orlandi, Sebastian Ramacher, Christian Rechberger, Daniel Slamanig, and Greg Zaverucha
    CCS 2017, paper, CDG+17

  • Improved non-interactive zero knowledge with applications to post-quantum signatures
    Jonathan Katz, Vladimir Kolesnikov, and Xiao Wang
    CCS 2018, paper, KKW18

  • BBQ: Using AES in picnic signatures
    Cyprien de Saint Guilhem, Lauren De Meyer, Emmanuela Orsini, and Nigel P. Smart
    SAC 2019, paper, dDOS19

  • Improving the Performance of the Picnic Signature Scheme
    Daniel Kales and Greg Zaverucha
    TCHES20, paper, The picnic signature scheme, design document v2.1, KZ20

  • Banquet: Short and fast signatures from AES
    Carsten Baum, Cyprien de Saint Guilhem, Daniel Kales, Emmanuela Orsini, Peter Scholl, and Greg Zaverucha
    PKC 2021, paper, BdK+21

  • Limbo: Efficient zero-knowledge MPCitH-based arguments
    Cyprien de Saint Guilhem, Emmanuela Orsini, and Titouan Tanguy
    CCS 2021, paper, dOT21

  • Shorter signatures based on tailor-made minimalist symmetric-key crypto
    Christoph Dobraunig, Daniel Kales, Christian Rechberger, Markus Schofnegger, and Greg Zaverucha
    CCS 2022, paper, DKR+21

ZKP Standard Efforts

  • RFC: Schnorr Non-Interactive Zero-Knowledge Proof
    Hao, Feng
    IETF rfc8235, paper, Hao21

Below are from organization zkproof:

ZKProof is an open-industry academic initiative that seeks to mainstream zero-knowledge proof (ZKP) cryptography through an inclusive, community-driven standardization process that focuses on interoperability and security.

  • Proposal: Commit-and-Prove Zero-Knowledge Proof Systems and Extensions
    Daniel Benarroch, Matteo Campanelli, Dario Fiore, Jihye Kim, Jiwon Lee, Hyunok Oh, and Anaıs Querol
    ZKProof 2,3,4th workshop, paper, BCF+21

  • Rinocchio: SNARKs for Ring Arithmetic
    Ganesh, Chaya, Anca Nitulescu, and Eduardo Soria-Vazquez
    ZKProof 4th workshop, 2021, paper, CNS21

  • Zk-Proof Community——Proposal: Σ-Protocols
    Stephan Krenn and Michele Orrù
    ZKProof 4th workshop, 2021, paper, KO21

  • See more at zkproof proposals.