SNARKs for C: Verifying Program Executions Succinctly and in Zero Knowledge

A note on two problems in connexion with graphs

Dijkstra, E. (1959) · Numerische Mathematik · doi:10.1007/bf01386390 · Cited by 24,351 · see citing works

How to play ANY mental game

Goldreich, O., Micali, S., & Wigderson, A. (1987) · Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87 · doi:10.1145/28395.28420 · Cited by 3,590 · see citing works

Completeness theorems for non-cryptographic fault-tolerant distributed computation

Ben-Or, M., & Wigderson, A. (1988) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/62212.62213 · Cited by 2,529 · see citing works

Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes

Leighton, F. T. (1991) · CERN Document Server (European Organization for Nuclear Research) · Cited by 2,467 · see citing works

Minimum disclosure proofs of knowledge

Gilles Brassard, A., Chaum, D., & Crépeau, C. (1988) · Journal of Computer and System Sciences · doi:10.1016/0022-0000(88)90005-0 · Cited by 954 · see citing works

Mathematical Theory of Connecting Networks and Telephone Traffic

Mullin, A. A., & Beneš, V. (1966) · Mathematics of Computation · doi:10.2307/2003526 · Cited by 814 · see citing works

Fairplay—a secure two-party computation system

Malkhi, D., Nisan, N., Benny Pinkas, B., & Sella, Y. (2004) · Cited by 791 · see citing works

Quadratic Span Programs and Succinct NIZKs without PCPs

Gennaro, R., Gentry, C., Parno, B. J., & Raykova, M. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-38348-9_37 · Cited by 751 · see citing works

Checking computations in polylogarithmic time

Babai, L., Fortnow, L., Levin, L. A., & Szegedy, M. (1991) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/103418.103428 · Cited by 627 · see citing works

A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves

Frey, G., & Rück, H.-G. (1994) · Mathematics of Computation · doi:10.2307/2153546 · Cited by 553 · see citing works

The PCP theorem by gap amplification

Dinur, I. (2006) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/1132516.1132553 · Cited by 506 · see citing works

From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again

Bitansky, N., Canetti, R., Chiesa, A., & Tromer, E. (2012) · Proceedings of the 3rd Innovations in Theoretical Computer Science Conference · doi:10.1145/2090236.2090263 · Cited by 493 · see citing works

FairplayMP

Ben-David, A., Nisan, N., & Pinkas, B. (2008) · Proceedings of the ACM Conference on Computer and Communications Security · doi:10.1145/1455770.1455804 · Cited by 481 · see citing works

A Taxonomy of Pairing-Friendly Elliptic Curves

Freeman, D. M., Scott, M., & Teske, E. (2009) · Journal of Cryptology · doi:10.1007/s00145-009-9048-z · Cited by 469 · see citing works

Short Pairing-Based Non-interactive Zero-Knowledge Arguments

Groth, J. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-17373-8_19 · Cited by 454 · see citing works

A Permutation Network

Waksman, A. (1968) · Journal of the ACM · doi:10.1145/321439.321449 · Cited by 448 · see citing works

Computationally sound proofs

Micali, S. (2000) · SIAM Journal on Computing · doi:10.1137/s0097539795284959 · Cited by 424 · see citing works

Simulation-Sound NIZK Proofs for a Practical Language and Constant Size Group Signatures

Groth, J. (2006) · Lecture notes in computer science · doi:10.1007/11935230_29 · Cited by 390 · see citing works

Perfect Non-interactive Zero Knowledge for NP

Groth, J., Ostrovsky, R., & Sahai, A. (2006) · Lecture notes in computer science · doi:10.1007/11761679_21 · Cited by 381 · see citing works

Does co-NP have short interactive proofs?

Boppana, R. B., Håstad, J., & Zachos, S. (1987) · Information Processing Letters · doi:10.1016/0020-0190(87)90232-8 · Cited by 365 · see citing works

Towards Practical Public Key Systems Secure Against Chosen Ciphertext attacks

Damgård, I. (2007) · Springer eBooks · doi:10.1007/3-540-46766-1_36 · Cited by 358 · see citing works

Recursive composition and bootstrapping for SNARKS and proof-carrying data

Bitansky, N., Canetti, R., Chiesa, A., & Tromer, E. (2013) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/2488608.2488623 · Cited by 305 · see citing works

Succinct Non-interactive Arguments via Linear Interactive Proofs

Bitansky, N., Chiesa, A., Ishai, Y., Paneth, O., & Ostrovsky, R. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-36594-2_18 · Cited by 285 · see citing works

Randomizable Proofs and Delegatable Anonymous Credentials

Belenkiy, M., Camenisch, J. L., Chase, M., et al. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-03356-8_7 · Cited by 271 · see citing works

On a Class of Rearrangeable Switching Networks Part I: Control Algorithm

Opferman, D. C., & Tsao-Wu, N. T. (1971) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1971.tb02569.x · Cited by 253 · see citing works

Compact Group Signatures Without Random Oracles

Boyen, X., & Waters, B. R. (2006) · Lecture notes in computer science · doi:10.1007/11761679_26 · Cited by 252 · see citing works

Universal Arguments and their Applications

Barak, B., & Goldreich, O. (2003) · Proceedings - IEEE Conference on Computational Complexity/Proceedings · doi:10.1109/ccc.2002.1004355 · Cited by 244 · see citing works

Space-time tradeoffs for approximate nearest neighbor searching

Arya, S., Malamatos, T., & Mount, D. M. (2009) · Journal of the ACM · doi:10.1145/1613676.1613677 · Cited by 243 · see citing works

The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems

Frey, G., Muller, M., & Rück, H.-G. (1999) · IEEE Transactions on Information Theory · doi:10.1109/18.771254 · Cited by 243 · see citing works

The Knowledge-of-Exponent Assumptions and 3-Round Zero-Knowledge Protocols

Bellare, M., & Palacio, A. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-28628-8_17 · Cited by 236 · see citing works

Progression-Free Sets and Sublinear Pairing-Based Non-Interactive Zero-Knowledge Arguments

Lipmaa, H. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-28914-9_10 · Cited by 223 · see citing works

P-signatures and Noninteractive Anonymous Credentials

Belenkiy, M., Chase, M., Kohlweiss, M., et al. (2008) · Springer eBooks · doi:10.1007/978-3-540-78524-8_20 · Cited by 208 · see citing works

Non-interactive Zaps and New Techniques for NIZK

Groth, J., Ostrovsky, R., & Sahai, A. (2006) · Lecture notes in computer science · doi:10.1007/11818175_6 · Cited by 190 · see citing works

Two Query PCP with Sub-Constant Error

Moshkovitz, D., & Raz, R. (2008) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2008.60 · Cited by 186 · see citing works

On the existence of 3-round zero-knowledge protocols

Hada, S., & Tanaka, T. (1998) · Lecture notes in computer science · doi:10.1007/bfb0055744 · Cited by 176 · see citing works

Parallel Algorithms to Set Up the Benes Permutation Network

Nassimi, & Sahni (1982) · IEEE Transactions on Computers · doi:10.1109/tc.1982.1675960 · Cited by 159 · see citing works

Addition Chain Heuristics

Bos, J., & Coster, M. J. (2007) · Springer eBooks · doi:10.1007/0-387-34805-0_37 · Cited by 149 · see citing works

Short PCPs with Polylog Query Complexity

Ben‐Sasson, E., & Sudan, M. (2008) · SIAM Journal on Computing · doi:10.1137/050646445 · Cited by 148 · see citing works

Non-interactive Zero-Knowledge Arguments for Voting

Groth, J. (2005) · Lecture notes in computer science · doi:10.1007/11496137_32 · Cited by 145 · see citing works

Twisted Edwards Curves

Bernstein, D. J., Birkner, P., Jóye, M., et al. (2008) · Cited by 143 · see citing works

Linear Statistical Weakness of Alleged RC4 Keystream Generator

Golić, J. D. (1997) · Lecture notes in computer science · doi:10.1007/3-540-69053-0_16 · Cited by 133 · see citing works

Secure Two-Party Computation with Low Communication

Damgård, I., Faust, S., & Hazay, C. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-28914-9_4 · Cited by 119 · see citing works

Perfect NIZK with Adaptive Soundness

Abe, M., & Fehr, S. (2007) · Springer eBooks · doi:10.1007/978-3-540-70936-7_7 · Cited by 109 · see citing works

Fast probabilistic algorithms for hamiltonian circuits and matchings

Angluin, D., & Valiant, L. G. (1977) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/800105.803393 · Cited by 107 · see citing works

Linear Algebra with Sub-linear Zero-Knowledge Arguments

Groth, J. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-03356-8_12 · Cited by 106 · see citing works

Malleable Proof Systems and Applications

Chase, M., Kohlweiss, M., Lysyanskaya, A., et al. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-29011-4_18 · Cited by 104 · see citing works

Nearly linear time

Gurevich, Y. G., & Shelah, S. (1989) · Lecture notes in computer science · doi:10.1007/3-540-51237-3_10 · Cited by 94 · see citing works

Short PCPs Verifiable in Polylogarithmic Time

Ben‐Sasson, E., Goldreich, O., Harsha, P., et al. (2005) · Proceedings - IEEE Conference on Computational Complexity/Proceedings · doi:10.1109/ccc.2005.27 · Cited by 94 · see citing works

Mathematical Theory of Connecting Networks and Telephone Traffic

(1965) · Mathematics in Science and Engineering/Mathematics in science and engineering · doi:10.1016/s0076-5392(08)x6142-9 · Cited by 94 · see citing works

Ordinary abelian varieties having small embedding degree

Galbraith⋆, S. D., McKee, J., & Valença, P. C. (2007) · Finite Fields and Their Applications · doi:10.1016/j.ffa.2007.02.003 · Cited by 87 · see citing works

On interactive proofs with a laconic prover

Goldreich, O., Vadhan, S., & Wigderson, A. (2002) · Computational Complexity · doi:10.1007/s00037-002-0169-0 · Cited by 87 · see citing works

On the complexity of interactive proofs with bounded communication

Goldreich, O., & Håstad, J. (1998) · Information Processing Letters · doi:10.1016/s0020-0190(98)00116-1 · Cited by 86 · see citing works

Satisfiability Is Quasilinear Complete in NQL

Schnorr, C. P. (1978) · Journal of the ACM · doi:10.1145/322047.322060 · Cited by 82 · see citing works

Delegation of Computation without Rejection Problem from Designated Verifier CS-Proofs.

Goldwasser, S., Lin, H., & Rubinstein, A. (2011) · Cited by 77 · see citing works

Fast reductions from RAMs to delegatable succinct constraint satisfaction problems

Ben‐Sasson, E., Chiesa, A., Genkin, D., et al. (2013) · Conference on Innovations in Theoretical Computer Science · doi:10.1145/2422436.2422481 · Cited by 71 · see citing works

Cryptographic Counters and Applications to Electronic Voting

Katz, J. I., Myers, S., & Ostrovsky, R. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44987-6_6 · Cited by 61 · see citing works

Short Non-interactive Zero-Knowledge Proofs

Groth, J. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-17373-8_20 · Cited by 61 · see citing works

On the concrete efficiency of probabilistically-checkable proofs

Ben‐Sasson, E., Chiesa, A., Genkin, D., & Tromer, E. (2013) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/2488608.2488681 · Cited by 61 · see citing works

Time-bounded random access machines

Cook, S. A., & Reckhow, R. A. (1972) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/800152.804898 · Cited by 60 · see citing works

Succinct Arguments from Multi-prover Interactive Proofs and Their Efficiency Benefits

Bitansky, N., & Chiesa, A. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-32009-5_16 · Cited by 54 · see citing works

Proof-Carrying Data and Hearsay Arguments from Signature Cards.

Chiesa, A., & Tromer, E. (2010) · Cited by 44 · see citing works

Full proof cryptography

Almeida, J. B., Barbosa, M., Bangerter, E., Barthe, G., Krenn, S., & Zanella-Béguelin, S. (2012) · ACM SIGSAC Conference on Computer and Communications Security (CCS) · doi:10.1145/2382196.2382249 · Cited by 38 · see citing works

Fast Reductions from RAMs to Delegatable Succinct Constraint Satisfaction Problems.Preprint

Ben‐Sasson, E., Chiesa, A., Genkin, D., et al. (2012) · IACR Cryptology ePrint Archive · Cited by 35 · see citing works

On Round-Efficient Argument Systems

Wee, H. (2005) · Lecture notes in computer science · doi:10.1007/11523468_12 · Cited by 34 · see citing works

An O(T log T) reduction from RAM computations to satisfiability

Robson, J. M. (1991) · Theoretical Computer Science · doi:10.1016/0304-3975(91)90177-4 · Cited by 34 · see citing works

NP-completeness of the hamming salesman problem

Ernvall, J., Katajainen, J., & Penttonen, M. (1985) · BIT Numerical Mathematics · doi:10.1007/bf01935007 · Cited by 34 · see citing works

Bringing Zero-Knowledge Proofs of Knowledge to Practice

Bangerter, E., Barzan, S., Krenn, S., et al. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-36213-2_9 · Cited by 12 · see citing works

Bringing Zero-Knowledge Proofs of Knowledge to Practice

Krenn, S. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-36213-2_10 · Cited by 10 · see citing works

Two Simple Code-Verification Voting Protocols.

Lipmaa, H. (2011) · Cited by 9 · see citing works

On the Size of Pairing-Based Non-interactive Arguments

Groth, J. (2016) · Lecture Notes in Computer Science · doi:10.1007/978-3-662-49896-5_11 · Cited by 1,271 · see citing works

Bulletproofs: Short Proofs for Confidential Transactions and More

Bunz, B., Bootle, J., Boneh, D., Poelstra, A., Wuille, P., & Maxwell, G. (2018) · 2018 IEEE Symposium on Security and Privacy (SP) · doi:10.1109/sp.2018.00020 · Cited by 1,154 · see citing works

Privacy-Preserving Solutions for Blockchain: Review and Challenges

Bernal Bernabe, J., Canovas, J. L., Hernandez-Ramos, J. L., Torres Moreno, R., & Skarmeta, A. (2019) · IEEE Access · doi:10.1109/access.2019.2950872 · Cited by 430 · see citing works

Security, Performance, and Applications of Smart Contracts: A Systematic Survey

Rouhani, S., & Deters, R. (2019) · IEEE Access · doi:10.1109/access.2019.2911031 · Cited by 309 · see citing works

Doubly-Efficient zkSNARKs Without Trusted Setup

Wahby, R. S., Tzialla, I., Shelat, A., Thaler, J., & Walfish, M. (2018) · 2018 IEEE Symposium on Security and Privacy (SP) · doi:10.1109/sp.2018.00060 · Cited by 276 · see citing works

ZebraLancer: Private and Anonymous Crowdsourcing System atop Open Blockchain

Lu, Y., Tang, Q., & Wang, G. (2018) · 2018 IEEE 38th International Conference on Distributed Computing Systems (ICDCS) · doi:10.1109/icdcs.2018.00087 · Cited by 224 · see citing works

zkCrowd: a hybrid blockchain-based crowdsourcing platform

Zhu, S., Cai, Z., Hu, H., Li, Y., & Li, W. (2020) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2019.2941735 · Cited by 206 · see citing works

A Survey of Self-Sovereign Identity Ecosystem

Soltani, R., Nguyen, U. T., & An, A. (2021) · Security and Communication Networks · doi:10.1155/2021/8873429 · Cited by 131 · see citing works

reclaimID: Secure, Self-Sovereign Identities Using Name Systems and Attribute-Based Encryption

Schanzenbach, M., Bramm, G., & Schutte, J. (2018) · 2018 17th IEEE International Conference On Trust, Security And Privacy In Computing And Communications/ 12th IEEE International Conference On Big Data Science And Engineering (TrustCom/BigDataSE) · doi:10.1109/trustcom/bigdatase.2018.00134 · Cited by 36 · see citing works

Outlining Traceability: A Principle for Operationalizing Accountability in Computing Systems

Kroll, J. A. (2021) · Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency · doi:10.1145/3442188.3445937 · Cited by 2 · see citing works

Zero-knowledge proofs of knowledge without interaction

Santis, A. D., & Persiano, G. (1992) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1992.267809 · Cited by 162 · see citing works

Comparative study of diverse zero-knowledge argument systems

Kuriakose, J., Sisodia, P. S., Amruth, V., et al. (2016) · doi:10.1109/sapience.2016.7684134 · Cited by 2 · see citing works

Efficient card-based zero-knowledge proof for Sudoku

Sasaki, T., Miyahara, D., Mizuki, T., et al. (2020) · Theoretical Computer Science · doi:10.1016/j.tcs.2020.05.036 · Cited by 71 · see citing works

Zero-Knowledge Proofs of Knowledge Without Interaction (Extended Abstract)

Santis, A. D., & Persiano, G. (1992) · Cited by 46 · see citing works

Card-Based Zero-Knowledge Proof for Sudoku

Sasaki, T., Mizuki, T., & Sone, H. (2018) · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · doi:10.4230/lipics.fun.2018.29 · Cited by 22 · see citing works