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Bulletproofs: Short Proofs for Confidential Transactions and More
Open accessAbstract
We propose Bulletproofs, a new non-interactive zero-knowledge proof protocol with very short proofs and without a trusted setup; the proof size is only logarithmic in the witness size. Bulletproofs are especially well suited for efficient range proofs on committed values: they enable proving that a committed value is in a range using only 2 log_2(n)+9 group and field elements, where n is the bit length of the range. Proof generation and verification times are linear in n. Bulletproofs greatly improve on the linear (in n) sized range proofs in existing proposals for confidential transactions in Bitcoin and other cryptocurrencies. Moreover, Bulletproofs supports aggregation of range proofs, so that a party can prove that m commitments lie in a given range by providing only an additive O(log(m)) group elements over the length of a single proof. To aggregate proofs from multiple parties, we enable the parties to generate a single proof without revealing their inputs to each other via a simple multi-party computation (MPC) protocol for constructing Bulletproofs. This MPC protocol uses either a constant number of rounds and linear communication, or a logarithmic number of rounds and logarithmic communication. We show that verification time, while asymptotically linear, is very efficient in practice. The marginal cost of batch verifying 32 aggregated range proofs is less than the cost of verifying 32 ECDSA signatures. Bulletproofs build on the techniques of Bootle et al. (EUROCRYPT 2016). Beyond range proofs, Bulletproofs provide short zero-knowledge proofs for general arithmetic circuits while only relying on the discrete logarithm assumption and without requiring a trusted setup. We discuss many applications that would benefit from Bulletproofs, primarily in the area of cryptocurrencies. The efficiency of Bulletproofs is particularly well suited for the distributed and trustless nature of blockchains. The full version of this article is available on ePrint.
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“The B ulletproofs p rotocol by B¨ unz et al. [130] has contributed significantly to the progress of ZKP.”
From A Survey of Self-Sovereign Identity Ecosystem (2021) · cites this paper as [130]
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“In this sense, Key-Policy Attribute-Based Encryption (KP-ABE) [129] or Ciphertext-Policy Attribute-Based Encryption (CP-ABE) [130], which allows to de ne access control policies in the encryption itself, allows that only the users with the right attributes can decrypt the data.”
From Privacy-Preserving Solutions for Blockchain: Review and Challenges (2019) · cites this paper as [130]
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Items 601–700 of 1,000
A Trusted Privacy-Preserving Model for Cross-Chain Transactions Based on zk_SNARKs
Wang, Y., Tie, J., Hei, X., Li, Z., & Zhang, X. (2023) · International Conference on Networking and Network Applications (NaNA) · doi:10.1109/nana60121.2023.00039 · Cited by 4
“Moreover, BulletProof [13] is an efficient zero-knowledge proof and range proof that does not use trusted settings, and Monero [14] uses it as a range proof to reduce transaction costs and transaction sizes.”
BackgroundzkHealthChain - Blockchain Enabled Supply Chain in Healthcare Using Zero Knowledge
Nithin, G. N., Pradhan, A. K., & Swain, G. (2023) · IFIP advances in information and communication technology · doi:10.1007/978-3-031-45882-8_10 · Cited by 4
A Holistic Security Analysis of Monero Transactions
Cremers, C. J. F., Loss, J., & Wagner, B. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-58734-4_5 · Cited by 4
Invisible Warning Line: Efficient and Generic Regulation for Anonymous Cryptocurrencies
Gao, R. H., Wan, Z., Wang, H., & Luo, S. (2024) · IEEE Transactions on Dependable and Secure Computing · doi:10.1109/tdsc.2024.3475391 · Cited by 4
Somewhere Statistically Binding Commitment Schemes with Applications
Fauzi, P., Lipmaa, H., Pindado, Z., & Siim, J. (2021) · Lecture notes in computer science · doi:10.1007/978-3-662-64322-8_21 · Cited by 4
Practical Verifiable Computation by Using a Hardware-Based Correct Execution Environment
Lee, J., Nicopoulos, C. A., Jeong, G., Kim, J., & Oh, H. (2020) · IEEE Access · doi:10.1109/access.2020.3041308 · Cited by 4
“Bulletproof [8] efficiently reduces the proof size logarithmically with the circuit size, by optimizing inner product operations.”
BackgroundNon-malleable Vector Commitments via Local Equivocability
Rotem, L., & Segev, G. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-90456-2_14 · Cited by 4
CBOL: Cross-Bank Over-Loan Prevention, Revisited
Hu, X., Zhao, H., Zheng, S., & Wang, L. (2020) · Entropy · doi:10.3390/e22060619 · Cited by 4
Seet, J., & Griffin, P. (2019) · IEEE Asia-Pacific Conference on Computer Science and Data Engineering (CSDE) · doi:10.1109/csde48274.2019.9162386 · Cited by 4
Xu, S., Cai, X., Zhao, Y., Ren, Z., Wu, L., Zhang, H., Du, L., & Tong, Y. (2020) · IEEE International Conference on Trust, Security and Privacy in Computing and Communications (TrustCom) · doi:10.1109/trustcom50675.2020.00092 · Cited by 4
Forward-Secure Multi-User Aggregate Signatures Based on zk-SNARKs
Lee, J., Kim, J., & Oh, H. (2021) · IEEE Access · doi:10.1109/access.2021.3093925 · Cited by 4
“In our construction, any kind of simulation extractable zk-SNARK from the pre-processing SNARKs such as GM17 [25], and KLO20 [30] to universal structured reference string based SNARKs such as MBKM19 [31], GWC19 [32], and BBB + 18 [33] can be utilized as a building block.”
BackgroundMethodCRSA: A Cryptocurrency Recovery Scheme Based on Hidden Assistance Relationships
Dai, W., Lv, Y., Choo, K. R., Liu, Z., Zou, D., & Jin, H. (2021) · IEEE Transactions on Information Forensics and Security · doi:10.1109/tifs.2021.3104142 · Cited by 4
Flow: Separating Consensus and ComputePreprint
Hentschel, A., Shirley, D., & Lafrance, L. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.05821 · Cited by 4
“Potential solutions include zkSnarks [17], Bulletproofs [18], and TrueBit ’s approach [19].”
DeFi risk assessment: MakerDAO loan portfolio case
Melnikov, I., Lebedeva, I., Petrov, A., & Yanovich, Y. (2024) · Blockchain Research and Applications · doi:10.1016/j.bcra.2024.100259 · Cited by 3
Tang, B., Yao, S., Su, L., & Xu, F. (2025) · Symmetry · doi:10.3390/sym17020253 · Cited by 3
Privacy-preserving cross-chain asset transfers using notary schemes and zero-knowledge proofs
Wu, X., Zhang, T., Chen, L., & Wang, Z. (2025) · Cluster Computing · doi:10.1007/s10586-024-05039-5 · Cited by 3
A ZKP-based anonymous biometric authentication scheme for the E-health systems
Mao, X., Zhou, X., Zhao, X., & Chen, Y. (2025) · PLoS ONE · doi:10.1371/journal.pone.0324289 · Cited by 3
“Referring to [12,25], we give the definition of DL assumption, RSA group and Pedersen vector commitment in this section.”
Szczegielniak-Rekiel, A., Kanciak, K., & Kelner, J. M. (2025) · IEEE Access · doi:10.1109/access.2025.3596122 · Cited by 3
“Bulletproofs were introduced in 2017 [54].”
ZKProphet: Understanding Performance of Zero-Knowledge Proofs on GPUs
Verma, T., Yuan, Y., Talati, N., & Austin, T. M. (2025) · IEEE International Symposium on Workload Characterization · doi:10.1109/iiswc66894.2025.00021 · Cited by 3
Founding Zero-Knowledge Proof of Training on Optimum Vicinity
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On the Security and Privacy of CKKS-Based Homomorphic Evaluation Protocols
Hwang, I., Min, S., Seo, J., & Song, Y. (2025) · Lecture notes in computer science · doi:10.1007/978-981-95-5122-4_10 · Cited by 3
“Bell et al. [8] also construct a proof system for BGV ciphertexts based on the inner product argument of Bulletproofs [16].”
AI-RMF-Governed, Zero-Trust Architecture for AI-Enabled IoTaaS: An Industrial Perspective
Julio, Y. R., Viloria-Núñez, C., Sacoto-Cabrera, E. J., Tello, E. A., Mubarik, M., & Pinto, A. D. (2025) · IEEE Global Conference on Artificial Intelligence and Internet of Things (GCAIoT) · doi:10.1109/gcaiot68269.2025.11275565 · Cited by 3
Universally Composable SNARKs with Transparent Setup without Programmable Random Oracle
Badertscher, C., Campanelli, M., Ciampi, M., Russo, L., & Siniscalchi, L. (2025) · Lecture notes in computer science · doi:10.1007/978-3-032-01907-3_8 · Cited by 3
Klooß, M., Lai, R. W. F., Nguyen, N. K., & Osadnik, M. (2025) · Lecture notes in computer science · doi:10.1007/978-981-95-5099-9_10 · Cited by 3
Chang, K., & Seneviratne, O. W. (2026) · ACM Transactions on the Web · doi:10.1145/3795774 · Cited by 3
“…Variable Proof Systems: The framework can be conigured to support multiple ZKP backends, including zkSNARKs [11], zkSTARKs [9], and Bulletproofs [12], allowing users to choose the protocol that best suits their needs, which ensures that organizations can implement the framework across a variety…”
Nguidjoï, T. E. M. M., Onana, F. S. M., & Ndié, T. D. (2026) · IEEE Access · doi:10.1109/access.2026.3660105 · Cited by 3
“References [8] and [11] address setup trust but miss a crucial distinction: cryptographic transparency differs from institutional interpretability.”
Two-Round 2PC ECDSA at the Cost of 1 OLE: Applications to Embedded Cryptocurrency Wallets
Adjedj, M., Blokh, C., Couteau, G., Galansky, A., Joux, A., & Makriyannis, N. (2026) · Lecture notes in computer science · doi:10.1007/978-3-032-26734-4_12 · Cited by 3
Overview of Zero-Knowledge Proof and Its Applications in Blockchain
Zhou, Y., Wei, Z., Ma, S., & Hua, T. (2022) · Communications in computer and information science · doi:10.1007/978-981-19-8877-6_5 · Cited by 3
Lower Bound on SNARGs in the Random Oracle Model
Haitner, I., Nukrai, D., & Yogev, E. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-15982-4_4 · Cited by 3
“As such, improving the concrete efficiency of SNARGs is the focus of long line of work c.f., [Gro16; ZGKPP17; AHIV17; BBHR19; WTSTW18; BBBPWM18; BCRSVW19; CHMMVW20; BFS20; COS20; Sta18; LSTW21; CY21b; CY21a; GNS21].”
Poster: Verifiable Encodings for Maliciously-Secure Homomorphic Encryption Evaluation
Chatel, S., Knabenhans, C., Pyrgelis, A., Troncoso, C., & Hubaux, J. (2023) · ACM SIGSAC Conference on Computer and Communications Security (CCS) · doi:10.1145/3576915.3624403 · Cited by 3
“To address this problem, researchers have proposed generic verifiable computation techniques, e.g., [5, 19, 21, 26], to check the integrity of server computations.”
BackgroundDecentralized universally verifiable stake voting system with perfect privacy
Pavithra, G., & Singh, K. (2023) · Cryptologia · doi:10.1080/01611194.2023.2279147 · Cited by 3
“They have provided methods to deposit, transfer, and withdraw funds to/from accounts through cryptographic proofs like ZKP (Goldwasser, Micali, and Rackoff 1985), and Bullet proofs (B € unz et al. 2018).”
A Benchmark for Different Implementations of Zero-Knowledge Proof Systems
Kobelt, M., Sober, M., & Schulte, S. (2023) · IEEE International Conference on Blockchain (Blockchain) · doi:10.1109/blockchain60715.2023.00015 · Cited by 3
“Since the relatively recent achievement of the first practically usable construction of a ZKP [8], many different ZKP systems and implementations have emerged, e.g., [9]– [13].”
BackgroundBPA: A decentralized payment system that balances privacy and auditability
Gao, L., Zhang, J., Yu, J., Tang, Y., & Zeng, Z. (2024) · AIMS Mathematics · doi:10.3934/math.2024302 · Cited by 3
ZeroMT: Towards Multi-Transfer transactions with privacy for account-based blockchain
Scala, E., Dong, C., Corradini, F., & Mostarda, L. (2024) · Journal of Information Security and Applications · doi:10.1016/j.jisa.2024.103794 · Cited by 3
Vijayakumar, G., Singh, K., & Karthika, S. K. (2024) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2024.109510 · Cited by 4
Monero Traceability Heuristics: Wallet Application Bugs and the Mordinal-P2Pool Perspective
Hammad, N., & Victor, F. (2024) · IEEE International Conference on Blockchain and Cryptocurrency (ICBC) · doi:10.1109/icbc59979.2024.10634447 · Cited by 3
“RingCT hides the transaction amounts using bulletproofs [11].”
BackgroundGuo, Y., Karthikeyan, H., Polychroniadou, A., & Huussin, C. (2024) · IEEE Symposium on Security and Privacy (S&P) · doi:10.1109/sp54263.2024.00170 · Cited by 3
“It avoided trusted setup but unfortunately cannot support an efficient wallet nor resolve the issue of storage.”
BackgroundMethodInfluentialBoudgoust, K., & Simkin, M. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-78011-0_2 · Cited by 3
Bitcoin-Compatible Privacy-Preserving Multi-Party Payment Channels Supporting Variable Amounts
Chen, R., Zhang, Y., Li, D., Liu, Y., Liu, J., Wu, Q., Zhou, J., & Susilo, W. (2025) · IEEE Transactions on Information Forensics and Security · doi:10.1109/tifs.2025.3528827 · Cited by 3
“There are three algorithms involved in a NIZK protocol [35], ( Setup NIZK , P NIZK ( · ) , V NIZK ( · )).”
Transparent SNARKs over Galois Rings
Wei, Y., Zhang, X., & Deng, Y. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-91820-9_14 · Cited by 4
Practical Zero-Knowledge PIOP for Maliciously Secure Multiparty Homomorphic Encryption
Hwang, I., Lee, H., Seo, J., & Song, Y. (2025) · ACM SIGSAC Conference on Computer and Communications Security (CCS) · doi:10.1145/3719027.3765229 · Cited by 3
LZKSA: Lattice-Based Special Zero-Knowledge Proofs for Secure Aggregation's Input Verification
Lu, Z. G., & Lu, S. (2025) · ACM SIGSAC Conference on Computer and Communications Security (CCS) · doi:10.1145/3719027.3744812 · Cited by 2
Privacy-Preserving Data Aggregation with Probabilistic Range Validation
Dekker, F. W., & Erkin, Z. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-78375-4_4 · Cited by 3
“[14] are more efficient than generic zero-knowledge proofs, they still incur a relatively high complexity for the users (i.”
BackgroundA Practical NIZK Argument for Confidential Transactions over Account-Model Blockchain
Ma, S., Deng, Y., Bai, M., He, D., Zhang, J., & Xie, X. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-62576-4_12 · Cited by 3
Transparent Electricity Pricing with Privacy
Reijsbergen, D., Yang, Z., Maw, A., Dinh, T. T. A., & Zhou, J. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-88428-4_22 · Cited by 3
A range proof scheme analysis for the Mimblewimble cryptocurrency protocol
Silveira, A., Betarte, G., Cristiá, M., & Luna, C. (2021) · IEEE URUCON · doi:10.1109/urucon53396.2021.9647414 · Cited by 3
Efficient Sum-Check Protocol for Convolution
Ju, C., Lee, H., Chung, H., Seo, J. H., & Kim, S. (2021) · IEEE Access · doi:10.1109/access.2021.3133442 · Cited by 4
“The trusted setup issue is addressed in [19]–[21].”
BackgroundCircuitree: A Datalog Reasoner in Zero-Knowledge
Godden, T., Smet, R. D., Debruyne, C., Vandervelden, T., Steenhaut, K., & Braeken, A. (2022) · IEEE Access · doi:10.1109/access.2022.3153366 · Cited by 3
“We demonstrate its performance with a Datalog reasoner using the zero-knowledge system Bulletproofs [17].”
BackgroundMethodInfluentialATSSIA: Asynchronous Truly-Threshold Schnorr Signing for Inconsistent Availability
Joshi, S., Pandey, D., & Srinathan, K. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-08896-4_4 · Cited by 3
Distributed Key Generation with Smart Contracts using zk-SNARKs
Sober, M., Kobelt, M., Scaffino, G., Kaaser, D., & Schulte, S. (2023) · ACM Symposium on Applied Computing · doi:10.1145/3555776.3577677 · Cited by 3
“Knowledge (zk-STARKs) [5], and Bulletproofs [11].”
InfluentialBlockchain-Based Self-Sovereign Identity System with Attribute-Based Issuance
Lee, Y.-H., Liu, Z., Tso, R., & Tseng, Y. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-21280-2_2 · Cited by 3
Zhu, J., Feng, W., Zhong, W., Huang, M., & Feng, S. (2023) · Wireless Communications and Mobile Computing · doi:10.1155/2023/6196872 · Cited by 3
“[19] Bulletproof Short O 4 lg n ð Þ No 2 Wireless Communications and Mobile Computing”
BackgroundYu, L., He, M., Xiong, L., Luo, Q., & Niu, X. (2022) · IEEE International Conference on High Performance Computing and Communications; IEEE International Conference on Smart City; IEEE International Conference on Data Science and Systems (HPCC/SmartCity/DSS) · doi:10.1109/hpcc-dss-smartcity-dependsys57074.2022.00233 · Cited by 3
“Moreover, we adopt the range proof from BulletProofs [24] to ensure that a payer has enough balance to execute the transaction.”
MethodA Review of Privacy-Preserving Cryptographic Techniques Used in Blockchain Platforms
Barj, S., Ouaddah, A., & Mezrioui, A. (2023) · Lecture notes in networks and systems · doi:10.1007/978-3-031-29857-8_23 · Cited by 3
Leopard: Sublinear Verifier Inner Product Argument Under Discrete Logarithm Assumption
Kim, S., Lee, G., Lee, H., & Seo, J. H. (2023) · IEEE Transactions on Information Forensics and Security · doi:10.1109/tifs.2023.3300525 · Cited by 3
“IP arguments are crucial building blocks for range proofs, zero knowledge arguments, and various applications such as identification [2], [3], verifiable computation [4], [5], [6], [7], and confidential transactions [8], [9], [10], [11], [12].”
BackgroundMethodResultInfluentialPrivate Electronic Road Pricing Using Bulletproofs With Vector Commitments
Smet, R. D., Steenhaut, K., & Braeken, A. (2023) · IEEE Transactions on Dependable and Secure Computing · doi:10.1109/tdsc.2023.3314867 · Cited by 3
“Our zero-knowledge system of choice, Bulletproofs [7], produces extremely compact proofs, does not require trusted setup, provides information-theoretic zero-knowledgeness, and soundness based on the discrete logarithm assumption.”
BackgroundMethodInfluentialVerifying the Computational Integrity of Power Grid Controls with Zero-Knowledge Proof
Chang, C.-Y., Macwan, R., & Murphy, S. (2023) · IEEE Power Engineering Society General Meeting · doi:10.1109/pesgm52003.2023.10253173 · Cited by 3
Folding Schemes with Selective Verification
Ràfols, C., & Zacharakis, A. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-44469-2_12 · Cited by 3
“There, they use a tree like structure similar to ours in order to derive the same Fiat-Shamir challenge across multiple parallel executions of an inner product argument protocol [10] with different parties.”
BackgroundMethodLi, L., Xu, C., & Zhang, P. (2024) · Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering · doi:10.1007/978-3-031-51399-2_6 · Cited by 3
Efficient Zero-Knowledge Arguments and Digital Signatures via Sharing Conversion in the Head
Maire, J., & Vergnaud, D. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-50594-2_22 · Cited by 3
“It relies on the “ Bulletproofs ” technique proposed by B¨unz, Bootle, Boneh, Poelstra, Wuille and Maxwell in 2018 [BBB + 18].”
MethodElectronic Voting Privacy Protection Scheme Based on Double Signature in Consortium Blockchain
Xie, W., Li, W., & Zhang, H. (2024) · Lecture notes in computer science · doi:10.1007/978-981-99-9785-5_38 · Cited by 3
Nee, L., Gaba, G. S., & Gurtov, A. (2023) · IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON) · doi:10.1109/chilecon60335.2023.10418717 · Cited by 3
“Because scalability and resource efficiency are critical in VANETs, we chose Bulletproof NIZKP proofs over other typical NIZKP proofs [10].”
MethodIDEA-DAC: Integrity-Driven Editing for Accountable Decentralized Anonymous Credentials via ZK-JSON
Zheng, S. X., Li, Z., Luo, J., Xin, Z., & Liu, X. (2024) · International World Wide Web Conference (WWW) · doi:10.1145/3589334.3645658 · Cited by 3
A Practical Data Trading Protocol for Sudoku Solutions
Deng, J., & Wu, B. L. (2024) · IEEE Transactions on Information Forensics and Security · doi:10.1109/tifs.2024.3419702 · Cited by 3
“The symbols employed in this paper are mostly consistent with [9].”
MethodHadamard Product Argument from Lagrange-Based Univariate Polynomials
Xie, J., Hu, Y., & Yu, Y. (2024) · Lecture notes in computer science · doi:10.1007/978-981-97-5025-2_24 · Cited by 3
Zero-Knowledge Proofs for Blockchains
Ruj, S. (2024) · IEEE/IFIP International Conference on Dependable Systems and Networks - Supplemental Volume (DSN-S) · doi:10.1109/dsn-s60304.2024.00028 · Cited by 3
“We discuss different types like Groth16 [9], Plonk [10], Bulletproofs [11], STARKs [12] highlighting the differences.”
Efficient Maliciously Secure Oblivious Exponentiations
Baum, C., Berlips, J., Chen, W. Q., Damgård, I., Esvelt, K. M., Foner, L. N., Gretton, D., Kysel, M., Rivest, R. L., Roy, L., et al. (2024) · IACR Communications in Cryptology · doi:10.62056/a66cy7qiu · Cited by 3
Signer revocability for threshold ring signatures
Teng, D., & Yao, Y. (2024) · Computer Standards & Interfaces · doi:10.1016/j.csi.2024.103960 · Cited by 3
Updatable Privacy-Preserving Blueprints
David, B., Engelmann, F., Frederiksen, T. K., Kohlweiss, M., Pagnin, E., & Volkhov, M. (2024) · Lecture notes in computer science · doi:10.1007/978-981-96-0875-1_4 · Cited by 3
“History Binding (Theorem 5) is proven by unfolding simulation-extractability of Π , instantiating trace proofs, along the history.”
BackgroundZhang, T., Wang, Y., Gong, B., Xu, J., Wu, J., & Wan, C. (2025) · Concurrency and Computation Practice and Experience · doi:10.1002/cpe.70084 · Cited by 3
“In this paper, we use non-interactive Bulletproofs [18].”
$$\textsf{Polocolo}$$: A ZK-Friendly Hash Function Based on S-Boxes Using Power Residues
Ha, J., Hwang, S., Lee, J., Park, S., & Son, M. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-91134-7_11 · Cited by 3
Privacy Protection Model for Blockchain Data Sharing Based on zk-SNARK
Li, Y., Zhang, G., Zhu, J., & Wang, X. (2021) · Communications in computer and information science · doi:10.1007/978-981-16-5943-0_19 · Cited by 3
A Self-Tallying Electronic Voting Based on Blockchain
Zeng, G., He, M., Yiu, S., & Huang, Z. (2021) · The Computer Journal · doi:10.1093/comjnl/bxab123 · Cited by 3
Practical Verifiable Random Function with RKA Security
Yuen, T. H., Pan, S., Huang, S., & Zhang, X. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-35486-1_22 · Cited by 3
On Publicly-Accountable Zero-Knowledge and Small Shuffle Arguments
Fleischhacker, N., & Simkin, M. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-75248-4_22 · Cited by 3
“For Bulletproofs [17], we consider an instantiation in ristretto255 [48] for shuffling Pedersen commitments.”
BackgroundMethodInfluentialZKSENSE: A Friction-less Privacy-Preserving Human Attestation Mechanism for Mobile Devices
Querejeta-Azurmendi, I., Papadopoulos, P., Varvello, M., Nappa, A., Zhang, J., & Livshits, B. (2021) · Proceedings on Privacy Enhancing Technologies · doi:10.2478/popets-2021-0058 · Cited by 11
“By extending the inner product proof presented in [59] to a zero-knowledge proof and leveraging the arithmetic properties of Pedersen commitments, we present zkSVM, a privacy-preserving SVM evaluation model.”
BackgroundMethodInfluentialAn Optimized Inner Product Argument with More Application Scenarios
Zhang, Z., Zhou, Z., Li, W., & Tao, H. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-88052-1_20 · Cited by 3
Transparency or Anonymity Leak: Monero Mining Pools Data Publication
Wijaya, D. A., Liu, J. K., Steinfeld, R., & Liu, D. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-90567-5_22 · Cited by 3
Privacy preserving event based transaction system in a decentralized environment
Karanjai, R., Xu, L., Gao, Z., Chen, L., Kaleem, M., & Shi, W. L. (2021) · International Middleware Conference · doi:10.1145/3464298.3493401 · Cited by 3
“However, it is worthwhile pointing out that it is plausible to realize the described data models and protocol using alternative back-end zero-knowledge proving systems such as zk-STARK [2], bulletproof [7].”
BackgroundXue, Q., Yue, S., Ma, H., Hou, Z., & Tianhao, Z. (2021) · IEEE International Conference on Information, Communication and Networks (ICICN) · doi:10.1109/icicn52636.2021.9673891 · Cited by 3
A Privacy-preserving Outsourcing Scheme for Zero-knowledge Proof Generation
Nakamura, M. M., Miyamae, T., & Morinaga, M. (2022) · Journal of Information Processing · doi:10.2197/ipsjjip.30.151 · Cited by 3
Mjolnir: Breaking the Glass in a Publicly Verifiable Yet Private Manner
AlTawy, R., Galal, H. S., & Youssef, A. (2023) · IEEE Transactions on Network and Service Management · doi:10.1109/tnsm.2023.3244506 · Cited by 3
Provably Unforgeable Threshold EdDSA with an Offline Participant and Trustless Setup
Battagliola, M., Longo, R., Meneghetti, A., & Sala, M. (2023) · Mediterranean Journal of Mathematics · doi:10.1007/s00009-023-02452-9 · Cited by 3
emmy – Trust-Enhancing Authentication Library
Stopar, M., Bizjak, M., Modic, J., Hartman, J., Žitnik, A., & Marc, T. (2019) · IFIP advances in information and communication technology · doi:10.1007/978-3-030-33716-2_11 · Cited by 3
“Due to their efficiency, Bulletproofs and zk-SNARKs are highly suitable for blockchain-based applications and, in particular, cryptocurrencies.”
MethodConfidential and Auditable Payments
Mitani, T., & Otsuka, A. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-54455-3_33 · Cited by 3
“Zether has also used the zero-knowledge proof Bulletproofs [5] proposed by their group.”
MethodEcoBoost: Efficient Bootstrapping for Confidential Transactions
Wang, C., Wang, B., & Fan, X. (2020) · IEEE International Conference on Blockchain and Cryptocurrency (ICBC) · doi:10.1109/icbc48266.2020.9169416 · Cited by 3
“If the system supports 32-bit precession in terms of transaction amounts and we choose 256 bits as the size of each element of group G, the size of one range proof is about 2.5 KB [4] or 608 bytes (with the optimization in Bulletproofs [4]).”
BackgroundMethodInfluentialPrivate and Atomic Exchange of Assets over Zero Knowledge Based Payment LedgerPreprint
Gao, Z., Xu, L., Kasichainula, K., Chen, L., Cărbunar, B., & Shi, W. L. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.06535 · Cited by 3
“However, it is worthwhile pointing out that it is possible to realize OMAP using other zero-knowledge proof systems, for instance, zk-STARK [25], bulletproof [26], or alternative approaches such as [27].”
BackgroundAgatha: Smart Contract for DNN ComputationPreprint
Zheng, Z., Xie, P., Zhang, X., Chen, S., Chen, Y., Guo, X., Sun, G., Sun, G., & Zhou, L. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.04919 · Cited by 13
“However, current VC and ZKP use expensive cryptographic primitives [13, 15, 30, 68], which are currently impractical to support the complicated computations like DNN computations.”
A supervised privacy preservation transaction system for aviation business
Zhou, X., Li, W., & Zhong, L. (2024) · Peer-to-Peer Networking and Applications · doi:10.1007/s12083-024-01647-5 · Cited by 2
“The zero-knowledge proof used in our paper is based on the standard Sigma protocol [32] and Bulletproofs [6].”
BlindShuffler: Universal and Trustless Mixing for Confidential Transactions
Wang, C., Ge, Z., Long, Y., Xu, X., Sun, S.-F., & Gu, D. (2024) · ACM Asia Conference on Computer and Communications Security (ASIA CCS) · doi:10.1145/3634737.3637669 · Cited by 2
Threshold ring signature: generic construction and logarithmic size instantiation
Wang, H., Tao, Y., & Zhang, R. (2024) · Cybersecurity · doi:10.1186/s42400-024-00233-9 · Cited by 2
“The vector argument extends from the inner product argument (Bünz et al. 2018), which serves as a proof sys-tem for the relation A verifier, who interacts with a prover and outputs accept, can confidently ascertain that the prover has a , s.t.”
BackgroundMethodImproved Constant-Sized Polynomial Commitment Schemes Without Trusted Setup
Fu, S. (2025) · IACR Communications in Cryptology · doi:10.62056/anudy76bm · Cited by 2
Dyna-hinTS: Silent Threshold Signatures for Dynamic Committees
Kate, A., Mukherjee, P., Samanta, S., & Sarkar, P. (2025) · Crypto Valley Conference on Blockchain Technology (CVCBT) · doi:10.1109/cvc65719.2025.00019 · Cited by 2
“The first limitation was addressed by the compressed Σ protocol works of [15, 14] that use bulletproofs [24] to prove that the aggregated public key correctly generated and the signature size grows logarithmic with the number of signers at the cost of increasing the verification time to be linear…”
Ethical AI Design in Blockchain-Powered Surveillance Systems
Kumar, D. M. (2024) · Scientific Journal of Artificial Intelligence and Blockchain Technologies · doi:10.63345/sjaibt.v1.i3.103 · Cited by 2
Scalable batch verification of ECDSA for blockchain using IVC
Liu, L., Wei, P., Liu, S., Wang, Z., Hu, D., & Kou, Z. (2025) · Frontiers of Computer Science · doi:10.1007/s11704-025-41269-5 · Cited by 2
Fang, S., Zhou, J., Cao, Z., Dong, X., & Choo, K. R. (2025) · IEEE Internet of Things Journal · doi:10.1109/jiot.2025.3631877 · Cited by 2
“Due to the soundness of ZKRP, which has been formally proved in [34], Adv soundness B 3 , ZKRP ( λ )) holds.”
Scalable zkSNARKs for Matrix Computations
Cong, M., Chow, S. S. M., Yiu, S., & Yuen, T. H. (2025) · Lecture notes in computer science · doi:10.1007/978-981-95-5116-3_12 · Cited by 2
Nair, V., Sharma, A., & Thankey, B. (2025) · Lecture notes in computer science · doi:10.1007/978-981-95-5116-3_14 · Cited by 2
“In comparison, transparent setups are used in schemes such as Bulletproof [BBB + 18], Dory [Lee21], FRI [BBHR18], Ligero [AHIV17], Brakedown [GLS + 23], and Basefold [ZCF24].”
MethodBi, Y., & Jia, C. (2025) · IEEE Transactions on Mobile Computing · doi:10.1109/tmc.2025.3599376 · Cited by 2
“P algorithms [51], [52].”
Straight-Line Knowledge Extraction for Multi-Round Protocols
Rotem, L., & Tessaro, S. (2025) · Lecture notes in computer science · doi:10.1007/978-3-032-01907-3_4 · Cited by 2
“This shows that assuming that τ (0) and τ (1) satisfiability arguments [17].”
Influential
Metadata
- Authors
- Bunz, B., Bootle, J., Boneh, D., Poelstra, A., Wuille, P., & Maxwell, G.
- Affiliations
- University College London (GB)
- Stanford University (US)
- Venue
- 2018 IEEE Symposium on Security and Privacy (SP)
- Publisher
- IEEE
- Published
- 2018-05
- Pages
- 315-334
- ISSN
- 1081-6011 (ISSN-L)
- OpenAlex
- W2883748642
- Cited by
- 1,154
- References
- 63
- Citations by year
- 2026: 148 · 2025: 184 · 2024: 199 · 2023: 175 · 2022: 147 · 2021: 128 · 2020: 104 · 2019: 60 · 2018: 9
- FWCI
- 30.72
- Type
- conference paper
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- IEEE Symposium on Security and Privacy (S&P) (publishedVersion)
- Funders
- National Science Foundation
- Simons Foundation
- Defense Advanced Research Projects Agency
- Office of Naval Research
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Cryptography and Data Security
- Physical Sciences › Computer Science › Information Systems › Blockchain Technology Applications and Security
- Physical Sciences › Computer Science › Computer Networks and Communications › Advanced Authentication Protocols Security
- Keywords
- Bulletproofs, non-interactive zero-knowledge proofs, range proofs, confidential transactions, Bitcoin, multi-party computation, arithmetic circuits, discrete logarithm assumption, blockchain privacy
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