The DOI matches its Crossref record; 56 of the 63 references it cites were found in a registry or an index.
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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Cites
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Self-citationNon-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
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Zerocash: Decentralized Anonymous Payments from Bitcoin
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Short Signatures Without Random Oracles
Boneh, D., & Boyen, X. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-24676-3_4 · Cited by 1,448
Self-citationOn 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
SoK: Research Perspectives and Challenges for Bitcoin and Cryptocurrencies
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Groth, J., & Sahai, A. (2008) · Springer eBooks · doi:10.1007/978-3-540-78967-3_24 · Cited by 1,078
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Cited by
Sorted by citations
Advances and Open Problems in Federated Learning
Kairouz, P., & McMahan, H. B. (2021) · Foundations and Trends in Machine Learning · doi:10.1561/2200000083 · Cited by 7,772
“If we relax the requirements for succinctness or non-interactiveness for the construction, there is a large body of constructions that achieve a wide range of efficiency trade-offs, avoid the trusted setup requirement and use more standard cryptographic assumptions [84, 397, 23, 58].”
BackgroundMarlin: Preprocessing zkSNARKs with Universal and Updatable SRS
Chiesa, A., Hu, Y., Maller, M., Mishra, P., Vesely, N., & Ward, N. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-45721-1_26 · Cited by 377
Aurora: Transparent Succinct Arguments for R1CS
Ben‐Sasson, E., Chiesa, A., Riabzev, M., Spooner, N., Virza, M., & Ward, N. P. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-17653-2_4 · Cited by 340
“Bulletproofs [31, 35] proves the satisfaction of an N -gate arithmetic circuit via a recursive use of a low-communication protocol for inner products, achieving a proof with O(logN) group elements.”
BackgroundMethodA Survey on Zero-Knowledge Proof in Blockchain
Sun, X., Yu, F. R., Zhang, P., Sun, Z., Xie, W., & Peng, X. (2021) · IEEE Network · doi:10.1109/mnet.011.2000473 · Cited by 328
Zether: Towards Privacy in a Smart Contract World
Bünz, B., Agrawal, S., Zamani, M., & Boneh, D. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-51280-4_23 · Cited by 317
“Bulletproofs [61] enable proofs on Pedersen committed values by computing a linear combination of commitments and opening that combination.”
BackgroundSelf-citation
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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