Cited By
View all- Applebaum BPinkas B(2024)Distributing Keys and Random Secrets with Constant ComplexityTheory of Cryptography10.1007/978-3-031-78023-3_16(485-516)Online publication date: 2-Dec-2024
GRandLine: Adaptively Secure DKG and Randomness Beacon with (Log-)Quadratic Communication Complexity
Authors: 
Renas Bacho, Christoph Lenzen, Julian Loss, Simon Ochsenreither, Dimitrios PapachristoudisAuthors Info & Claims
Renas Bacho, Christoph Lenzen, Julian Loss, Simon Ochsenreither, Dimitrios PapachristoudisAuthors Info & ClaimsPages 941 - 955
Abstract
A randomness beacon is a source of continuous and publicly verifiable randomness which is of crucial importance for many applications. Existing works on randomness beacons suffer from at least one of the following drawbacks: (i) security only against static (i.e., non-adaptive) adversaries, (ii) each epoch takes many rounds of communication, or (iii) computationally expensive tools such as proof-of-work (PoW) or verifiable delay functions (VDF). In this work, we introduce GRandLine, the first adaptively secure randomness beacon protocol that overcomes all these limitations while preserving simplicity and optimal resilience in the synchronous network setting. We achieve our result in two steps. First, we design a novel distributed key generation (DKG) protocol GRand that runs in O(λ n2 log n ) bits of communication but, unlike most conventional DKG protocols, outputs both secret and public keys as group elements. Here, λ denotes the security parameter. Second, following termination of GRand, parties can use their keys to derive a sequence of randomness beacon values, where each random value costs only a single asynchronous round and O(λ n2) bits of communication. We implement GRandLine and evaluate it using a network of up to 64 parties running in geographically distributed AWS instances. Our evaluation shows that GRandLine can produce about 2 beacon outputs per second in a network of 64 parties. We compare our protocol to the state-of-the-art randomness beacon protocols OptRand (NDSS '23), BRandPiper (CCS '21), and Drand, in the same setting and observe that it vastly outperforms them.
References
[1]
2023. Library implementation for the BN254 pairing-friendly elliptic curve. docs.rs. https://docs.rs/ark-bn254/0.4.0/ark_bn254/index.html
[2]
Ittai Abraham, Philipp Jovanovic, Mary Maller, Sarah Meiklejohn, and Gilad Stern. 2023. Bingo: Adaptivity and Asynchrony in Verifiable Secret Sharing and Distributed Key Generation. In Advances in Cryptology -- CRYPTO 2023: 43rd Annual International Cryptology Conference, CRYPTO 2023, Santa Barbara, CA, USA, August 20--24, 2023, Proceedings, Part I (Santa Barbara, CA, USA). Springer- Verlag, Berlin, Heidelberg, 39--70. https://doi.org/10.1007/978--3-031--38557--5_2
[3]
Ittai Abraham, Philipp Jovanovic, Mary Maller, Sarah Meiklejohn, Gilad Stern, and Alin Tomescu. 2021. Reaching Consensus for Asynchronous Distributed Key Generation. In 40th ACM Symposium Annual on Principles of Distributed Computing. Association for Computing Machinery, Portland, OR, USA, 363--373.
[4]
Ittai Abraham, Dahlia Malkhi, Kartik Nayak, and Ling Ren. 2018. Dfinity Consensus, Explored. Cryptology ePrint Archive, Report 2018/1153. https: //eprint.iacr.org/2018/1153.
[5]
Nicolas Alhaddad, Mayank Varia, and Haibin Zhang. 2021. High-Threshold AVSS with Optimal Communication Complexity. 479--498. https://doi.org/10.1007/978- 3--662--64331-0_25
[6]
Anonymous. 2023. Cryptography for GRandLine. GitHub repository. https: //github.com/DiPa0123/Optrand-PVSS
[7]
Anonymous. 2023. Implementation of GRandLine. GitHub repository. https: //github.com/DiPa0123/GRandLine
[8]
arkworks contributors. 2022. arkworks zkSNARK ecosystem. https://arkworks.rs
[9]
Thomas Attema, Ronald Cramer, and Matthieu Rambaud. 2021. Compressed Sigma- Protocols for Bilinear Group Arithmetic Circuits and Application to Logarithmic Transparent Threshold Signatures. 526--556. https://doi.org/10.1007/978--3-030- 92068--5_18
[10]
Renas Bacho, Daniel Collins, Chen-Da Liu-Zhang, and Julian Loss. 2023. Network- Agnostic Security Comes (Almost) for Free in DKG and MPC. In Advances in Cryptology -- CRYPTO 2023: 43rd Annual International Cryptology Conference, CRYPTO 2023, Santa Barbara, CA, USA, August 20--24, 2023, Proceedings, Part I (Santa Barbara, CA, USA). Springer-Verlag, Berlin, Heidelberg, 71--106. https: //doi.org/10.1007/978--3-031--38557--5_3
[11]
Renas Bacho, Christoph Lenzen, Julian Loss, Simon Ochsenreither, and Dimitrios Papachristoudis. 2023. GRandLine: Adaptively Secure DKG and Randomness Beacon with (Log-)Quadratic Communication Complexity. Cryptology ePrint Archive, Paper 2023/1887. https://eprint.iacr.org/2023/1887
[12]
Renas Bacho and Julian Loss. 2022. On the Adaptive Security of the Threshold BLS Signature Scheme. 193--207. https://doi.org/10.1145/3548606.3560656
[13]
Renas Bacho and Julian Loss. 2023. Adaptively Secure (Aggregatable) PVSS and Application to Distributed Randomness Beacons. In Proceedings of the 2023 ACM SIGSAC Conference on Computer and Communications Security (, Copenhagen, Denmark,) (CCS '23). Association for Computing Machinery, New York, NY, USA, 1791--1804. https://doi.org/10.1145/3576915.3623106
[14]
Renas Bacho, Julian Loss, Gilad Stern, and Benedikt Wagner. 2024. HARTS: High-Threshold, Adaptively Secure, and Robust Threshold Schnorr Signatures. Cryptology ePrint Archive, Paper 2024/280. https://eprint.iacr.org/2024/280 https://eprint.iacr.org/2024/280.
[15]
Akhil Bandarupalli, Adithya Bhat, Saurabh Bagchi, Aniket Kate, and Michael Reiter. 2023. HashRand: Efficient Asynchronous Random Beacon without Threshold Cryptographic Setup. Cryptology ePrint Archive, Paper 2023/1755. https://eprint.iacr.org/2023/1755 https://eprint.iacr.org/2023/1755.
[16]
Mihir Bellare and Phillip Rogaway. 1993. Random Oracles are Practical: A Paradigm for Designing Efficient Protocols. 62--73. https://doi.org/10.1145/168588. 168596
[17]
Piotr Berman, Juan A. Garay, and Kenneth J. Perry. 1989. Towards Optimal Distributed Consensus (Extended Abstract). 410--415. https://doi.org/10.1109/ SFCS.1989.63511
[18]
Adithya Bhat, Nibesh Shrestha, Aniket Kate, and Kartik Nayak. 2023. OptRand: Optimistically Responsive Reconfigurable Distributed Randomness. Proceedings 2023 Network and Distributed System Security Symposium (2023). https://api. semanticscholar.org/CorpusID:257499606
[19]
Adithya Bhat, Nibesh Shrestha, Zhongtang Luo, Aniket Kate, and Kartik Nayak. 2021. RandPiper - Reconfiguration-Friendly Random Beacons with Quadratic Communication. 3502--3524. https://doi.org/10.1145/3460120.3484574
[20]
Alexandra Boldyreva. 2003. Threshold Signatures, Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme. 31--46. https://doi.org/10.1007/3--540--36288--6_3
[21]
Dan Boneh, Joseph Bonneau, Benedikt Bünz, and Ben Fisch. 2018. Verifiable Delay Functions. 757--788. https://doi.org/10.1007/978--3--319--96884--1_25
[22]
Dan Boneh, Benedikt Bünz, and Ben Fisch. 2019. Batching Techniques for Accumulators with Applications to IOPs and Stateless Blockchains. 561--586. https://doi.org/10.1007/978--3-030--26948--7_20
[23]
Benedikt Bünz, Steven Goldfeder, and Joseph Bonneau. 2017. Proofs-of-delay and randomness beacons in Ethereum.
[24]
Christian Cachin, Klaus Kursawe, and Victor Shoup. 2005. Random Oracles in Constantinople: Practical Asynchronous Byzantine Agreement Using Cryptography. 18, 3 (July 2005), 219--246. https://doi.org/10.1007/s00145-005-0318-0
[25]
Ran Canetti, Rosario Gennaro, Stanislaw Jarecki, Hugo Krawczyk, and Tal Rabin. 1999. Adaptive Security for Threshold Cryptosystems. 98--115. https://doi.org/ 10.1007/3--540--48405--1_7
[26]
Ignacio Cascudo and Bernardo David. 2017. SCRAPE: Scalable Randomness Attested by Public Entities. 537--556. https://doi.org/10.1007/978--3--319--61204--1_27
[27]
Ignacio Cascudo and Bernardo David. 2020. ALBATROSS: Publicly AttestabLe BATched Randomness Based On Secret Sharing. 311--341. https://doi.org/10.1007/978--3-030--64840--4_11
[28]
Ignacio Cascudo and Bernardo David. 2024. Publicly Verifiable Secret Sharing Over lass Groups and Applications to DKG and YOSO. In Advances in Cryptology -- EUROCRYPT 2024: 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zurich, Switzerland, May 26--30, 2024, Proceedings, Part V (Zurich, Switzerland). Springer-Verlag, Berlin, Heidelberg, 216--248. https://doi.org/10.1007/978--3-031--58740--5_8
[29]
David Chaum and Torben P. Pedersen. 1993. Wallet Databases with Observers. 89--105. https://doi.org/10.1007/3--540--48071--4_7
[30]
Alisa Cherniaeva, Ilia Shirobokov, and Omer Shlomovits. 2019. Homomorphic Encryption Random Beacon. Cryptology ePrint Archive, Report 2019/1320. https://eprint.iacr.org/2019/1320.
[31]
Kevin Choi, Arasu Arun, Nirvan Tyagi, and Joseph Bonneau. 2023. Bicorn: An optimistically efficient distributed randomness beacon. Cryptology ePrint Archive, Report 2023/221. https://eprint.iacr.org/2023/221.
[32]
Kevin Choi, Aathira Manoj, and Joseph Bonneau. 2023. SoK: Distributed Randomness Beacons. In 44th IEEE Symposium on Security and Privacy, SP 2023, San Francisco, CA, USA, May 21--25, 2023. IEEE, 75--92. https://doi.org/10.1109/ SP46215.2023.10179419
[33]
Tokio contributors. 2023. Tokio library for networking in Rust. https://tokio.rs/
[34]
Sourav Das, Vinith Krishnan, Irene Miriam Isaac, and Ling Ren. 2022. Spurt: Scalable Distributed Randomness Beacon with Transparent Setup. 2502--2517. https://doi.org/10.1109/SP46214.2022.9833580
[35]
Sourav Das, Benny Pinkas, Alin Tomescu, and Zhuolun Xiang. 2024. Distributed Randomness using Weighted VRFs. Cryptology ePrint Archive, Paper 2024/198. https://eprint.iacr.org/2024/198 https://eprint.iacr.org/2024/198.
[36]
Sourav Das, Zhuolun Xiang, Lefteris Kokoris-Kogias, and Ling Ren. 2023. Practical Asynchronous High-threshold Distributed Key Generation and Distributed Polynomial Sampling. In 32nd USENIX Security Symposium (USENIX Security . USENIX Association, Anaheim, CA, 5359--5376. https://www.usenix.org/ conference/usenixsecurity23/presentation/das
[37]
Sourav Das, Thomas Yurek, Zhuolun Xiang, Andrew K. Miller, Lefteris Kokoris- Kogias, and Ling Ren. 2022. Practical Asynchronous Distributed Key Generation. 2518--2534. https://doi.org/10.1109/SP46214.2022.9833584
[38]
Bernardo David, Peter Gazi, Aggelos Kiayias, and Alexander Russell. 2018. Ouroboros Praos: An Adaptively-Secure, Semi-synchronous Proof-of-Stake Blockchain. 66--98. https://doi.org/10.1007/978--3--319--78375--8_3
[39]
Roger Dingledine, Nick Mathewson, and Paul F. Syverson. 2004. Tor: The Second- Generation Onion Router. 303--320.
[40]
Danny Dolev and Rüdiger Reischuk. 1985. Bounds on information exchange for Byzantine agreement. J. ACM 32, 1 (jan 1985), 191--204. https://doi.org/10.1145/ 2455.214112
[41]
D. Dolev and H. R. Strong. 1983. Authenticated Algorithms for Byzantine Agreement. SIAM J. Comput. 12, 4 (1983), 656--666. https://doi.org/10.1137/0212045 arXiv:https://doi.org/10.1137/0212045
[42]
D. Dolev and A. Yao. 1983. On the security of public key protocols. IEEE Transactions on Information Theory 29, 2 (1983), 198--208. https://doi.org/10.1109/ TIT.1983.1056650
[43]
Justin Drake. 2018. Minimal VDF randomness beacon. (2018). https://ethresear. ch/t/minimal-vdf-randomness-beacon/3566
[44]
Hanwen Feng, Zhenliang Lu, and Qiang Tang. 2024. Breaking the Cubic Barrier: Distributed Key and Randomness Generation through Deterministic Sharding. Cryptology ePrint Archive, Paper 2024/168. https://eprint.iacr.org/2024/168 https://eprint.iacr.org/2024/168.
[45]
Georg Fuchsbauer, Eike Kiltz, and Julian Loss. 2018. The Algebraic Group Model and its Applications. 33--62. https://doi.org/10.1007/978--3--319--96881-0_2
[46]
Yingzi Gao, Yuan Lu, Zhenliang Lu, Qiang Tang, Jing Xu, and Zhenfeng Zhang. 2021. Efficient Asynchronous Byzantine Agreement without Private Setups. Cryptology ePrint Archive, Report 2021/810. https://eprint.iacr.org/2021/810.
[47]
Rosario Gennaro, Stanislaw Jarecki, Hugo Krawczyk, and Tal Rabin. 2007. Secure Distributed Key Generation for Discrete-Log Based Cryptosystems. 20, 1 (Jan. 2007), 51--83. https://doi.org/10.1007/s00145-006-0347--3
[48]
Craig Gentry, Shai Halevi, Bernardo Magri, Jesper Buus Nielsen, and Sophia Yakoubov. 2021. Random-Index PIR and Applications. 32--61. https://doi.org/10. 1007/978--3-030--90456--2_2
[49]
Yossi Gilad, Rotem Hemo, Silvio Micali, Georgios Vlachos, and Nickolai Zeldovich. 2017. Algorand: Scaling Byzantine Agreements for Cryptocurrencies. In Proceedings of the 26th Symposium on Operating Systems Principles (Shanghai, China) (SOSP '17). Association for Computing Machinery, New York, NY, USA, 51--68. https://doi.org/10.1145/3132747.3132757
[50]
Jens Groth. 2021. Non-interactive distributed key generation and key resharing. Cryptology ePrint Archive, Report 2021/339. https://eprint.iacr.org/2021/339.
[51]
Kobi Gurkan, Philipp Jovanovic, Mary Maller, Sarah Meiklejohn, Gilad Stern, and Alin Tomescu. 2021. Aggregatable Distributed Key Generation. 147--176. https://doi.org/10.1007/978--3-030--77870--5_6
[52]
Runchao Han, Jiangshan Yu, and Haoyu Lin. 2020. RandChain: Decentralised Randomness Beacon from Sequential Proof-of-Work. Cryptology ePrint Archive, Report 2020/1033. https://eprint.iacr.org/2020/1033.
[53]
Timo Hanke, Mahnush Movahedi, and Dominic Williams. 2018. DFINITY Technology Overview Series, Consensus System. arXiv:1805.04548 [cs.DC]
[54]
Stanislaw Jarecki and Anna Lysyanskaya. 2000. Adaptively Secure Threshold Cryptography: Introducing Concurrency, Removing Erasures. 221--242. https: //doi.org/10.1007/3--540--45539--6_16
[55]
Aniket Kate, Easwar Vivek Mangipudi, Pratyay Mukherjee, Hamza Saleem, and Sri Aravinda Krishnan Thyagarajan. 2023. Non-interactive VSS using Class Groups and Application to DKG. Cryptology ePrint Archive, Paper 2023/451. https://eprint.iacr.org/2023/451 https://eprint.iacr.org/2023/451.
[56]
Alireza Kavousi, Zhipeng Wang, and Philipp Jovanovic. 2023. SoK: Public Randomness. Cryptology ePrint Archive, Paper 2023/1121. https://eprint.iacr.org/ 2023/1121 https://eprint.iacr.org/2023/1121.
[57]
Eleftherios Kokoris-Kogias, Dahlia Malkhi, and Alexander Spiegelman. 2020. Asynchronous Distributed Key Generation for Computationally-Secure Randomness, Consensus, and Threshold Signatures. 1751--1767. https://doi.org/10.1145/ 3372297.3423364
[58]
SCIPR Lab. 2021. C library for Finite Fields and Elliptic Curves. GitHub repository. https://github.com/scipr-lab/libff
[59]
Leslie Lamport, Robert Shostak, and Marshall Pease. 1982. The Byzantine Generals Problem. ACM Trans. Program. Lang. Syst. 4, 3 (jul 1982), 382--401. https://doi.org/10.1145/357172.357176
[60]
Christoph Lenzen and Sahar Sheikholeslami. 2022. A Recursive Early-Stopping Phase King Protocol. In Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing (Salerno, Italy) (PODC'22). Association for Computing Machinery, New York, NY, USA, 60--69. https://doi.org/10.1145/3519270.3538425
[61]
Zhongtang Luo. 2022. Implementation for RandPiper. Github. https://github. com/zhtluo/randpiper-rs
[62]
Atsuki Momose and Ling Ren. 2021. Optimal Communication Complexity of Authenticated Byzantine Agreement. In 35th International Symposium on Distributed Computing (DISC 2021) (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 209), Seth Gilbert (Ed.). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 32:1--32:16. https://doi.org/10.4230/LIPIcs.DISC.2021.32
[63]
Satoshi Nakamoto. 2008. Bitcoin: A Peer-to-Peer Electronic Cash System. (2008). https://bitcoin.org/bitcoin.pdf
[64]
Kartik Nayak, Ling Ren, Elaine Shi, Nitin H. Vaidya, and Zhuolun Xiang. 2020. Improved Extension Protocols for Byzantine Broadcast and Agreement. In 34th International Symposium on Distributed Computing (DISC 2020) (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 179), Hagit Attiya (Ed.). Schloss Dagstuhl--Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 28:1-- 28:17. https://doi.org/10.4230/LIPIcs.DISC.2020.28
[65]
Lan Nguyen. 2005. Accumulators from Bilinear Pairings and Applications. In Topics in Cryptology -- CT-RSA 2005, Alfred Menezes (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 275--292.
[66]
Valeria Nikolaenko, Sam Ragsdale, Joseph Bonneau, and Dan Boneh. 2022. Powers-of-Tau to the People: Decentralizing Setup Ceremonies. Cryptology ePrint Archive, Report 2022/1592. https://eprint.iacr.org/2022/1592.
[67]
Drand Organization. 2020. Drand - A Distributed Randomness Beacon Daemon. GitHub repository. https://github.com/drand/drand
[68]
Torben P. Pedersen. 1992. Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing. 129--140. https://doi.org/10.1007/3--540--46766--1_9
[69]
Irving S Reed and Gustave Solomon. 1960. Polynomial codes over certain finite fields. Journal of the society for industrial and applied mathematics 8, 2 (1960), 300--304.
[70]
Yumi Sakemi, Tetsutaro Kobayashi, Tsunekazu Saito, and Riad S. Wahby. 2022. Internet Research Task Force (IRTF) Draft for Pairing-Friendly Curves. https: //datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/
[71]
Philipp Schindler, Aljosha Judmayer, Markus Hittmeir, Nicholas Stifter, and Edgar R. Weippl. 2021. RandRunner: Distributed Randomness from Trapdoor VDFs with Strong Uniqueness.
[72]
Philipp Schindler, Aljosha Judmayer, Nicholas Stifter, and Edgar R. Weippl. 2020. HydRand: Efficient Continuous Distributed Randomness. 73--89. https://doi.org/ 10.1109/SP40000.2020.00003
[73]
Nibesh Shrestha. 2022. Implementation for OptRand. Github. https://github. com/nibeshrestha/optrand/tree/crypto_dev
[74]
Nibesh Shrestha, Adithya Bhat, Aniket Kate, and Kartik Nayak. 2021. Synchronous Distributed Key Generation without Broadcasts. Cryptology ePrint Archive, Report 2021/1635. https://eprint.iacr.org/2021/1635.
[75]
Markus Stadler. 1996. Publicly Verifiable Secret Sharing. 190--199. https://doi. org/10.1007/3--540--68339--9_17
[76]
Ewa Syta, Philipp Jovanovic, Eleftherios Kokoris-Kogias, Nicolas Gailly, Linus Gasser, Ismail Khoffi, Michael J. Fischer, and Bryan Ford. 2017. Scalable Bias-Resistant Distributed Randomness. 444--460. https://doi.org/10.1109/SP.2017.45
[77]
Alin Tomescu, Robert Chen, Yiming Zheng, Ittai Abraham, Benny Pinkas, Guy Golan-Gueta, and Srinivas Devadas. 2020. Towards Scalable Threshold Cryptosystems. 877--893. https://doi.org/10.1109/SP40000.2020.00059
[78]
Maofan Yin, Dahlia Malkhi, Michael K. Reiter, Guy Golan-Gueta, and Ittai Abraham. 2019. HotStuff: BFT Consensus with Linearity and Responsiveness. 347--356. https://doi.org/10.1145/3293611.3331591
Index Terms
- GRandLine: Adaptively Secure DKG and Randomness Beacon with (Log-)Quadratic Communication Complexity
Recommendations
Two-Round Adaptively Secure Multiparty Computation from Standard Assumptions
Theory of CryptographyAbstractWe present the first two-round multiparty computation (MPC) protocols secure against malicious adaptive corruption in the common reference string (CRS) model, based on DDH, LWE, or QR. Prior two-round adaptively secure protocols were known only in ...
Adaptively Secure (Aggregatable) PVSS and Application to Distributed Randomness Beacons
CCS '23: Proceedings of the 2023 ACM SIGSAC Conference on Computer and Communications SecurityPublicly Verifiable Secret Sharing (PVSS) is a fundamental primitive that allows to share a secret S among n parties via a publicly verifiable transcript T. Existing (efficient) PVSS are only proven secure against static adversaries who must choose who ...
Adaptively Secure MPC with Sublinear Communication Complexity
AbstractA central challenge in the study of MPC is to balance between security guarantees, hardness assumptions, and resources required for the protocol. In this work, we study the cost of tolerating adaptive corruptions in MPC protocols under various ...
Comments
Information & Contributors
Information
Published In
December 2024
5188 pages
ISBN:9798400706363
DOI:10.1145/3658644
- General Chairs:
- Bo Luo,
- Xiaojing Liao,
- Jun Xu,
- Program Chairs:
- Engin Kirda,
- David Lie
Copyright © 2024 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
Sponsors
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 09 December 2024
Check for updates
Author Tags
Qualifiers
- Research-article
Funding Sources
Conference
CCS '24
Sponsor:
CCS '24: ACM SIGSAC Conference on Computer and Communications Security
October 14 - 18, 2024
UT, Salt Lake City, USA
Acceptance Rates
Overall Acceptance Rate 1,261 of 6,999 submissions, 18%
Upcoming Conference
CCS '25
- Sponsor:
- sigsac
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 177Total Downloads
- Downloads (Last 12 months)177
- Downloads (Last 6 weeks)79
Reflects downloads up to 07 Mar 2025
Other Metrics
Citations
Cited By
View all- Applebaum BPinkas B(2024)Distributing Keys and Random Secrets with Constant ComplexityTheory of Cryptography10.1007/978-3-031-78023-3_16(485-516)Online publication date: 2-Dec-2024
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in