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CHURP: Dynamic-Committee Proactive Secret Sharing

Authors:

Sai Krishna Deepak Maram,

Dawn SongAuthors Info & Claims

CCS '19: Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security

Pages 2369 - 2386

https://doi.org/10.1145/3319535.3363203

Published: 06 November 2019 Publication History

Abstract

We introduce CHURP (CHUrn-Robust Proactive secret sharing). CHURP enables secure secret-sharing in dynamic settings, where the committee of nodes storing a secret changes over time. Designed for blockchains, CHURP has lower communication complexity than previous schemes: $O(n)$ on-chain and $O(n^2)$ off-chain in the optimistic case of no node failures. CHURP includes several technical innovations: An efficient new proactivization scheme of independent interest, a technique (using asymmetric bivariate polynomials) for efficiently changing secret-sharing thresholds, and a hedge against setup failures in an efficient polynomial commitment scheme. We also introduce a general new technique for inexpensive off-chain communication across the peer-to-peer networks of permissionless blockchains. We formally prove the security of CHURP, report on an implementation, and present performance measurements.

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References

[1]

Yazin Akkawi. 21 Dec. 2017. Bitcoin's Most Pressing Issue Summarized in Two Letters: UX. Inc. ( 21 Dec. 2017).

[2]

Brian Armstrong. Feb. 25, 2018. Coinbase is not a wallet. https://blog.coinbase.com/coinbase-is-not-a-wallet-b5b9293ca0e7.

[3]

Avi Asayag, Gad Cohen, Ido Grayevsky, Maya Leshkowitz, Ori Rottenstreich, Ronen Tamari, and David Yakira. 2018. Helix: a scalable and fair consensus algorithm. Technical Report. Technical report, Orbs Research.

[4]

Michael Backes, Amit Datta, and Aniket Kate. 2013. Asynchronous computational VSS with reduced communication complexity. In CT-RSA. Springer.

[5]

Joshua Baron, Karim El Defrawy, Joshua Lampkins, and Rafail Ostrovsky. 2015. Communication-optimal proactive secret sharing for dynamic groups. In ACNS.

[6]

Mihir Bellare, Zvika Brakerski, Moni Naor, Thomas Ristenpart, Gil Segev, Hovav Shacham, and Scott Yilek. 2009. Hedged public-key encryption: How to protect against bad randomness. In ASIACRYPT. Springer, 232--249.

[7]

Michael Ben-Or, Shafi Goldwasser, and Avi Wigderson. 1988. Completeness theorems for non-cryptographic fault-tolerant distributed computation. In ACM TOCS.

[8]

Joseph Bonneau, Jeremy Clark, and Steven Goldfeder. 2015. On Bitcoin as a public randomness source. IACR ePrint Archive, Vol. 2015 (2015), 1015.

[9]

Kevin D Bowers, Ari Juels, and Alina Oprea. 2009. HAIL: A high-availability and integrity layer for cloud storage. In 16th ACM CCS.

Digital Library

[10]

Christian Cachin, Klaus Kursawe, Anna Lysyanskaya, and Reto Strobl. 2002. Asynchronous verifiable secret sharing and proactive cryptosystems. In ACM CCS.

[11]

Miguel Castro and Barbara Liskov. 2002. Practical Byzantine fault tolerance and proactive recovery. ACM TOCS (2002).

[12]

Raymond Cheng, Fan Zhang, Jernej Kos, Warren He, Nicholas Hynes, Noah Johnson, Ari Juels, Andrew Miller, and Dawn Song. 2019. Ekiden: A Platform for Confidentiality-Preserving, Trustworthy, and Performant Smart Contracts. In 2019 IEEE EuroS&P.

[13]

Ronald Cramer, Rosario Gennaro, and Berry Schoenmakers. 1997. A secure and optimally efficient multi-authority election scheme. ETT (1997).

[14]

Phil Daian, Rafael Pass, and Elaine Shi. 2016. Snow White: Provably Secure Proofs of Stake. Cryptology ePrint Archive, Report 2016/919.

[15]

Ivan Damgård, Yuval Ishai, Mikkel Krøigaard, Jesper Buus Nielsen, and Adam Smith. 2008. Scalable multiparty computation with nearly optimal work and resilience. In CRYPTO. Springer, 241--261.

[16]

Yvo Desmedt and Yair Frankel. 1991. Shared generation of authenticators and signatures. In CRYPTO.

[17]

Yvo Desmedt and Sushil Jajodia. 1997. Redistributing secret shares to new access structures and its applications. Technical Report.

[18]

Yvo Desmedt and Kirill Morozov. 2015. Parity check based redistribution of secret shares. In ISIT.

[19]

Shlomi Dolev, Juan Garay, Niv Gilboa, and Vladimir Kolesnikov. 2009. Swarming secrets.

[20]

Michael Egorov, MacLane Wilkison, and David Nu nez. 2017. Nucypher KMS: decentralized key management system. arXiv preprint arXiv:1707.06140 (2017).

[21]

Ethereum. [n.d.] a. Devp2p. https://github.com/ethereum/devp2p

[22]

Ethereum. [n.d.] b. Whisper. https://github.com/ethereum/wiki/wiki/Whisper

[23]

Paul Feldman. 1987. A practical scheme for non-interactive verifiable secret sharing. In FOCS.

[24]

Pesech Feldman and Silvio Micali. 1997. An optimal probabilistic protocol for synchronous Byzantine agreement. SIAM J. Comput. (1997).

[25]

Yair Frankel, Peter Gemmell, Philip D MacKenzie, and Moti Yung. 1997 a. Optimal-resilience proactive public-key cryptosystems. In FOCS.

[26]

Yair Frankel, Peter Gemmell, Philip D MacKenzie, and Moti Yung. 1997 b. Proactive rsa. In CRYPTO.

[27]

frontrun.me. [n.d.]. Visualizing Ethereum gas auctions. http://frontrun.me/.

[28]

Georg Fuchsbauer. 2018. Subversion-zero-knowledge SNARKs. In IACR International Workshop on Public Key Cryptography. Springer, 315--347.

[29]

Rosario Gennaro, Stanisław Jarecki, Hugo Krawczyk, and Tal Rabin. 1996. Robust threshold DSS signatures. In EUROCRYPT.

[30]

Rosario Gennaro, Stanisław Jarecki, Hugo Krawczyk, and Tal Rabin. 1999. Secure distributed key generation for discrete-log based cryptosystems. In EUROCRYPT.

[31]

Rosario Gennaro, Michael O Rabin, and Tal Rabin. [n.d.]. Simplified VSS and fast-track multiparty computations with applications to threshold cryptography.

[32]

geth. [n.d.]. The maximum data size in a transaction is 32 KB. https://github.com/ethereum/go-ethereum/blob/6a33954731658667056466bf7573ed1c397f4750/core/tx_pool.go#L570.

[33]

Yossi Gilad, Rotem Hemo, Silvio Micali, Georgios Vlachos, and Nickolai Zeldovich. 2017. Algorand: Scaling Byzantine Agreements for Cryptocurrencies. In SOSP.

Digital Library

[34]

Jens Groth. 2010. Short pairing-based non-interactive zero-knowledge arguments. In ASIACRYPT.

[35]

Amir Herzberg. 2009. Folklore, practice and theory of robust combiners. Journal of Computer Security, Vol. 17, 2 (2009), 159--189.

[36]

Amir Herzberg, Markus Jakobsson, Stanislław Jarecki, Hugo Krawczyk, and Moti Yung. 1997. Proactive public key and signature systems. In ACM CCS.

[37]

Amir Herzberg, Stanisław Jarecki, Hugo Krawczyk, and Moti Yung. 1995. Proactive secret sharing or: How to cope with perpetual leakage. In CRYPTO.

[38]

Aniket Kate, Gregory M Zaverucha, and Ian Goldberg. 2010. Constant-size commitments to polynomials and their applications. In ASIACRYPT.

[39]

Aggelos Kiayias, Alexander Russell, Bernardo David, and Roman Oliynykov. 2017. Ouroboros: A provably secure proof-of-stake blockchain protocol. In CRYPTO.

[40]

Eleftherios Kokoris-Kogias, Enis Ceyhun Alp, Sandra Deepthy Siby, Nicolas Gailly, Linus Gasser, Philipp Jovanovic, Ewa Syta, and Bryan Ford. 2018. CALYPSO: Auditable Sharing of Private Data over Blockchains. Cryptology ePrint Archive.

[41]

A. Kosba, A. Miller, E. Shi, Z. Wen, and C. Papamanthou. 2016. Hawk: The Blockchain Model of Cryptography and Privacy-Preserving Smart Contracts. In IEEE S&P.

[42]

Haiyun Luo, Petros Zerfos, Jiejun Kong, Songwu Lu, and Lixia Zhang. 2002. Self-Securing Ad Hoc Wireless Networks. In ISCC.

[43]

Sai Krishna Deepak Maram, Fan Zhang, Lun Wang, Andrew Low, Yupeng Zhang, Ari Juels, and Dawn Song. 2019. CHURP: Dynamic-Committee Proactive Secret Sharing. https://eprint.iacr.org/2019/017.

[44]

Ventzislav Nikov and Svetla Nikova. 2004. On proactive secret sharing schemes. In International Workshop on Selected Areas in Cryptography.

Digital Library

[45]

John P. Njui. [n.d.]. Coinbase Custody Service Secures Major Institutional Investor Worth $20 Billion. Ethereum World News ( [n.,d.]).

[46]

Mehrdad Nojoumian and Douglas R Stinson. 2013. On dealer-free dynamic threshold schemes. Adv. in Math. of Comm. (2013).

[47]

Mehrdad Nojoumian, Douglas R Stinson, and Morgan Grainger. 2010. Unconditionally secure social secret sharing scheme. IET information security (2010).

[48]

Rafail Ostrovsky and Moti Yung. 1991. How to withstand mobile virus attacks. In ACM PODC.

[49]

Parity. [n.d.]. Transaction Queue. https://wiki.parity.io/Transactions-Queue.

[50]

Rafael Pass, Lior Seeman, and Abhi Shelat. 2017. Analysis of the blockchain protocol in asynchronous networks. In EUROCRYPT. Springer, 643--673.

[51]

Rafael Pass and Elaine Shi. 2018. Thunderella: Blockchains with Optimistic Instant Confirmation. In EUROCRYPT.

[52]

Torben Pryds Pedersen. 1991. Non-interactive and information-theoretic secure verifiable secret sharing. In CRYPTO.

[53]

Bartosz Przydatek and Reto Strobl. 2004. Asynchronous proactive cryptosystems without agreement. In ASIACRYPT. Springer, 152--169.

[54]

Michael O Rabin. 1983. Randomized byzantine generals. In FOCS.

[55]

Tal Rabin. 1998. A simplified approach to threshold and proactive RSA. In CRYPTO.

[56]

Jeff John Roberts and Nicolas Rapp. 2017. Exclusive: Nearly 4 Million Bitcoins Lost Forever, New Study Says. http://fortune.com/2017/11/25/lost-bitcoins/

[57]

Nitesh Saxena, Gene Tsudik, and Jeong Hyun Yi. 2005. Efficient node admission for short-lived mobile ad hoc networks. In 13th ICNP.

[58]

Berry Schoenmakers, Meilof Veeningen, and Niels de Vreede. 2016. Trinocchio: privacy-preserving outsourcing by distributed verifiable computation. In ACNS.

[59]

David A Schultz, Barbara Liskov, and Moses Liskov. 2008. Mobile proactive secret sharing. In ACM PODC.

[60]

Adi Shamir. 1979. How to share a secret. Commun. ACM (1979).

[61]

Douglas R Stinson and Ruizhong Wei. 1999. Unconditionally secure proactive secret sharing scheme with combinatorial structures. In SAC.

[62]

Paul Syverson, R Dingledine, and N Mathewson. 2004. Tor: The secondgeneration onion router. In Usenix Security.

Digital Library

[63]

Tamir Tassa and Nira Dyn. 2009. Multipartite secret sharing by bivariate interpolation. Journal of Cryptology (2009).

[64]

Theodore M Wong, Chenxi Wang, and Jeannette M Wing. 2002. Verifiable secret redistribution for archive systems. In the 1st Security in Storage Workshop.

[65]

Fan Zhang, Philip Daian, Gabriel Kaptchuk, Iddo Bentov, Ian Miers, and Ari Juels. 2018. Paralysis Proofs: Secure Access-Structure Updates for Cryptocurrencies and More. Cryptology ePrint Archive, Report 2018/096.

[66]

Lidong Zhou, Fred B Schneider, and Robbert Van Renesse. 2005. APSS: Proactive secret sharing in asynchronous systems. ACM TISSEC (2005).

Digital Library

[67]

Guy Zyskind, Oz Nathan, et al. 2015. Decentralizing privacy: Using blockchain to protect personal data. In Security and Privacy Workshops.

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Index Terms

CHURP: Dynamic-Committee Proactive Secret Sharing
1. Security and privacy
  1. Cryptography
    1. Key management
2. Theory of computation
  1. Computational complexity and cryptography
    1. Cryptographic protocols

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cover image ACM Conferences

CCS '19: Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security

November 2019

2755 pages

ISBN:9781450367479

DOI:10.1145/3319535

General Chairs:
Lorenzo Cavallaro
King's College London, UK
,
Johannes Kinder
Bundeswehr University Munich, Germany
,
Program Chairs:
XiaoFeng Wang
Indiana University, USA
,
Jonathan Katz
George Mason University, USA

Copyright © 2019 ACM.

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Published: 06 November 2019

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CCS '19: 2019 ACM SIGSAC Conference on Computer and Communications Security

November 11 - 15, 2019

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CCS '19 Paper Acceptance Rate 149 of 934 submissions, 16%;

Overall Acceptance Rate 1,261 of 6,999 submissions, 18%

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Cited By

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https://dl.acm.org/doi/10.1145/3634737.3661142
Guo YXi YWang HWang MWang CJia X(2024)FedEDB: Building a Federated and Encrypted Data Store via Consortium BlockchainsIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2023.334114936:11(6210-6224)Online publication date: Nov-2024
https://doi.org/10.1109/TKDE.2023.3341149
Wang WWang LDuan JTong XPeng H(2024)Redactable Blockchain Based on Decentralized Trapdoor Verifiable Delay FunctionsIEEE Transactions on Information Forensics and Security10.1109/TIFS.2024.343191719(7492-7507)Online publication date: 2024
https://doi.org/10.1109/TIFS.2024.3431917
Tian YLiu BLi YSzalachowski PZhou J(2024)Accountable Fine-Grained Blockchain Rewriting in the Permissionless SettingIEEE Transactions on Information Forensics and Security10.1109/TIFS.2023.334091719(1756-1766)Online publication date: 2024
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Chen HZhang L(2024)A Dynamic Proactive Secret Sharing Scheme for Quadratic FunctionsIEEE Access10.1109/ACCESS.2024.336668812(25749-25761)Online publication date: 2024
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Shiriaev EKucherov NMovzalevskaya VKhamidov M(2024)Modification and Adaptation of Methods and Algorithms of the Active Security Concept for Fog SystemsAISMA-2024: International Workshop on Advanced Information Security Management and Applications10.1007/978-3-031-72171-7_28(277-285)Online publication date: 16-Oct-2024
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