COMPARISON OF BLOCK EXPECTATION TIME FOR VARIOUS CONSENSUS ALGORITHMS
Keywords:blockchain, Bitcoin, proof-of-work, GHOST, proof-of-stake, Ouroboros
AbstractContext. We consider security properties of decentralized blockchain-based consensus protocols. The object of research is block
confirmation time for users to get assurance that their transaction will not be reverted.
Objective. The goal of the paper is to analyze double-spend attacks on the different blockchain-based systems and compare
resulting probabilities of attacker’s success.
Method. We presented two models for two types of attacks on the Ouroboros protocol (for the general and covert adversaries).
The models allow calculating the exact number of slots needed to achieve the required level of security. It was shown that the
Ouroboros protocol allows achieving the required security level with significantly shorter confirmation period in comparison with
Bitcoin. We estimated minimal number of confirmation blocks and compare estimation time for Bitcoin, GHOST and Ouroboros
protocols. As a measure of comparison, we considered transaction confirmation time for which the probability of a double-spend
attack is less than 0.1%. We use different standard probability distribution and different properties of Markov chains and Random
Walks to get comparison of estimated security properties of Bitcoin blockchain against three different models of Bitcoin double
spend attack. The splitting attack based on the model where resources of honest participants are divided to compete different chains
is applied to Bitcoin and GHOST consensus protocols. Properties of Markov chains and Random Walks are also applied to obtain
security estimations for the Ouroboros protocol.
Results. We developed methods to get specific numbers for average block confirmation time for Ouroboros protocol. We
compared minimal number of confirmation blocks needed to ensure a high security for considered protocols: Bitcoin, GHOST and
Conclusions. The obtained results allow determination of security bounds for the Bitcoin, GHOST and Ouroboros consensus
protocols. Users of the practically deployed blockchain systems may get specific parameters for a given assurance level.
Kiayias A. Ouroboros: A provably secure proof-of-stake blockchain protocol [Electronic resource], Cryptology ePrint Archive. Electronic data. [International Association for Cryptologic Research, 2016]. Mode of access:
http://eprint.iacr.org/2016/889 (viewed on May 13, 2018). Title from the screen.
Nakamoto S. A. peer-to-peer electronic cash system”
[Electronic resource], Bitcoin. Electronic data, 2008. Mode
of access: https: //bitcoin.org/bitcoin.pdf (viewed on May
, 2018). Title from the screen.
Sompolinsky Y., Zohar Aviv Accelerating bitcoin as
transaction processing. Fast money grows on trees, not
chains [Electronic resource], Cryptology ePrint Archive.
Electronic data. [International Association for Cryptologic
Research, 2013]. Mode of access:
http://eprint.iacr.org/2013/881 (viewed on May 13, 2018). Title from the screen.
Pinzon C., Rocha C. Double-Spend Attack Models with
Time Advantage for Bitcoin, Electronic Notes in Theoretical Computer Science, 2016, Vol. 329, pp. 79–103.
Rosenfeld M. Analysis of hashrate-based double-spending races [Electronic resource], Preprint arXiv. Electronic data, [Cornell: Cornell University, 2017], Mode of access:
https://arxiv.org/abs/1402.2009 (viewed on May 13, 2018). Title from the screen.
Grunspan C., Pérez-Marco R. Double spend races
[Electronic resource], Preprint arXiv. Electronic data,
[Cornell: Cornell University, 2017]. Mode of access:
https://arxiv.org/abs/1702.02867.pdf (viewed on May 13, 2018). Title from the screen.
Kiayias A., Panagiotakos G. Speed-security tradeoffs in blockchain protocols [Electronic resource] / A. Kiayias, // Electronic data. – [International Association for Cryptologic Research, Cryptology ePrint Archive, 2015]. – Mode of access: http://eprint.iacr.org/2015/1019 (viewed on May 13,
. Title from the screen.
Double-spending [Electronic resource], BitcoinWiki. Mode of access: https://en.bitcoin.it/wiki/Double-spending (viewed on May 13, 2018). Title from the screen.
Garay J. A. Kiayias Aggelos, and Leonardos Nikos The
Bitcoin Backbone Protocol: Analysis and Applications”,
Advances in Cryptology, EUROCRYPT 2015, 34th Annual
International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, April 26–30, 2015: proceedings. Berlin, Springer, 2017. Part II, pp. 281– 310. DOI: 10.1007/978-3-662-46803-6_10.
Decker C., Wattenhofer R. Information Propagation in the Bitcoin Net-work, Peer-to-Peer Computing: IEEE
International Conference on Peer-to-Peer Computing (P2P), Trento, Italy, September 9–11, 2013, proceedings. Trento, IEEE Xplore, 2013, pp. 1–10. DOI:
Sompolinsky Y., Zohar A. Secure high-rate transaction processing in Bitcoin, Financial Cryptography and Data Security – 19th International Conference, FC 2015, San Juan, Puerto Rico, January 26–30, 2015: proceedings. Berlin, Springer, Lecture Notes in Computer Science, 2004, Vol. 8975, pp. 507–527. DOI: 0.1007/978-3-662-47854-7_32.
Schoenmakers B. A simple publicly verifiable secret sharing scheme and its application to electronic voting, Advances in Cryptology – CRYPTO 99, 19th Annual International Cryptology Conference, Santa Barbara, California, USA, August 15–19, 1999: proceedings. – Berlin: Springer, 1999,
Volume 1666 of Lecture Notes in Computer Science,
Russel A. Forkable Strings are Rare [Electronic resource], Cryptology ePrint Archive. Electronic data. [International Association for Cryptologic Research, 2017]. Mode of access: http://eprint.iacr.org/2017/241 (viewed on May 13, 2018). Title from the screen.
Feller W. An Introduction to Probability Theory and its Applications. New York: John Wiley & Sons, 1970, 700 p. DOI: 10.1137/1014119
How to Cite
Copyright (c) 2019 D. S. Kaidalov, L. V. Kovalchuk, A. O. Nastenko, M. Yu. Rodinko, O. V. Shevtsov, R. V. Oliynykov
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.
The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.
The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.