Abstract
We prove Bitcoin is secure under temporary dishonest majority. We assume the adversary can corrupt a specific fraction of parties and also introduce crash failures, i.e., some honest participants are offline during the execution of the protocol. We demand a majority of honest online participants on expectation. We explore three different models and present the requirements for proving Bitcoin’s security in all of them: we first examine a synchronous model, then extend to a bounded delay model and last we consider a synchronous model that allows message losses.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The Chain-Growth Property in [7] is defined slightly different: ...it holds that for any s rounds, there are at least \(\tau \cdot s\) blocks added to the chain of P. Considering the proof for Theorem 1 (of [2]), one can see, why we use \(s+1\) instead of s. It follows by the fact that the sum in Lemma 13 (of [2]) only goes from \(i=r\) to \(s-1\) and not to s.
- 2.
- 3.
According to Theorem 11 of [12], the parameter \(\varDelta \) has to be known by the honest parties to achieve state machine replication, e.g. achieving consensus.
- 4.
One might notice that our lower bound of \(\delta \) differs from the lower bound from [7]. First of all, they provided two different values for \(\delta \), where both of them are wrong in the sense that they are too small in order to prove the needed bounds.
- 5.
Note that \(\delta \) is dependent on \(E[X_i]\), which is again dependent on s. If we would remove this dependency, the results would be at most 2% better than the actual results shown in Fig. 1.
References
Apostolaki, M., Zohar, A., Vanbever, L.: Hijacking bitcoin: routing attacks on cryptocurrencies. In: 2017 IEEE Symposium on Security and Privacy, SP 2017, San Jose, CA, USA, 22–26 May 2017, pp. 375–392 (2017)
Avarikioti, G., Käppeli, L., Wang, Y., Wattenhofer, R.: Bitcoin Security under Temporary Dishonest Majority (2019)
Bonneau, J.: Hostile blockchain takeovers (short paper). In: Bitcoin’18: Proceedings of the 5th Workshop on Bitcoin and Blockchain Research (2018)
Decker, C., Wattenhofer, R.: Information propagation in the bitcoin network. In: IEEE P2P 2013 Proceedings, September 2013
Eyal, I.: The miner’s dilemma. In: 2015 IEEE Symposium on Security and Privacy, SP 2015, San Jose, CA, USA, 17–21 May 2015, pp. 89–103 (2015)
Eyal, I., Sirer, E.G.: Majority is not enough: bitcoin mining is vulnerable. Commun. ACM 61(7), 95–102 (2013)
Garay, J., Kiayias, A., Leonardos, N.: The bitcoin backbone protocol: analysis and applications. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 281–310. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_10
Heilman, E., Kendler, A., Zohar, A., Goldberg, S.: Eclipse attacks on bitcoin’s peer-to-peer network. In: Proceedings of the 24th USENIX Conference on Security Symposium, SEC 2015, pp. 129–144. USENIX Association, Berkeley (2015)
Kwon, Y., Kim, D., Son, Y., Vasserman, E.Y., Kim, Y.: Be selfish and avoid dilemmas: fork after withholding (FAW) attacks on bitcoin. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, CCS 2017, Dallas, TX, USA, 30 October–03 November 2017, pp. 195–209 (2017)
Nakamoto, S.: Bitcoin: A peer-to-peer electronic cash system, October 2008. https://bitcoin.org/bitcoin.pdf
Nayak, K., Kumar, S., Miller, A., Shi, E.: Stubborn mining: generalizing selfish mining and combining with an eclipse attack. In: 2016 IEEE European Symposium on Security and Privacy (EuroS&P), pp. 305–320 (2015)
Pass, R., Shi, E.: The sleepy model of consensus. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10625, pp. 380–409. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70697-9_14
Sapirshtein, A., Sompolinsky, Y., Zohar, A.: Optimal selfish mining strategies in bitcoin. In: Grossklags, J., Preneel, B. (eds.) FC 2016. LNCS, vol. 9603, pp. 515–532. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54970-4_30
Singh, A., Ngan, T.W.J., Druschel, P., Wallach, D.S.: Eclipse attacks on overlay networks: threats and defenses. In: IEEE INFOCOM 2006, April 2006
Sit, E., Morris, R.: Security considerations for peer-to-peer distributed hash tables. In: Druschel, P., Kaashoek, F., Rowstron, A. (eds.) IPTPS 2002. LNCS, vol. 2429, pp. 261–269. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45748-8_25
Acknowledgments
We thank Dionysis Zindros for the helpful and productive discussions. Y. W. is partially supported by X-Order Lab.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 International Financial Cryptography Association
About this paper
Cite this paper
Avarikioti, G., Käppeli, L., Wang, Y., Wattenhofer, R. (2019). Bitcoin Security Under Temporary Dishonest Majority. In: Goldberg, I., Moore, T. (eds) Financial Cryptography and Data Security. FC 2019. Lecture Notes in Computer Science(), vol 11598. Springer, Cham. https://doi.org/10.1007/978-3-030-32101-7_28
Download citation
DOI: https://doi.org/10.1007/978-3-030-32101-7_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32100-0
Online ISBN: 978-3-030-32101-7
eBook Packages: Computer ScienceComputer Science (R0)