Refinement of estimates of the success probability of a double-spend attack on the Blockchain System, Based on the Independent Players Model
Keywords:double spend attack, blockchain technology, consensus protocols, decentralized systems
Blockchain technology is being studied in many innovative applications, such as: cryptocurrencies, smart contracts, communication systems, healthcare, Internet of Things, financial systems, software development, electronic voting and many others. Using a transparent and fully distributed peer-to-peer blockchain architecture, applications benefit from a data-only model, in which “transactions” are accepted into the blockchain ledger and, if the system is functioning properly, cannot be modified or deleted. The transparency of blockchain systems makes it possible to store publicly available and irrefutable records. A peer-to-peer blockchain system provides verifiable ledger maintenance without centralized management, which solves the problems of a single point of failure and a single point of trust. The article deals with the issue of the security of application of accounting systems built on decentralized principles using blockchain technology. Particular attention is paid to the problem of the possibility of double spending in such accounting systems. The article exemplifies the reorganization of records in blockchain ledgers, performed by successfully carrying out a 51% attack on consensus algorithms based on proof of work. Given refinement of analytical expressions of 51% attack probability obtained in the works of S. Nakamoto and M. Rosenfeld using a more general model, namely, the model of independent players, where the probability of block formation by attackers and an honest network are independent events. The results of comparing of the success probability of a double-spending attack on the blockchain systems calculated according to different models are presented.
Saad M., Spaulding J., Njilla L., Kamhoua C.,Shetty S., Nyang D., Mohaisen A. Exploring the Attack Surface of Blockchain: A Systematic Overview. (2019) https://www.researchgate.net/publication/331806569_Overview_of_Attack_Surfaces_in_Blockchain
L. Mauri, S. Cimato, and E. Damiani. A comparative analysisof current cryptocurrencies // Proceedings of the 4th InternationalConference on Information Systems Security and Privacy, ICISSP, Funchal, Madeira – Portugal, Jan. 2018, pp. 127–138. https://doi.org/10.5220/0006648801270138
G. Danezis and S. Meiklejohn. Centrally banked cryptocurrencies // Proceedings of the 2016 Annual Network and Distributed SystemSecurity Symposium (NDSS), San Diego, CA, Feb. 2016. http://wp.internetsociety.org/ndss/wp-content/uploads/sites/25/2017/09/centrally-banked-cryptocurrencies.pdf
J. Bonneau, A. Miller, J. Clark, A. Narayanan, J. A. Kroll, andE. W. Felten. Research perspectives and challenges for bitcoin andcryptocurrencies // IACR Cryptology ePrint Archive, vol. 2015, p. 261, 2015. http://eprint.iacr.org/2015/261
A. E. Kosba, A. Miller, E. Shi, Z. Wen, and C. Papamanthou Hawk:The blockchain model of cryptography and privacy-preserving smartcontracts // Proceedings of the 37th IEEE Symposium on Securityand Privacy (Oakland), San Jose, CA, May 2016, pp. 839–858. https://doi.org/10.1109/SP.2016.55
K. Bhargavan, A. Delignat-Lavaud, C. Fournet, A. Gollamudi,G. Gonthier, N. Kobeissi, N. Kulatova, A. Rastogi, T. Sibut-Pinote, N. Swamy, and S. Z. Béguelin. Formal veriﬁcationof smart contracts: Short paper // Pro-ceedings of the 23rdACM Conference on Computer and Communications Security(CCS), Vienna, Austria, Oct. 2016, pp. 91–96. http://doi.acm.org/10.1145/2993600.2993611
P. K. Sharma, S. Rathore, and J. H. Park. Distarch-scnet: Blockchain-based distributed architecture with li-fi communication for a scalable smart city network // IEEE Consumer Electronics Magazine, vol. 7, no. 4, pp. 55–64, 2018. Available: https://doi.org/10.1109/MCE.2018.2816745
K. Fan, Y. Ren, Y. Wang, H. Li, and Y. Yang. Blockchain-based efficient privacy preserving and data sharing scheme of content-centric network in 5g // IET Communications, vol. 12, no. 5, pp. 527–532, 2018. Available: https://doi.org/10.1049/iet-com.2017.0619
Sharma P.K., Singh S., Jeong Y.-S., Park J.H. DistBlockNet: A Distributed Blockchains-Based Secure SDN Architecture for IoT Networks // IEEE Communications Magazine, 2017, vol. 55 (9), pp. 78–85
R. Guo, H. Shi, Q. Zhao, and D. Zheng. Secure attribute-based signature scheme with multiple authorities for blockchain in electronic health records systems // IEEE Access, vol. 6, pp. 11 676–11 686, 2018. Available: https://doi.org/10.1109/ACCESS.2018.2801266
D. Rakic. Blockchain technology in healthcare // Proceedings of the 4th International Conference on Information and Communication Technologies for Ageing Well and e-Health, Funchal, Madeira, Portugal, March 2018., pp. 13–20. Available: https://doi.org/10.5220/0006531600130020
A. Ekblaw, A. Azaria, J. D. Halamka, A. Lippman. A case study for blockchain in healthcare: “medrec” prototype for electronic health records and medical research data (2016). URL https://www.media.mit.edu/publications/medrec-whitepaper/
A. Azaria, A. Ekblaw, T. Vieira, A. Lippman. Medrec: Using blockchain for medical data access and permission management // International Conference on Open and Big Data (OBD), 2016, pp. 25-30.
Yue, H. Wang, D. Jin, M. Li, W. Jiang. Healthcare data gateways: Found healthcare intelligence on blockchain with novel privacy risk control // Journal of medical systems, 2016, p. 218
E. F. Jesus, V. R. L. Chicarino, C. V. N. de Albuquerque, and A. A. de A. Rocha. A survey of how to use blockchain to secure internet of things and the stalker attack // Security and Communication Networks, vol. 2018, pp. 9. 675 050:1–9 675 050:27, 2018. Available: https://doi.org/10.1155/2018/9675050
P. K. Sharma, S. Singh, Y. Jeong, and J. H. Park. Distblocknet: A distributed blockchains-based secure SDN architecture for iot networks // IEEE Communications Magazine, vol. 55, no. 9, pp. 78–85, 2017. Available: https://goo.gl/UBv1Sf
A. Dorri, S. S. Kanhere, R. Jurdak, P. Gauravaram. Blockchain for iot security and privacy: The case study of a smart home // IEEE Percom workshop on security privacy and trust in the internet of thing, 2017
Y. Zhang, J. Wen. The iot electric business model: Using blockchain technology for the internet of things // Peer-to-Peer Networking and Applications, 2016, pp. 1-12.
J. Sun, J. Yan, K. Z. Zhang, Blockchain-based sharing services: What blockchain technology can contribute to smart cities // Financial Innovation, 2016, p. 26.
H. Hyvärinen, M. Risius, and G. Friis. A blockchain-based approach towards overcoming financial fraud in public sector services // Business & Information Systems Engineering, vol. 59, no. 6, pp. 441–456, 2017. Available: https://doi.org/10.1007/s12599-017-0502-4
F. Holotiuk, F. Pisani, and J. Moormann. The impact of blockchain technology on business models in the payments industry // Towards Thought Leadership in Digital Transformation: 13. Internationale Tagung Wirtschaftsinformatik, St.Gallen, Switzerland, Feb, 2017. Available: http://aisel.aisnet.org/wi2017/track09/paper/6
S. Huckle, R. Bhattacharya, M. White, N. Beloff. Internet of things, blockchain and shared economy applications // Procedia Computer Science, Vol. 98, 2016, pp. 461-466.
P. Hurich, The virtual is real: An argument for characterizing bitcoins as private property // Banking & Finance Law Review, Vol. 31, Carswell Publishing, 2016, p. 573.
Xu, C. Pautasso, L. Zhu, V. Gramoli, A. Ponomarev, A. B. Tran, S. Chen. The blockchain as a software connector // The 13th Working IEEE/IFIP Conference on Software Architecture, 2016
E.Nordstr¨om., Personal clouds: Concedo, Masters thesis, Lulea University of Technology (2015).
J. S. Czepluch, N. Z. Lollike, S. O. Malone. The use of block chain technology in different application domains // The IT University of Copenhagen, Copenhagen, 2015.
G. G. Dagher, P. B. Marella, M. Milojkovic, and J. Mohler, Broncovote: Secure voting system using ethereum’s blockchain // Proceedings of the 4th International Conference on Information Systems Security and Privacy, ICISSP, Funchal, Madeira – Portugal, Jan 2018, pp. 96–107. Available: https://doi.org/10.5220/0006609700960107
F. S. Hardwick, R. N. Akram, and K. Markantonakis. E-voting with blockchain: An e-voting protocol with decentralisation and voter privacy // CoRR, vol. abs/1805.10258, 2018. Available: http://arxiv.org/abs/1805.10258
K.-H. Wang, S. K. Mondal, K. Chan, and X. Xie. A review of contemporary e-voting: Requirements, technology, systems and usability // Data Science and Pattern Recognition, vol. 1, no. 1, pp. 31–47, 2017
D. A. Gritzalis. Principles and requirements for a secure e-voting system // Computers & Security, vol. 21, no. 6, pp. 539–556, 2002
R. Anane, R. Freeland, and G. Theodoropoulos. E-voting requirements and implementation // The 9th IEEE CEC/EEE 2007. IEEE, 2007, pp. 382–392
A. Dorri, S. S. Kanhere, R. Jurdak, and P. Gauravaram.LSB: A lightweight scalable blockchain for IoT security and anonymity // J. Parallel Distrib. Comput., vol. 134, pp. 180–197, 2019
Arif S., Khan M.A., Rehman S.U., Kabir M.A. & Imran M. Investigating Smart Home Security: Is Blockchain the Answer? // IEEE Access, 2020, 8, 117802-117816
Younghun Lee, Shailendra Rathore, Jin Ho Park, Jong Hyuk Park. A blockchain-based smart home gateway architecture for preventing data forgery // Human-centric Computing and Information Sciences, 2020, Volume 10, Number 1, Page 1
PR Wire (2016) Gartner: blockchain and connected home are almost at the peak of the hype cycle. htt-ps://prwire.com.au/pr/62010/gartner-blockchain-andconnected-home-are-almost-at-the-peak-of-the-hype-cycle
J. DESJARDINS, Its official: Bitcoin was the top performing currency of 2015 (2016). URL http://money.visualcapitalist.com/its-official-bitcoin-was-the-top-performing-currency-of-2015/
J. Adinolfi, And 2016s best-performing commodity is ... bitcoin? (2016). URL http://www.marketwatch.com/story/and-2016s-best-performing-commodity-is-bitcoin-2016-12-22
Blockchain.info. Confirmed transactions per day (2020). URL https://blockchain.info/charts/n-transactions?timespan=all#
G. Zyskind, O. Nathan, and A. Pentland. Decentralizing privacy: Using blockchain to protect personal data // 2015 IEEE Symposium on Security and Privacy Workshops, SPW, San Jose, CA, USA, May 2015, pp. 180–184. Available: https://goo.gl/kTNim3
A. Back, M. Corallo, L. Dashjr, M. Friedenbach, G. Maxwell, A. Miller, A. Poelstra, J. Timón, and P. Wuille. Enabling blockchain innovations with pegged sidechains. 2014
G. Zyskind, O. Nathan, and A. Pentland. Enigma: Decentralized Computation Platform with Guaranteed Privacy, 2015. https://arxiv.org/abs/1506.03471
M. Swan. Blockchain thinking: The brain as a dac (decentralized autonomous organization) // Proceedings of the Texas Bitcoin Conferenc, pp. 27–29, 2015.
X. Li, P. Jiang, T. Chen, X. Luo, and Q. Wen. A survey on the security of blockchain systems // CoRR, vol. abs/1802.06993, 2018. Available: http://arxiv.org/abs/1802.06993
I.-C. Lin and T.-C. Liao. A survey of blockchain security issues and challenges // IJ Network Security, vol. 19, no. 5, pp. 653–659, 2017
N. Atzei, M. Bartoletti, T. Cimoli. A survey of attacks on Ethereum smart contracts sok // Proceedings of the 6th International Conference on Principles of Security and Trust -Volume 10204, 2017, pp. 164–186. Available: https://doi.org/10.1007/978-3-662-54455-6_8
M. C. K. Khalilov and A. Levi. A survey on anonymity and privacy in bitcoin-like digital cash systems // IEEE Communications Surveys and Tutorials, vol. 20, no. 3, pp. 2543–2585, 2018. Available: https://doi.org/10.1109/COMST.2018.2818623
D. Siegel. Understanding The DAO Attack. https://www.coindesk.com/understanding-dao-hack-journalists/
V. Buterin, Critical update re: Dao vulnerability (2016). URL https://blog.ethereum.org/2016/06/17/critical-update-re-dao-vulnerability/
M. Saad, M. T. Thai, and A. Mohaisen. POSTER: deterring ddos attacks on blockchain-based cryptocurrencies through mempool optimization // Proceedings of Asia Conference on Computer and Communications Security, ASIACCS, Incheon, Republic of Korea, Jun 2018, pp. 809–811. Available: https://goo.gl/4kgiCM
I. Eyal, A. E. Gencer, E. G. Sirer, and R. van Renesse. Bitcoin-ng: A scalable blockchain protocol // Proceedings of the 13th USENIX Symposium on Networked Systems Design and Implementation (NSDI), Santa Clara, CA, Mar. 2016, pp. 45–59. Available: https://goo.gl/VGN4yw
R. McMillan.The inside story of mt. gox, bitcoin’s 460 million usd disaster. 2014. Available: https://www.wired.com/2014/03/bitcoin-exchange/
J. Adelstein, Behind the biggest Bitcoin heist in history: Inside the implosion of mt.gox (2016). URL http://www.thedailybeast.com/articles/2016/05/19/behind-the-biggest-bitcoin-heist-in-history-inside-the-implosion-of-mt-gox.html
Irreversible Transactions https://en.bitcoin.it/wiki/Irreversible_Transactions.
Partz H. Bittrex to Delist Bitcoin Gold by Mid-September, Following $18 Million Hack of BTG in May. 04.09.2018 https://cointelegraph.com/news/bittrex-to-delist-bitcoin-gold-by-mid-september-following-18-million-hack-of-btg-in-may
Cimpanu C. Hacker Makes Over $18 Million in Double-Spend Attack on Bitcoin Gold Network 24.05.2018 https://www.bleepingcomputer.com/news/security/hacker-makes-over-18-million-in-double-spend-attack-on-bitcoin-gold-network/
Iskra E. Responding to Attacks 24.05.2018 https://bitcoingold.org/responding-to-attacks/
Wilmoth J. Spend Attack, Exchanges Lose Millions https://www.ccn.com/bitcoin-gold-hit-by-double-spend-attack-exchanges-lose-millions/
Martin J. Bitcoin Gold Blockchain Hit by 51% Attack Leading to $70K Double Spend 27.01.2020 https://cointelegraph.com/news/bitcoin-gold-blockchain-hit-by-51-attack-leading-to-70k-double-spend
Lovejoy J. Bitcoin Gold (BTG) was 51% attacked. 25.01.2020 https://gist.github.com/metalicjames/71321570a105940529e709651d0a9765
Coinbase: Deep Chain Reorganization Detected on Ethereum Classic (ETC) htt-ps://blog.coinbase.com/ethereum-classic-etc-is-currently-being-51-attacked-33be13ce32de
Bitfly (@etherchain_org) / Твиттер https://twitter.com/etherchain_org/status/1289489999004463111
HackMD: ETC Chain Split Diagnosis https://hackmd.io/@cUBb4hAvQciAEPoU2yfrzQ/Skd4X6MZw
Bitquery: Attacker Stole 807K ETC in Ethereum Classic 51% Attack https://blog.bitquery.io/attacker-stole-807k-etc-in-ethereum-classic-51-attack
Bitfly (@etherchain_org) / Твиттер https://twitter.com/etherchain_org/status/1291216063628226562
Binance (@binance) / Твиттер https://twitter.com/binance/status/1291225022866944000
Bitquery: Ethereum Classic Attack, 8 August: Catch me if you can https://blog.bitquery.io/ethereum-classic-attack-8-august-catch-me-if-you-can
Bitfly (@etherchain_org) / Твиттер https://twitter.com/etherchain_org/status/1299822510607917056
Ethereum Classic (@eth_classic) / Твиттер https://twitter.com/eth_classic/status/1299824170260340737
Wilmoth J. Privacy Coin Verge Succumbs to 51% Attack [Again] 22.05.2020 https://www.ccn.com/privacy-coin-verge-succumbs-to-51-attack-again/
Ville Savolainen, Jorge Soria Ruiz-Ogarrio. Too Big to Cheat: Mining Pools’ Incentives to Double Spend in Blockchain Based Cryptocurrencies. 2019. https://helda.helsinki.fi//bitstream/handle/10138/309233/SSRN_id3506748.pdf
Gencer, A. E., Basu, S., Eyal, I., Van Renesse, R., and Sirer, E. G. (2018). Decentralization in bitcoin and ethereum networks. https://arxiv.org/pdf/1801.03998.pdf
Lovejoy J. Reorgs on Bitcoin Gold: Counterattacks in the wild. 11.03.2020 https://medium.com/mit-media-lab-digital-currency-initiative/reorgs-on-bitcoin-gold-counterattacks-in-the-wild-da7e2b797c21
Nakamoto S. Bitcoin: A Peer-to-Peer Electronic Cash System. 2009. 9 р.
Rosenfeld M. Analysis of hashrate-based double-spending. 2014. 13 р. (arXiv preprint arXiv:1402.2009).
Poluyanenko N., Kuznetsov A., Lisickiy K., Datsenko S., Nakisko O., Rudenko S. (2021) The Problem of Double Costs in Blockchain Systems // Hu Z., Petoukhov S., Dychka I., He M. (eds) Advances in Computer Science for Engineering and Education III. ICCSEEA 2020. Advances in Intelligent Systems and Computing, vol 1247. Springer, Cham. PP 640-652. ISSN 2194-5357, ISSN 2194-5365 (electronic), ISBN 978-3-030-55505-4, ISBN 978-3-030-55506-1 (eBook) https://doi.org/10.1007/978-3-030-55506-1_57
Poluyanenko N, Kuznetsov A., Lazareva E., Marakushyn A. Extrapolation to calculate the probability of a double spending attack. CMIS 2020: 610-620.
Малахов Е.И. Случайные блуждания на полупрямой с поглощающим экраном с возможностью остановки http://math.isu.ru/ru/chairs/tpdm/docs/Platonovskie2017/Malahov.pdf
Гмурман В.Е. Теория вероятностей и математическая статистика. Москва : Высш. шк., 1997.
Ширяев А. Н. Вероятность : в 2-х кн. ; 4-е изд., переработ. и доп. Москва : МЦНМО, 2007.
K. Sigman. Gambler's ruin problem. www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GR.pdf , June 7 2016
Зубков А.М. Конспект лекций по теории случайных процессов. Москва : МГУ. Мех.-мат. факультет. 6-й семестр. 2008. – 90 с. https://epdf.pub/-6-88e2c451ff9dcbefcfbfacfb1bca654742391.html
Poluyanenko N., Pisarenko N., Safonenko V., Makushenko T., Pushko O., Zaburmekha Y., Kuznetsova K. Simulation of a double spending attack on the proof of work consensus protocol // CEUR Workshop Proceedings. Volume 2654, 2020, Pages 32-59. 2019 International Workshop on Cyber Hygiene, CybHyg 2019; Kyiv; Ukraine; 30 November 2019. ISSN: 16130073.
How to Cite
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. 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.3. 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 (See The Effect of Open Access).