DOI
10.34229/KCA2522-9664.26.1.4
UDC 621.391:519.2:519.7
L.V Kovalchuk
Institute of Physics and Technology of the National Technical University
“Igor Sikorsky Kyiv Polytechnic Institute;”
G.E. Pukhov Institute for Modelling in Energy Engineering, National Academy
of Sciences of Ukraine, Kyiv, Ukraine, 
lusi.kovalchuk@gmail.com
I.M. Kuznetsov
Institute of Physics and Technology of the National Technical University
“Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine,
sea_hawk@icloud.com
M.Yu. Kuznetsov
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine; Institute of Physics and Technology of the National Technical University
“Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine,
kuznetsov2024@ukr.net
FAST SIMULATION OF A STRATEGY FOR A SPLITTING ATTACK
ON A BLOCKCHAIN BASED ON THE PROOF-OF-STAKE CONSENSUS PROTOCOL
Abstract. One of the most important and dangerous attacks on the blockchain is a splitting attack, when an attacker manages to build an alternative chain of blocks of the largest possible length. The article proposes a new model for implementing such an attack, defines the main rules for its implementation: under what conditions attackers start creating branches and to which branch they add a new block. In this case, a standard approach is used to determine the behavior of honest slot leaders: they always add new blocks to a longer branch; in the case of a fork, or two branches of the same length, they can choose any of them. A fast simulation modeling method is proposed, which allows estimating the probability that the fork length will reach a certain value. This method is based on the combined use of both elements of the Monte Carlo method and implanted recurrent formulas. To verify the correctness of the proposed method, a comparison of the estimates obtained by this method and the standard Monte Carlo method was carried out on numerical examples. Depending on the estimated probability, the fast simulation modeling method provides a time gain of several orders of magnitude.
Keywords: blockchain, Proof-of-Stake, splitting attack, stakeholder, timeslot, slotleader, Monte Carlo method, fast simulation.
full text
REFERENCES
- 1. Kovalchuk L., Kaidalov D., Shevtsov O., Nastenko A., Rodinko M., Oliynykov R. Analysis of splitting attacks on Bitcoin and GHOST consensus protocols. 9th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS). (21–23 September, 2017, Bucharest, Romania). Bucharest, 2017. P. 978–982. https://doi.org/10.1109/IDAACS.2017.8095233.
- 2. Kovalchuk L.V., Kuznetsov M.Yu., Shumska A.A. Modeling a simplified version of a branching attack on a blockchain based on the Proof-of-Stake consensus protocol. Kibernetyka ta systemnyi analiz. 2025. Vol. 61, No. 4. P. 134–145.
- 3. Nakamoto S. Bitcoin: A peer-to-peer electronic cash system, 2008. URL: https://bitcoin.org/bitcoin.pdf.
- 4. Naz S., Lee S.U.-J., Sea shield: A blockchain technology consensus to improve Proof-of-Stake-based consensus blockchain safety. Mathematics. 2024. Vol. 12, N 6. P. 1–40. https://doi.org/10.3390/math12060833.
- 5. Zhiqiang D., Liangxin L., Muhong H., Yanfang F., Wendong Z. Bulwark: A Proof-of-Stake protocol with strong consistency and liveness. Computer Networks. 2024. Vol. 242, Iss. C. https://doi.org/10.1016/j.comnet.2024.110245.
- 6. Golait P., Tomar D.S., Pateriya R.K., Sharma Y.K. Blockchain security and challenges: A review. 2023 IEEE 2nd International Conference on Industrial Electronics: Developments & Applications (ICIDeA). Imphal, India, 2023. P. 140–145. https://doi.org/10.1109/ICIDeA59866. 2023.10295211.
- 7. Stephen R., Alex A. A review on blockchain security. IOP Conference Series: Materials Science and Engineering. Int. Conf. Rec. Adv. Eff. Res. Engin. Sci. Techn. (RAEREST). 2018. Vol. 396. P. 1–7. https://doi.org/10.1088/1757-899X/396/1/012030.
- 8. Mssassi S., Abou El Kalam A. The blockchain trilemma: A formal proof of the inherent trade-offs among decentralization, security, and scalability. Applied Sciences. 2025. Vol. 15, Iss. 1. P. 1–26. https://doi.org/10.3390/app15010019.
- 9. Li X., Jiang P., Chen T., Luo X., Wen Q. A survey on the security of blockchain systems. Future Generation Computer Systems. 2020. Vol. 107. P. 841–853. https://doi.org/10.1016/j.future.2017.08.020.
- 10. A comprehensive study of blockchain services: Future of cryptography. Int. J. Adv. Comp. Sci. Appl. (IJACSA). 2020. Vol. 11, No. 10. P. 279–288. https://doi.org/10.14569/IJACSA.2020.0111037.
- 11. Kovalenko I.N., Kuznetsov N.Yu., Pegg Ph.A. Mathematical theory of reliability of time dependent systems with practical applications. Chichester: Wiley, 1997. 303 p. https://doi.org/10.34229/1028-0979-2023-3-5.
- 12. Kuznetsov N.Yu. Fast simulation technique in reliability evaluation of Markovian and non-Markovian systems. Simulation and optimization methods in risk and reliability theory. Knopov P.S., Pardalos P.M. (Ed.). New York: Nova Science Publishers, 2009. P. 69–112.
- 13. Kuznetsov I.M., Shumska A.A. Application of accelerated modeling to finding the probability of blocking requests in a multi-channel service system with multiple access. Kibernetyka ta systemnyi analiz. 2024. Vol. 60, No. 2. P. 51–63. https://doi.org/10.34229/KCA2522-9664.24.2.5.
- 14. Blanchet J., Lam H. Rare event simulation techniques. Proc. of the 2011 Winter Simulation Conference. Phoenix: IEEE, 2011. P. 146–160. https://doi.org/10.1109/WSC.2011.6147747.
- 15. Glasserman P. Monte Carlo methods in financial engineering. New York: Springer, 2004. 575 p. https://doi.org/10.1007/978-0-387-21617-1.
- 16. Gertsbakh I.B., Shpungin Y. Models of network reliability: Analysis, combinatorics, and Monte Carlo. Boca Raton: CRC Press, 2009. 203 p. https://doi.org/10.1201/b12536.
