A survey: Reward distribution mechanisms and withholding attacks in Bitcoin pool mining

Saide Zhu; Wei Li; Hong Li; Chunqiang Hu; Zhipeng Cai

doi:10.3934/mfc.2018020

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November 2018, 1(4): 393-414. doi: 10.3934/mfc.2018020

A survey: Reward distribution mechanisms and withholding attacks in Bitcoin pool mining

Saide Zhu ^1, , Wei Li ^1,, , Hong Li ^2, , Chunqiang Hu ^3, and Zhipeng Cai ^1,

1.	Department of Computer Science, Georgia State University, Atlanta, GA, USA
2.	Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China
3.	School of Big Data & Software Engineering, Chongqing University, Chongqing, China

Corresponding author: Wei Li

Received August 2018 Revised October 2018 Published December 2018

The past three years have seen the rapid increase of Bitcoin difficulty, which has led to a substantial variance in solo mining. As a result, miners tend to join a large open pool to get a more stable reward. Nowadays, mining pools take up over 98% of Bitcoins total computation power. In a sense, this is a manifestation of Bitcoin that tends to be centralized. Thus, researchers have shown an increased interest in pool mining payoff and security. The purpose of this paper is to review and summarize recent research in Bitcoin pool mining system. We first introduce several common reward distribution schemes, and analyze their advantages and disadvantages with some improvement mechanisms; In the second section, to address pool security problems, we examined the practical utility of some existing and potential attack strategies. To study those malicious attack in details, several defense methods are collected. Finally, we make an outlook on Bitcoin future.

Keywords: Bitcoin, pool mining, reward distribution, withholding attack.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation: Saide Zhu, Wei Li, Hong Li, Chunqiang Hu, Zhipeng Cai. A survey: Reward distribution mechanisms and withholding attacks in Bitcoin pool mining. Mathematical Foundations of Computing, 2018, 1 (4) : 393-414. doi: 10.3934/mfc.2018020

References:

[1]	S. Bag, S. Ruj and K. Sakurai, Bitcoin block withholding attack: Analysis and mitigation, IEEE Trans. Information Forensics and Security, 12 (2017), 1967-1978. doi: 10.1109/TIFS.2016.2623588. Google Scholar
[2]	L. Bahack, Theoretical bitcoin attacks with less than half of the computational power (draft), CoRR, vol. abs/1312.7013, 2013. [Online]. Available: arXiv: 1312.7013 Google Scholar
[3]	T. Bamert, C. Decker, L. Elsen, R. Wattenhofer and S. Welten, Have a snack, pay with bitcoins, IEEE P2P 2013, Proceedings, 2013, 1–5. doi: 10.1109/P2P.2013.6688717. Google Scholar
[4]	J. Bonneau, A. Miller, J. Clark, A. Narayanan, J. A. Kroll and E. W. Felten, Sok: Research perspectives and challenges for bitcoin and cryptocurrencies, in 2015 IEEE Symposium on Security and Privacy, 2015, 104–121. doi: 10.1109/SP.2015.14. Google Scholar
[5]	Z. Cai, Z. He, X. Guan and Y. Li, Collective data-sanitization for preventing sensitive information inference attacks in social networks, IEEE Transactions on Dependable and Secure Computing, 15 (2018), 577-590. doi: 10.1109/TDSC.2016.2613521. Google Scholar
[6]	Z. Cai and X. Zheng, A private and efficient mechanism for data uploading in smart cyber-physical systems, IEEE Transactions on Network Science and Engineering (Early Access), 2018, 1–1. doi: 10.1109/TNSE.2018.2830307. Google Scholar
[7]	M. Carlsten, H. Kalodner, S. M. Weinberg and A. Narayanan, On the instability of bitcoin without the block reward, in Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, 2016, 154–167. doi: 10.1145/2976749.2978408. Google Scholar
[8]	N. T. Courtois and L. Bahack, On subversive miner strategies and block withholding attack in bitcoin digital currency, CoRR, vol. abs/1402.1718, 2014. [Online]. Available: arXiv: 1402.1718 Google Scholar
[9]	N. T. Courtois, M. Grajek and R. Naik, Optimizing sha256 in bitcoin mining, in Cryptography and Security Systems - Third International Conference, CSS 2014, Proceedings, 2014, 131–144. doi: 10.1007/978-3-662-44893-9_12. Google Scholar
[10]	C. Decker and R. Wattenhofer, Information propagation in the bitcoin network, in IEEEP2P 2013, Proceedings, 2013, 1–10. doi: 10.1109/P2P.2013.6688704. Google Scholar
[11]	I. Eyal, The miner's dilemma, in 2015 IEEE Symposium on Security and Privacy, SP 2015, San Jose, CA, USA, May 17-21, 2015, 2015, 89–103. doi: 10.1109/SP.2015.13. Google Scholar
[12]	I. Eyal and E. G. Sirer, Majority is not enough: Bitcoin mining is vulnerable, Communications of the ACM CACM Homepage Archive, 61 (2018), 95-102. doi: 10.1145/3212998. Google Scholar
[13]	B. A. Fisch, R. Pass and A. Shelat, Socially optimal mining pools, in International Conference on Web and Internet Economics, 2017, 205–218. Google Scholar
[14]	J. Garay, A. Kiayias and N. Leonardos, The bitcoin backbone protocol: Analysis and applications, in Advances in Cryptology - EUROCRYPT 2015 - 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, April 26-30, 2015, Proceedings, Part Ⅱ, 9057 (2015), 281–310. doi: 10.1007/978-3-662-46803-6_10. Google Scholar
[15]	Z. He, Z. Cai, J. Yu, X. Wang, Y. Sun and Y. Li, Cost-efficient strategies for restraining rumor spreading in mobile social networks, IEEE Transactions on Vehicular Technology, 66 (2017), 2789-2800. doi: 10.1109/TVT.2016.2585591. Google Scholar
[16]	Z. He, Z. Cai and X. Wang, Modeling propagation dynamics and developing optimized countermeasures for rumor spreading in online social networks, in IEEE ICDCS, 2015, 205–214. doi: 10.1109/ICDCS.2015.29. Google Scholar
[17]	Z. He, Z. Cai and J. Yu, Latent-data privacy preserving with customized data utility for social network data, IEEE Transactions on Vehicular Technology, 67 (2018), 665-673. doi: 10.1109/TVT.2017.2738018. Google Scholar
[18]	E. Heilman, One weird trick to stop selfish miners: Fresh bitcoins, a solution for the honest miner, in Financial Cryptography and Data Security - FC 2014 Workshops, BITCOIN and WAHC 2014, Christ Church, Barbados, March 7, 2014, Revised Selected Papers, 2014, 161–162. doi: 10.1007/978-3-662-44774-1_12. Google Scholar
[19]	C. Hu, W. Li, X. Cheng, J. Yu, S. Wang and R. Bie, A secure and verifiable access control scheme for big data storage in clouds, IEEE Transactions on Big Data (Early Access), 4 (2018), 341-355. doi: 10.1109/TBDATA.2016.2621106. Google Scholar
[20]	Q. Hu, S. Wang, C. Hu, J. Huang, W. Li and X. Cheng, Messages in a concealed bottle: Achieving query content privacy with accurate location-based services, to appear in IEEE Transactions on Vehicular Technology, 67 (2018), 7698-7711. doi: 10.1109/TVT.2018.2838041. Google Scholar
[21]	G. O. Karame, E. Androulaki and S. Capkun, Double-spending fast payments in bitcoin, in the ACM Conference on Computer and Communications Security, CCS'12, Raleigh, NC, USA, October 16-18, 2012, 2012, 906–917. doi: 10.1145/2382196.2382292. Google Scholar
[22]	A. Kothapalli, A. Miller and N. Borisov, Smartcast: An incentive compatible consensus protocol using smart contracts, in International Conference on Financial Cryptography and Data Security, 2017, 536–552. Google Scholar
[23]	J. A. Kroll, I. C. Davey and E. W. Felten, The economics of bitcoin mining, or bitcoin in the presence of adversaries, in Proceedings of WEIS, 2013 (2013), p. 11. Google Scholar
[24]	W. Li, M. Larson, C. Hu, R. Li, X. Cheng and R. Bie, Secure multi-unit sealed first-price auction mechanisms, Security and Communication Netowrks SI on Cyber Security, Crime, and Forensices of Wireless Networks and Applications, 9 (2016), 3833-3843. doi: 10.1002/sec.1522. Google Scholar
[25]	Y. Liang, Z. Cai, J. Yu, Q. Han and Y. Li, Deep learning based inference of private information using embedded sensors in smart devices, IEEE Network Magazine, 32 (2018), 8-14. doi: 10.1109/MNET.2018.1700349. Google Scholar
[26]	Y. Liang, Z. Cai, Q. Han and Y. Li, Location privacy leakage through sensory data, Security and Communication Networks, 2017 (2017), Article ID 7576307, 12 pages. doi: 10.1155/2017/7576307. Google Scholar
[27]	L. Luu, R. Saha, I. Parameshwaran, P. Saxena and A. Hobor, On power splitting games in distributed computation: The case of bitcoin pooled mining, in IEEE 28th Computer Security Foundations Symposium, CSF 2015, Verona, Italy, 13-17 July, 2015, 2015, 397–411. doi: 10.1109/CSF.2015.34. Google Scholar
[28]	L. Luu, Y. Velner, J. Teutsch and P. Saxena, Smart pool: Practical decentralized pooled mining, in 26th USENIX Security Symposium, USENIX Security 2017, Vancouver, BC, Canada, August 16-18, 2017., 2017, 1409–1426. [Online]. Available: https://www.usenix.org/conference/usenixsecurity17/technical-sessions/presentation/luu Google Scholar
[29]	R. Meni, A short note about variance and pool payouts, [Online], 2011, Available: https://bitcointalk.org/index.php?topic=5264.0 Google Scholar
[30]	C. Mooney and S. Mufson, Why the bitcoin craze is using up so much energy, 2018, [Online]. Available: https://www.washingtonpost.com/news/energy-environment/wp/2017/12/19/why-the-bitcoin-craze-is-using-up-so-much-energy/?utm_term=.2ec154762efa Google Scholar
[31]	S. Nakamoto, Bitcoin: A peer-to-peer electronic cash system, [Online], 2009, Available: http://www.bitcoin.org/bitcoin.pdf Google Scholar
[32]	K. Nayak, S. Kumar, A. Miller and E. Shi, Stubborn mining: Generalizing selfish mining and combining with an eclipse attack, in IEEE European Symposium on Security and Privacy, EuroS & P 2016, Saarbrücken, Germany, March 21-24, 2016, 2016, 305–320. doi: 10.1109/EuroSP.2016.32. Google Scholar
[33]	M. Rosenfeld, Analysis of bitcoin pooled mining reward systems, CoRR, vol. abs/1112.4980, 2011. [Online]. Available: arXiv: 1112.4980 Google Scholar
[34]	M. Rosenfeld, Mining pools reward methods, presentation at bitcoin 2013 conference, [Online]. Available: http://www.youtube.com/watch?v=5sgdD4mGPfg Google Scholar
[35]	M. Rosenfeld, Double geometric method: Hopping-proof, low-variance reward system, [Online], Available: https://bitcointalk.org/index.php?topic=39497.0 Google Scholar
[36]	A. Sapirshtein, Y. Sompolinsky and A. Zohar, Optimal selfish mining strategies in bitcoin, in Financial Cryptography and Data Security - 20th International Conference, FC 2016, Christ Church, Barbados, February 22-26, 2016, Revised Selected Papers, 9603 (2017), 515–532. doi: 10.1007/978-3-662-54970-4\_30. Google Scholar
[37]	O. Schrijvers, J. Bonneau, D. Boneh and T. Roughgarden, Incentive compatibility of bitcoin mining pool reward functions, in Financial Cryptography and Data Security - 20th International Conference, FC 2016, Christ Church, Barbados, February 22-26, 2016, Revised Selected Papers, 9603 (2017), 477–498. doi: 10.1007/978-3-662-54970-4\_28. Google Scholar
[38]	B. L. Shultz and D. Bayer, Certification of witness: Mitigating blockchain fork attacks, Undergraduate Thesis in Mathematics, Columbia University in the City of New York, 2015. Google Scholar
[39]	S. Solat and M. Potop-Butucaru, Brief announcement: Zeroblock: Timestamp-free prevention of block-withholding attack in bitcoin, in Stabilization, Safety, and Security of Distributed Systems - 19th International Symposium, SSS 2017, Boston, MA, USA, November 5-8, 2017, Proceedings, 2017, 356–360. doi: 10.1007/978-3-319-69084-1_25. Google Scholar
[40]	E. Swanson, Bitcoin mining calculator, 2013, [Online], Available: https://alloscomp.com/bitcoin/calculator/ Google Scholar
[41]	D. K. Tosh, S. Shetty, X. Liang, C. A. Kamhoua, K. A. Kwiat and L. Njilla, Security implications of blockchain cloud with analysis of block withholding attack, in 17th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing, CCGRID, 2017, 458–467. doi: 10.1109/CCGRID.2017.111. Google Scholar
[42]	Y. Velner, J. Teutsch and L. Luu, Smart contracts make bitcoin mining pools vulnerable, in Financial Cryptography and Data Security - FC 2017 International Workshops, WAHC, BITCOIN, VOTING, WTSC, and TA, Sliema, Malta, April 7, 2017, Revised Selected Papers, 2017, 298–316. doi: 10.1007/978-3-319-70278-0_19. Google Scholar
[43]	J. Wang, Z. Cai, Y. Li, D. Yang, J. Li and H. Gao, Protecting query privacy with differentially private k-anonymity in location-based services, Personal and Ubiquitous Computing, 2018, 1–17. Google Scholar
[44]	G. Wood, Ethereum: A secure decentralised generalised transaction ledger, Ethereum Project Yellow Paper, 151 (2014), 1-32. Google Scholar
[45]	R. Zhang and B. Preneel, Publish or perish: A backward-compatible defense against selfish mining in bitcoin, in Topics in Cryptology - CT-RSA 2017 - The Cryptographers' Track at the RSA Conference 2017, San Francisco, CA, USA, February 14-17, 2017, Proceedings, 10159 (2017), 277–292. doi: 10.1007/978-3-319-52153-4\_16. Google Scholar
[46]	X. Zheng, Z. Cai, J. Yu, C. Wang and Y. Li, Follow but no track: Privacy preserved profile publishing in cyber-physical social systems, IEEE Internet of Things Journal, 4 (2017), 1868-1878. doi: 10.1109/JIOT.2017.2679483. Google Scholar
[47]	X. Zheng, Z. Cai and Y. Li, Data linkage in smart iot systems: A consideration from privacy perspective, to appear in IEEE Communications Magazine, 2018. Google Scholar
[48]	X. Zheng, Z. Cai, J. Li and H. Gao, Location-privacy-aware review publication mechanism for local business service systems, in IEEE INFOCOM, Atlanta, USA, 2017, 1–9. doi: 10.1109/INFOCOM.2017.8056976. Google Scholar
[49]	X. Zheng, G. Luo and Z. Cai, A fair mechanism for private data publication in online social networks, IEEE Transactions on Network Science and Engineering (Early Access), 2018, 1–1. doi: 10.1109/TNSE.2018.2801798. Google Scholar
[50]	Y. Zolotavkin, J. García and C. Rudolph, Incentive compatibility of pay per last N shares in bitcoin mining pools, in Decision and Game Theory for Security - 8th International Conference, GameSec, 2017, 21–39. doi: 10.1007/978-3-319-68711-7_2. Google Scholar
[51]	Blockchain info: Detailed information and charts on all bitcoin transactions and blocks, [Online], Available: https://blockchain.info/ Google Scholar
[52]	Bitcoin block reward halving countdown, [Online], Available: https://www.bitcoinblockhalf.com/ Google Scholar
[53]	Comparison of mining pools, [Online], Available: https://en.bitcoin.it/wiki/Comparison of mining pools Google Scholar
[54]	The cryptocurrency for payments based on blockchain technology, [Online], Available: https://litecoin.org/ Google Scholar
[55]	How to destroy bitcoin with 51, [Online], Available: https://medium.com/@homakov/how-to-destroy-bitcoin-with-51-pocked-guide-for-governments-83d9bdf2ef6b Google Scholar
[56]	Pps vs pplns – mining pool payment reward structure explained, [Online], 2018, Available: https://coinguides.org/pps-vs-pplns/ Google Scholar
[57]	Slush pool reward system, [Online], Available: https://slushpool.com/help/manual/rewards Google Scholar

show all references

References:

[1]	S. Bag, S. Ruj and K. Sakurai, Bitcoin block withholding attack: Analysis and mitigation, IEEE Trans. Information Forensics and Security, 12 (2017), 1967-1978. doi: 10.1109/TIFS.2016.2623588. Google Scholar
[2]	L. Bahack, Theoretical bitcoin attacks with less than half of the computational power (draft), CoRR, vol. abs/1312.7013, 2013. [Online]. Available: arXiv: 1312.7013 Google Scholar
[3]	T. Bamert, C. Decker, L. Elsen, R. Wattenhofer and S. Welten, Have a snack, pay with bitcoins, IEEE P2P 2013, Proceedings, 2013, 1–5. doi: 10.1109/P2P.2013.6688717. Google Scholar
[4]	J. Bonneau, A. Miller, J. Clark, A. Narayanan, J. A. Kroll and E. W. Felten, Sok: Research perspectives and challenges for bitcoin and cryptocurrencies, in 2015 IEEE Symposium on Security and Privacy, 2015, 104–121. doi: 10.1109/SP.2015.14. Google Scholar
[5]	Z. Cai, Z. He, X. Guan and Y. Li, Collective data-sanitization for preventing sensitive information inference attacks in social networks, IEEE Transactions on Dependable and Secure Computing, 15 (2018), 577-590. doi: 10.1109/TDSC.2016.2613521. Google Scholar
[6]	Z. Cai and X. Zheng, A private and efficient mechanism for data uploading in smart cyber-physical systems, IEEE Transactions on Network Science and Engineering (Early Access), 2018, 1–1. doi: 10.1109/TNSE.2018.2830307. Google Scholar
[7]	M. Carlsten, H. Kalodner, S. M. Weinberg and A. Narayanan, On the instability of bitcoin without the block reward, in Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, 2016, 154–167. doi: 10.1145/2976749.2978408. Google Scholar
[8]	N. T. Courtois and L. Bahack, On subversive miner strategies and block withholding attack in bitcoin digital currency, CoRR, vol. abs/1402.1718, 2014. [Online]. Available: arXiv: 1402.1718 Google Scholar
[9]	N. T. Courtois, M. Grajek and R. Naik, Optimizing sha256 in bitcoin mining, in Cryptography and Security Systems - Third International Conference, CSS 2014, Proceedings, 2014, 131–144. doi: 10.1007/978-3-662-44893-9_12. Google Scholar
[10]	C. Decker and R. Wattenhofer, Information propagation in the bitcoin network, in IEEEP2P 2013, Proceedings, 2013, 1–10. doi: 10.1109/P2P.2013.6688704. Google Scholar
[11]	I. Eyal, The miner's dilemma, in 2015 IEEE Symposium on Security and Privacy, SP 2015, San Jose, CA, USA, May 17-21, 2015, 2015, 89–103. doi: 10.1109/SP.2015.13. Google Scholar
[12]	I. Eyal and E. G. Sirer, Majority is not enough: Bitcoin mining is vulnerable, Communications of the ACM CACM Homepage Archive, 61 (2018), 95-102. doi: 10.1145/3212998. Google Scholar
[13]	B. A. Fisch, R. Pass and A. Shelat, Socially optimal mining pools, in International Conference on Web and Internet Economics, 2017, 205–218. Google Scholar
[14]	J. Garay, A. Kiayias and N. Leonardos, The bitcoin backbone protocol: Analysis and applications, in Advances in Cryptology - EUROCRYPT 2015 - 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, April 26-30, 2015, Proceedings, Part Ⅱ, 9057 (2015), 281–310. doi: 10.1007/978-3-662-46803-6_10. Google Scholar
[15]	Z. He, Z. Cai, J. Yu, X. Wang, Y. Sun and Y. Li, Cost-efficient strategies for restraining rumor spreading in mobile social networks, IEEE Transactions on Vehicular Technology, 66 (2017), 2789-2800. doi: 10.1109/TVT.2016.2585591. Google Scholar
[16]	Z. He, Z. Cai and X. Wang, Modeling propagation dynamics and developing optimized countermeasures for rumor spreading in online social networks, in IEEE ICDCS, 2015, 205–214. doi: 10.1109/ICDCS.2015.29. Google Scholar
[17]	Z. He, Z. Cai and J. Yu, Latent-data privacy preserving with customized data utility for social network data, IEEE Transactions on Vehicular Technology, 67 (2018), 665-673. doi: 10.1109/TVT.2017.2738018. Google Scholar
[18]	E. Heilman, One weird trick to stop selfish miners: Fresh bitcoins, a solution for the honest miner, in Financial Cryptography and Data Security - FC 2014 Workshops, BITCOIN and WAHC 2014, Christ Church, Barbados, March 7, 2014, Revised Selected Papers, 2014, 161–162. doi: 10.1007/978-3-662-44774-1_12. Google Scholar
[19]	C. Hu, W. Li, X. Cheng, J. Yu, S. Wang and R. Bie, A secure and verifiable access control scheme for big data storage in clouds, IEEE Transactions on Big Data (Early Access), 4 (2018), 341-355. doi: 10.1109/TBDATA.2016.2621106. Google Scholar
[20]	Q. Hu, S. Wang, C. Hu, J. Huang, W. Li and X. Cheng, Messages in a concealed bottle: Achieving query content privacy with accurate location-based services, to appear in IEEE Transactions on Vehicular Technology, 67 (2018), 7698-7711. doi: 10.1109/TVT.2018.2838041. Google Scholar
[21]	G. O. Karame, E. Androulaki and S. Capkun, Double-spending fast payments in bitcoin, in the ACM Conference on Computer and Communications Security, CCS'12, Raleigh, NC, USA, October 16-18, 2012, 2012, 906–917. doi: 10.1145/2382196.2382292. Google Scholar
[22]	A. Kothapalli, A. Miller and N. Borisov, Smartcast: An incentive compatible consensus protocol using smart contracts, in International Conference on Financial Cryptography and Data Security, 2017, 536–552. Google Scholar
[23]	J. A. Kroll, I. C. Davey and E. W. Felten, The economics of bitcoin mining, or bitcoin in the presence of adversaries, in Proceedings of WEIS, 2013 (2013), p. 11. Google Scholar
[24]	W. Li, M. Larson, C. Hu, R. Li, X. Cheng and R. Bie, Secure multi-unit sealed first-price auction mechanisms, Security and Communication Netowrks SI on Cyber Security, Crime, and Forensices of Wireless Networks and Applications, 9 (2016), 3833-3843. doi: 10.1002/sec.1522. Google Scholar
[25]	Y. Liang, Z. Cai, J. Yu, Q. Han and Y. Li, Deep learning based inference of private information using embedded sensors in smart devices, IEEE Network Magazine, 32 (2018), 8-14. doi: 10.1109/MNET.2018.1700349. Google Scholar
[26]	Y. Liang, Z. Cai, Q. Han and Y. Li, Location privacy leakage through sensory data, Security and Communication Networks, 2017 (2017), Article ID 7576307, 12 pages. doi: 10.1155/2017/7576307. Google Scholar
[27]	L. Luu, R. Saha, I. Parameshwaran, P. Saxena and A. Hobor, On power splitting games in distributed computation: The case of bitcoin pooled mining, in IEEE 28th Computer Security Foundations Symposium, CSF 2015, Verona, Italy, 13-17 July, 2015, 2015, 397–411. doi: 10.1109/CSF.2015.34. Google Scholar
[28]	L. Luu, Y. Velner, J. Teutsch and P. Saxena, Smart pool: Practical decentralized pooled mining, in 26th USENIX Security Symposium, USENIX Security 2017, Vancouver, BC, Canada, August 16-18, 2017., 2017, 1409–1426. [Online]. Available: https://www.usenix.org/conference/usenixsecurity17/technical-sessions/presentation/luu Google Scholar
[29]	R. Meni, A short note about variance and pool payouts, [Online], 2011, Available: https://bitcointalk.org/index.php?topic=5264.0 Google Scholar
[30]	C. Mooney and S. Mufson, Why the bitcoin craze is using up so much energy, 2018, [Online]. Available: https://www.washingtonpost.com/news/energy-environment/wp/2017/12/19/why-the-bitcoin-craze-is-using-up-so-much-energy/?utm_term=.2ec154762efa Google Scholar
[31]	S. Nakamoto, Bitcoin: A peer-to-peer electronic cash system, [Online], 2009, Available: http://www.bitcoin.org/bitcoin.pdf Google Scholar
[32]	K. Nayak, S. Kumar, A. Miller and E. Shi, Stubborn mining: Generalizing selfish mining and combining with an eclipse attack, in IEEE European Symposium on Security and Privacy, EuroS & P 2016, Saarbrücken, Germany, March 21-24, 2016, 2016, 305–320. doi: 10.1109/EuroSP.2016.32. Google Scholar
[33]	M. Rosenfeld, Analysis of bitcoin pooled mining reward systems, CoRR, vol. abs/1112.4980, 2011. [Online]. Available: arXiv: 1112.4980 Google Scholar
[34]	M. Rosenfeld, Mining pools reward methods, presentation at bitcoin 2013 conference, [Online]. Available: http://www.youtube.com/watch?v=5sgdD4mGPfg Google Scholar
[35]	M. Rosenfeld, Double geometric method: Hopping-proof, low-variance reward system, [Online], Available: https://bitcointalk.org/index.php?topic=39497.0 Google Scholar
[36]	A. Sapirshtein, Y. Sompolinsky and A. Zohar, Optimal selfish mining strategies in bitcoin, in Financial Cryptography and Data Security - 20th International Conference, FC 2016, Christ Church, Barbados, February 22-26, 2016, Revised Selected Papers, 9603 (2017), 515–532. doi: 10.1007/978-3-662-54970-4\_30. Google Scholar
[37]	O. Schrijvers, J. Bonneau, D. Boneh and T. Roughgarden, Incentive compatibility of bitcoin mining pool reward functions, in Financial Cryptography and Data Security - 20th International Conference, FC 2016, Christ Church, Barbados, February 22-26, 2016, Revised Selected Papers, 9603 (2017), 477–498. doi: 10.1007/978-3-662-54970-4\_28. Google Scholar
[38]	B. L. Shultz and D. Bayer, Certification of witness: Mitigating blockchain fork attacks, Undergraduate Thesis in Mathematics, Columbia University in the City of New York, 2015. Google Scholar
[39]	S. Solat and M. Potop-Butucaru, Brief announcement: Zeroblock: Timestamp-free prevention of block-withholding attack in bitcoin, in Stabilization, Safety, and Security of Distributed Systems - 19th International Symposium, SSS 2017, Boston, MA, USA, November 5-8, 2017, Proceedings, 2017, 356–360. doi: 10.1007/978-3-319-69084-1_25. Google Scholar
[40]	E. Swanson, Bitcoin mining calculator, 2013, [Online], Available: https://alloscomp.com/bitcoin/calculator/ Google Scholar
[41]	D. K. Tosh, S. Shetty, X. Liang, C. A. Kamhoua, K. A. Kwiat and L. Njilla, Security implications of blockchain cloud with analysis of block withholding attack, in 17th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing, CCGRID, 2017, 458–467. doi: 10.1109/CCGRID.2017.111. Google Scholar
[42]	Y. Velner, J. Teutsch and L. Luu, Smart contracts make bitcoin mining pools vulnerable, in Financial Cryptography and Data Security - FC 2017 International Workshops, WAHC, BITCOIN, VOTING, WTSC, and TA, Sliema, Malta, April 7, 2017, Revised Selected Papers, 2017, 298–316. doi: 10.1007/978-3-319-70278-0_19. Google Scholar
[43]	J. Wang, Z. Cai, Y. Li, D. Yang, J. Li and H. Gao, Protecting query privacy with differentially private k-anonymity in location-based services, Personal and Ubiquitous Computing, 2018, 1–17. Google Scholar
[44]	G. Wood, Ethereum: A secure decentralised generalised transaction ledger, Ethereum Project Yellow Paper, 151 (2014), 1-32. Google Scholar
[45]	R. Zhang and B. Preneel, Publish or perish: A backward-compatible defense against selfish mining in bitcoin, in Topics in Cryptology - CT-RSA 2017 - The Cryptographers' Track at the RSA Conference 2017, San Francisco, CA, USA, February 14-17, 2017, Proceedings, 10159 (2017), 277–292. doi: 10.1007/978-3-319-52153-4\_16. Google Scholar
[46]	X. Zheng, Z. Cai, J. Yu, C. Wang and Y. Li, Follow but no track: Privacy preserved profile publishing in cyber-physical social systems, IEEE Internet of Things Journal, 4 (2017), 1868-1878. doi: 10.1109/JIOT.2017.2679483. Google Scholar
[47]	X. Zheng, Z. Cai and Y. Li, Data linkage in smart iot systems: A consideration from privacy perspective, to appear in IEEE Communications Magazine, 2018. Google Scholar
[48]	X. Zheng, Z. Cai, J. Li and H. Gao, Location-privacy-aware review publication mechanism for local business service systems, in IEEE INFOCOM, Atlanta, USA, 2017, 1–9. doi: 10.1109/INFOCOM.2017.8056976. Google Scholar
[49]	X. Zheng, G. Luo and Z. Cai, A fair mechanism for private data publication in online social networks, IEEE Transactions on Network Science and Engineering (Early Access), 2018, 1–1. doi: 10.1109/TNSE.2018.2801798. Google Scholar
[50]	Y. Zolotavkin, J. García and C. Rudolph, Incentive compatibility of pay per last N shares in bitcoin mining pools, in Decision and Game Theory for Security - 8th International Conference, GameSec, 2017, 21–39. doi: 10.1007/978-3-319-68711-7_2. Google Scholar
[51]	Blockchain info: Detailed information and charts on all bitcoin transactions and blocks, [Online], Available: https://blockchain.info/ Google Scholar
[52]	Bitcoin block reward halving countdown, [Online], Available: https://www.bitcoinblockhalf.com/ Google Scholar
[53]	Comparison of mining pools, [Online], Available: https://en.bitcoin.it/wiki/Comparison of mining pools Google Scholar
[54]	The cryptocurrency for payments based on blockchain technology, [Online], Available: https://litecoin.org/ Google Scholar
[55]	How to destroy bitcoin with 51, [Online], Available: https://medium.com/@homakov/how-to-destroy-bitcoin-with-51-pocked-guide-for-governments-83d9bdf2ef6b Google Scholar
[56]	Pps vs pplns – mining pool payment reward structure explained, [Online], 2018, Available: https://coinguides.org/pps-vs-pplns/ Google Scholar
[57]	Slush pool reward system, [Online], Available: https://slushpool.com/help/manual/rewards Google Scholar