Abstract
In this paper, we first present a theoretical analysis model on the Proof-of-Work (PoW) for cryptocurrency blockchain. Based on this analysis, we present a new type of PoW, which relies on the hardness of solving a set of random quadratic equations over the finite field GF(2). We will present the advantages of such a PoW, in particular, in terms of its impact on decentralization and the incentives involved, and therefore demonstrate that this is a new good alternative as a new type for PoW in blockchain applications.
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Aggarwal, D., Brennen, G.K., Lee, T., Santha, M., Tomamichel, M.: Quantum-proofing the blockchain. Quantum attacks on Bitcoin, and how to protect against them. arXiv:1710.10377 (2017)
Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proceedings of the 1st ACM Conference on Computer and Communications Security, CCS 1993, pp. 62–73. ACM, New York (1993)
Bouillaguet, C., et al.: Fast exhaustive search for polynomial systems in \(\mathbb{F}_{\text{2 }}\). In: Mangard, S., Standaert, F.X. (eds.) CHES 2010. LNCS, vol. 6225, pp. 203–218. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15031-9_14
Buchberger., B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Ph.D. thesis, Innsbruck (1965)
Ding, J.: Quantum-proof blockchain. In: ETSI/IQC Quantum Safe Workshop 2018 (2018). https://www.etsi.org/events/1296-etsi-iqc-quantum-safe-workshop-2018#pane-6/
Ding, J., Gower, J.E., Schmidt, D.S.: Multivariate Public Key Cryptosystems. Springer, Boston (2006). https://doi.org/10.1007/978-0-387-36946-4
Ding, J., Liu, J.: Panel on quantum-proof blockchain. Money20/20 Hanzhou China (2018). https://www.money2020-china.com/portal/index/people/id/247.html
Ding, J., Ryan, P., Sarawathy, R.C.: Future of bitcoin (and blockchain) with quantum computers. Preprint of University of Cincinnati, 10.2016. Submitted to Bitcoin 2017 under Financial Cryptography 2017
Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005). https://doi.org/10.1007/11496137_12
Ding, J., Yang, B.-Y.: Multivariates polynomials for hashing. In: Pei, D., Yung, M., Lin, D., Wu, C. (eds.) Inscrypt 2007. LNCS, vol. 4990, pp. 358–371. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-79499-8_28
Dobbertin, H.: The status of MD5 after a recent attack. CryptoBytes (2016)
Dwork, C., Naor, M.: Pricing via processing or combatting junk mail. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 139–147. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-48071-4_10
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
Gheorghiu, V., Gorbunov, S., Mosca, M., Munson, B.: Quantum-proofing the blockchain, November 2017. https://www.evolutionq.com/assets/mosca_quantum-proofing-the-blockchain_blockchain-research-institute.pdf
Kim, S.: Primecoin: cryptocurrency with prime number proof-of-work, March 2013. assets.ctfassets.net
Nakamoto, S.: Bitcoin: a peer-to-peer electronic cash system, October 2008. academia.edu
NIST. Post-quantum cryptograhic standardization, January 2019. https://www.nist.gov/news-events/news/2019/01/nist-reveals-26-algorithms-advancing-post-quantum-crypto-semifinals
Sasaki, Y., Aoki, K.: Finding preimages in full MD5 faster than exhaustive search. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 134–152. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01001-9_8
Acknowledgment
We would like to thank Johannes Buchmann, Albrecht Petzolt, Lei Hu, Hong Xiang, Peter Ryan, Tsuyoshi Takagi, Antoine Joux, Ruben Niederhagen, Chengdong Tao, Chen-mou Cheng, Zheng Zhang, and Kurt Schmidt for useful discussions. We would like to thank the anonymous referees for useful comments. We also would like to thank the ABCMint Foundation, in particular, Jin Liu for support.
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Ding, J. (2019). A New Proof of Work for Blockchain Based on Random Multivariate Quadratic Equations. In: Zhou, J., et al. Applied Cryptography and Network Security Workshops. ACNS 2019. Lecture Notes in Computer Science(), vol 11605. Springer, Cham. https://doi.org/10.1007/978-3-030-29729-9_5
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DOI: https://doi.org/10.1007/978-3-030-29729-9_5
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