Abstract
Bitcoin is a “crypto currency”, a decentralized electronic payment scheme based on cryptography. It implements a particular type of peer-to-peer payment system. Bitcoin depends on well-known cryptographic standards such as SHA-256. In this paper we revisit the cryptographic process which allows one to make money by producing new bitcoins. We reformulate this problem as a specific sort of Constrained Input Small Output (CISO) hashing problem and reduce the problem to a pure block cipher problem, cf. Fig. 1. We estimate the speed of this process and we show that the amortized cost of this process is less than it seems and it depends on a certain cryptographic constant which is estimated to be at most 1.89. These optimizations enable bitcoin miners to save countless millions of dollars per year in electricity bills.
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
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aumasson, J.-P., Khovratovich, D.: First Analysis of Keccak (2009), http://131002.net/data/papers/AK09.pdf
Barber, S., Boyen, X., Shi, E., Uzun, E.: Bitter to Better — How to Make Bitcoin a Better Currency. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 399–414. Springer, Heidelberg (2012)
Nakamoto, S., et al.: Bitcoin QT: http://bitcoin.org/en/download
Boyar, J., Matthews, P., Peralta, R.: Logic Minimization Techniques with Applications to Cryptology. Journal of Cryptology 26, 280–312 (2013)
Chaves, R., Kuzmanov, G., Sousa, L., Vassiliadis, S.: Improving SHA-2 hardware implementations. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 298–310. Springer, Heidelberg (2006)
Courtois, N.T., Hulme, D., Mourouzis, T.: Solving Circuit Optimisation Problems in Cryptography and Cryptanalysis. In: Proceedings of SHARCS 2012 Workshop, UK, pp. 179–191 (2011)
Courtois, N.T., Hulme, D., Mourouzis, T.: Multiplicative Complexity and Solving Generalized Brent Equations With SAT Solvers. In: COMPUTATION TOOLS 2012, The Third International Conference on Computational Logics, Algebras, Programming, Tools, and Benchmarking. ARIA, Nice (2012)
Courtois, N.T., Grajek, M., Naik, R.: The Unreasonable Fundamental Incertitudes Behind Bitcoin Mining (2013), http://arxiv.org/abs/1310.7935
Courtois, N.T., Bahack, L.: On Subversive Miner Strategies and Block Withholding Attack in Bitcoin Digital Currency (2014), http://arxiv.org/abs/1402.1718
Courtois, N.T., Bard, G.V.: Algebraic Cryptanalysis of the Data Encryption Standard. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol. 4887, pp. 152–169. Springer, Heidelberg (2007)
Courtois, N.T., Mourouzis, T.: Black-Box Collision Attacks on the Compression Function of the GOST Hash Function. In: Proceedings of 6th International Conference on Security and Cryptography SECRYPT, Spain (2011)
Dadda, L., Macchetti, M., Jeff Owen, J.: An ASIC design for a high speed implementation of the hash function SHA-256 384, 512. In: ACM Great Lakes Symposium on VLSI, pp. 421–425. ACM (2004)
Dadda, L., Macchetti, M., Owen, J.: The Design of a High Speed ASIC Unit for the Hash Function SHA-256 (384, 512). In: DATE 2004, pp. 70–75. IEEE (2004)
Virtual currencies: Mining digital gold, From the print edition: Finance and economics, The Economist (2013)
National Institute of Standards and Technology (NIST). FIPS PUB 180-2, SHA256 Standard (2002), http://csrc.nist.gov/publications/fips/fips180-2/fips180-2withchangenotice.pdf
Feldhofer, M., Rechberger, C.: A Case Against Currently Used Hash Functions in RFID Protocols. In: Meersman, R., Tari, Z., Herrero, P. (eds.) OTM 2006 Workshops. LNCS, vol. 4277, pp. 372–381. Springer, Heidelberg (2006)
Knezevic, M.: Efficient Hardware Implementations of Cryptographic Primitives. PhD thesis, Katholieke Universiteit Leuven (2011)
Lee, Y.K., Chan, H., Verbauwhede, I.: Iteration bound analysis and throughput optimum architecture of SHA-256 (384,512) for hardware implementations. In: Kim, S., Yung, M., Lee, H.-W. (eds.) WISA 2007. LNCS, vol. 4867, pp. 102–114. Springer, Heidelberg (2008)
Macchetti, M., Dadda, L.: Quasi-Pipelined Hash Circuits. In: IEEE Symposium on Computer Arithmetic, pp. 222–229 (2005)
Michail, H.E., Athanasiou, G., Kritikakou, A., Goutis, C.E., Gregoriades, A., Papadopoulou, V.G.: Ultra High Speed SHA-256 Hashing Cryptographic Module for IPSec Hardware/Software Codesign. In: SECRYPT, pp. 309–313 (2010)
Michail, H.E., Athanasiou, G., Gregoriades, A., Panagiotou, C.L., Goutis, C.E.: High Throughput Hardware/Software Co-design Approach SHA-256 Hashing Cryptographic Module. Global Journal of Computer Science and Technology 10, 15 (2010)
Guo, J., Matusiewicz, K.: Preimages for Step-Reduced SHA-2 (2008), http://eprint.iacr.org/2009/477.pdf
Heusser, J.: SAT solving - An alternative to brute force bitcoin mining (2013), http://jheusser.github.io/2013/02/03/satcoin.html
Huang, J., Lai, X.: What is the Effective Key Length for a Block Cipher: an Attack on Every Block Cipher (2012), http://eprint.iacr.org/2012/677
Kim, M., Ryou, J., Jun, S.: Efficient Hardware Architecture of SHA-256 Algorithm for Trusted Mobile Computing. In: Yung, M., Liu, P., Lin, D. (eds.) Inscrypt 2008. LNCS, vol. 5487, pp. 240–252. Springer, Heidelberg (2009)
Matusiewicz, K., Pieprzyk, J., Pramstaller, N.: Rechberger, Ch., Rijmen, V.: Analysis of simplified variants of SHA-256: http://www2.mat.dtu.dk/people/K.Matusiewicz/papers/SimplifiedSHA256.pdf
Nakamoto, S.: Bitcoin: A Peer-to-Peer Electronic Cash System: http://bitcoin.org/bitcoin.pdf
Raddum, H., Semaev, I.: New Technique for Solving Sparse Equation Systems. In: ECRYPT STVL (2006), http://eprint.iacr.org/2006/475/
Sklavos, N., Koufopavlou, O.G.: On the hardware implementations of the SHA-2 (256, 384, 512) hash functions. ISCAS 5, 153–156 (2003)
Tillich, S., Feldhofer, M., Kirschbaum, M., Plos, T., Schmidt, J.-M., Alexander Szekely, A.: Uniform Evaluation of Hardware Implementations of the Round-Two SHA-3 Candidates. In: Second SHA-3 Conference (2010), http://csrc.nist.gov/groups/ST/hash/sha-3/Round2/Aug2010/documents/papers/TILLICH_sha3hw.pdf
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Courtois, N.T., Grajek, M., Naik, R. (2014). Optimizing SHA256 in Bitcoin Mining. In: Kotulski, Z., Księżopolski, B., Mazur, K. (eds) Cryptography and Security Systems. CSS 2014. Communications in Computer and Information Science, vol 448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44893-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-662-44893-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44892-2
Online ISBN: 978-3-662-44893-9
eBook Packages: Computer ScienceComputer Science (R0)