Abstract
Programmers are used to the rounding and error properties of IEEE double precision arithmetic, however in secure computing paradigms, such as provided by Multi-Party Computation (MPC), usually a different form of approximation is provided for real number arithmetic. We compare the two standard variants using for LSSS-based MPC, with an implementation of IEEE compliant double precision using binary circuit-based MPC. We compare the relative performance, and conclude that the addition cost of IEEE compliance maybe too great for some applications. Thus in the secure domain standards bodies may wish to examine a different form of real number approximations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
The closer they are to uniformly random, then the less information is leaked.
- 2.
A maximally unqualified set is a set of parties which cannot recover the secret, but for which adding an arbitrary additional player will make the set qualified.
References
Aliasgari, M., Blanton, M., Zhang, Y., Steele, A.: Secure computation on floating point numbers. In: ISOC Network and Distributed System Security Symposium - NDSS 2013, San Diego, CA, USA, 24–27 February 2013. The Internet Society (2013)
Aly, A., et al.: SCALE and MAMBA v1.11: documentation (2021). https://homes.esat.kuleuven.be/~nsmart/SCALE/Documentation.pdf
Aly, A., Orsini, E., Rotaru, D., Smart, N.P., Wood, T.: Zaphod: efficiently combining LSSS and garbled circuits in SCALE. In: Brenner, M., Lepoint, T., Rohloff, K. (eds.) Proceedings of the 7th ACM Workshop on Encrypted Computing & Applied Homomorphic Cryptography, WAHC@CCS 2019, London, UK, 11–15 November 2019, pp. 33–44. ACM (2019)
Aly, A., Smart, N.P.: Benchmarking privacy preserving scientific operations. In: Deng, R.H., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 509–529. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21568-2_25
Araki, T., et al.: Optimized honest-majority MPC for malicious adversaries - breaking the 1 billion-gate per second barrier. In: 2017 IEEE Symposium on Security and Privacy, San Jose, CA, USA, 22–26 May 2017, pp. 843–862. IEEE Computer Society Press (2017)
Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: 22nd Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, 14–16 May 1990, pp. 503–513. ACM Press (1990)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: 20th Annual ACM Symposium on Theory of Computing, Chicago, IL, USA, 2–4 May 1988, pp. 1–10. ACM Press (1988)
Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_11
Buescher, N., Holzer, A., Weber, A., Katzenbeisser, S.: Compiling low depth circuits for practical secure computation. In: Askoxylakis, I., Ioannidis, S., Katsikas, S., Meadows, C. (eds.) ESORICS 2016. LNCS, vol. 9879, pp. 80–98. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45741-3_5
Catrina, O., de Hoogh, S.: Improved primitives for secure multiparty integer computation. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 182–199. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15317-4_13
Catrina, O., Saxena, A.: Secure computation with fixed-point numbers. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 35–50. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14577-3_6
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: 20th Annual ACM Symposium on Theory of Computing, Chicago, IL, USA, 2–4 May 1988, pp. 11–19. ACM Press (1988)
Chida, K., et al.: Fast large-scale honest-majority MPC for malicious adversaries. Cryptology ePrint Archive, report 2018/570 (2018). https://eprint.iacr.org/2018/570
Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40203-6_1
Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_38
Hauser, J.: Berkeley SoftFloat (2018). http://www.jhauser.us/arithmetic/SoftFloat.html
Hazay, C., Scholl, P., Soria-Vazquez, E.: Low cost constant round MPC combining BMR and oblivious transfer. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 598–628. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_21
Kamm, L., Willemson, J.: Secure floating point arithmetic and private satellite collision analysis. Int. J. Inf. Secur. 14(6), 531–548 (2014). https://doi.org/10.1007/s10207-014-0271-8
Keller, M., Rotaru, D., Smart, N.P., Wood, T.: Reducing communication channels in MPC. In: Catalano, D., De Prisco, R. (eds.) SCN 2018. LNCS, vol. 11035, pp. 181–199. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98113-0_10
Kerik, L., Laud, P., Randmets, J.: Optimizing MPC for robust and scalable integer and floating-point arithmetic. In: Clark, J., Meiklejohn, S., Ryan, P.Y.A., Wallach, D., Brenner, M., Rohloff, K. (eds.) FC 2016. LNCS, vol. 9604, pp. 271–287. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53357-4_18
Liedel, M.: Secure distributed computation of the square root and applications. In: Ryan, M.D., Smyth, B., Wang, G. (eds.) ISPEC 2012. LNCS, vol. 7232, pp. 277–288. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29101-2_19
Maurer, U.M.: Secure multi-party computation made simple. Discrete Appl. Math. 154(2), 370–381 (2006)
Mishchenko, A., Chatterjee, S., Jiang, R., Brayton, R.: FRAIGs: a unifying representation for logic synthesis and verification (2005)
Pullonen, P., Siim, S.: Combining secret sharing and garbled circuits for efficient private IEEE 754 floating-point computations. In: Brenner, M., Christin, N., Johnson, B., Rohloff, K. (eds.) FC 2015. LNCS, vol. 8976, pp. 172–183. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48051-9_13
Rotaru, D., Wood, T.: MArBled circuits: mixing arithmetic and Boolean circuits with active security. In: Hao, F., Ruj, S., Sen Gupta, S. (eds.) INDOCRYPT 2019. LNCS, vol. 11898, pp. 227–249. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-35423-7_12
Shamir, A.: How to share a secret. Commun. Assoc. Comput. Mach. 22(11), 612–613 (1979)
Smart, N.P., Wood, T.: Error detection in monotone span programs with application to communication-efficient multi-party computation. In: Matsui, M. (ed.) CT-RSA 2019. LNCS, vol. 11405, pp. 210–229. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-12612-4_11
Wang, X., Ranellucci, S., Katz, J.: Global-scale secure multiparty computation. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017: 24th Conference on Computer and Communications Security, Dallas, TX, USA, 31 October–2 November 2017, pp. 39–56. ACM Press (2017)
Yao, A.C.C.: How to generate and exchange secrets (extended abstract). In: 27th Annual Symposium on Foundations of Computer Science, Toronto, Ontario, Canada, 27–29 October1986, pp. 162–167. IEEE Computer Society Press (1986)
Zhu, Q., Kitchen, N., Kuehlmann, A., Sangiovanni-Vincentelli, A.L.: SAT sweeping with local observability don’t-cares. In: Sentovich, E. (ed.) Proceedings of the 43rd Design Automation Conference, DAC 2006, San Francisco, CA, USA, 24–28 July 2006, pp. 229–234. ACM (2006)
Acknowledgments
This work was supported in part by CyberSecurity Research Flanders with reference number VR20192203, by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by the FWO under an Odysseus project GOH9718N, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contract No. FA8750-19-C-0502, and by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) via Contract No. 2019-1902070006. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either express or implied, of the ERC, DARPA, the FWO, ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Archer, D.W., Atapoor, S., Smart, N.P. (2021). The Cost of IEEE Arithmetic in Secure Computation. In: Longa, P., Ràfols, C. (eds) Progress in Cryptology – LATINCRYPT 2021. LATINCRYPT 2021. Lecture Notes in Computer Science(), vol 12912. Springer, Cham. https://doi.org/10.1007/978-3-030-88238-9_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-88238-9_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-88237-2
Online ISBN: 978-3-030-88238-9
eBook Packages: Computer ScienceComputer Science (R0)