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The Cost of IEEE Arithmetic in Secure Computation

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Progress in Cryptology – LATINCRYPT 2021 (LATINCRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12912))

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.

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Notes

  1. 1.

    The closer they are to uniformly random, then the less information is leaked.

  2. 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

  1. 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)

    Google Scholar 

  2. Aly, A., et al.: SCALE and MAMBA v1.11: documentation (2021). https://homes.esat.kuleuven.be/~nsmart/SCALE/Documentation.pdf

  3. 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)

    Google Scholar 

  4. 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

    Chapter  Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. 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)

    Google Scholar 

  8. 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

    Chapter  Google Scholar 

  9. 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

    Chapter  Google Scholar 

  10. 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

    Chapter  MATH  Google Scholar 

  11. 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

    Chapter  Google Scholar 

  12. 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)

    Google Scholar 

  13. 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

  14. 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

    Chapter  Google Scholar 

  15. 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

    Chapter  Google Scholar 

  16. Hauser, J.: Berkeley SoftFloat (2018). http://www.jhauser.us/arithmetic/SoftFloat.html

  17. 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

    Chapter  Google Scholar 

  18. 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

    Article  Google Scholar 

  19. 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

    Chapter  Google Scholar 

  20. 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

    Chapter  Google Scholar 

  21. 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

    Chapter  MATH  Google Scholar 

  22. Maurer, U.M.: Secure multi-party computation made simple. Discrete Appl. Math. 154(2), 370–381 (2006)

    Article  MathSciNet  Google Scholar 

  23. Mishchenko, A., Chatterjee, S., Jiang, R., Brayton, R.: FRAIGs: a unifying representation for logic synthesis and verification (2005)

    Google Scholar 

  24. 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

    Chapter  Google Scholar 

  25. 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

    Chapter  Google Scholar 

  26. Shamir, A.: How to share a secret. Commun. Assoc. Comput. Mach. 22(11), 612–613 (1979)

    MathSciNet  MATH  Google Scholar 

  27. 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

    Chapter  Google Scholar 

  28. 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)

    Google Scholar 

  29. 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)

    Google Scholar 

  30. 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)

    Google Scholar 

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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

  1. Galois Inc., Portland, USA

    David W. Archer

  2. imec-COSIC, KU Leuven, Leuven, Belgium

    Shahla Atapoor & Nigel P. Smart

  3. University of Bristol, Bristol, UK

    Nigel P. Smart

Authors
  1. David W. Archer
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  2. Shahla Atapoor
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  3. Nigel P. Smart
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Correspondence to Nigel P. Smart .

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Editors and Affiliations

  1. Microsoft Research, Redmond, WA, USA

    Patrick Longa

  2. Universitat Pompeu Fabra, Barcelona, Spain

    Carla Ràfols

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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

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  • DOI: https://doi.org/10.1007/978-3-030-88238-9_21

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