Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Secure and Accurate Summation of Many Floating-Point Numbers (2312.10247v1)

Published 15 Dec 2023 in cs.CR and cs.DS

Abstract: Motivated by the importance of floating-point computations, we study the problem of securely and accurately summing many floating-point numbers. Prior work has focused on security absent accuracy or accuracy absent security, whereas our approach achieves both of them. Specifically, we show how to implement floating-point superaccumulators using secure multi-party computation techniques, so that a number of participants holding secret shares of floating-point numbers can accurately compute their sum while keeping the individual values private.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (53)
  1. Secure floating-point summation implementation. https://github.com/chennyc/floating_point_summation.
  2. Secure computation of hidden markov models and secure floating-point arithmetic in the malicious model. International Journal of Information Security, 16(6):577–601, 2017.
  3. Secure computation on floating point numbers. In Network and Distributed System Security Symposium, 2013.
  4. How to choose suitable secure multiparty computation using generalized SPDZ. In Poster at ACM Conference on Computer and Communications Security (CCS), pages 2198–2200, 2018.
  5. High-throughput semi-honest secure three-party computation with an honest majority. In ACM Conference on Computer and Communications Security (CCS), pages 805–817, 2016.
  6. The cost of IEEE arithmetic in secure computation. In International Conference on Cryptology and Information Security in Latin America, pages 431–452, 2021.
  7. Multi-party replicated secret sharing over a ring with applications to privacy-preserving machine learning. Proceedings on Privacy Enhancing Technologies (PoPETs), 2023(1):608–626, 2023.
  8. Secure fingerprint alignment and matching protocols. arXiv Report 1702.03379, 2017.
  9. Improved building blocks for secure multi-party computation based on secret sharing with honest majority. In Applied Cryptography and Network Security (ACNS), pages 377–397, 2020.
  10. C. Burnikel et al. Exact Geometric Computation in LEDA. In Symposium on Computational Geometry (SoCG), pages 418–419, 1995.
  11. Octavian Catrina. Optimizing secure floating-point arithmetic: Sums, dot products, and polynomials. In Proceedings of the Romanian Academy, volume 21, pages 21–28, 2020.
  12. Octavian Catrina. Performance analysis of secure floating-point sums and dot products. In International Conference on Communications (COMM), pages 465–470, 2020.
  13. Octavian Catrina. Complexity and performance of secure floating-point polynomial evaluation protocols. In European Symposium on Research in Computer Security (ESORICS), pages 352–369, 2021.
  14. Octavian Catrina and Sebastiaan de Hoogh. Improved primitives for secure multiparty integer computation. In SCN, pages 182–199, 2010.
  15. Secure multiparty linear programming using fixed-point arithmetic. In European Symposium on Research in Computer Security (ESORICS), pages 134–150, 2010.
  16. Secure computation with fixed-point numbers. In Financial Cryptography and Data Security (FC), pages 35–50, 2010.
  17. A Reproducible Accurate Summation Algorithm for High-Performance Computing. In SIAM EX14 Workshop, 2014.
  18. Full-speed deterministic bit-accurate parallel floating-point summation on multi- and many-core architectures. HAL-CCSD, Tech. Rep. hal-00949355, 2014.
  19. SPDℤ2ksubscriptℤsuperscript2𝑘\mathbb{Z}_{2^{k}}blackboard_Z start_POSTSUBSCRIPT 2 start_POSTSUPERSCRIPT italic_k end_POSTSUPERSCRIPT end_POSTSUBSCRIPT: Efficient MPC mod 2ksuperscript2𝑘2^{k}2 start_POSTSUPERSCRIPT italic_k end_POSTSUPERSCRIPT for dishonest majority. In Advances in Cryptology – CRYPTO, pages 769–798, 2018.
  20. New primitives for actively-secure MPC over rings with applications to private machine learning. In IEEE Symposium on Security and Privacy (S&P), pages 1102–1120, 2019.
  21. J. Demmel and Hong Diep Nguyen. Parallel reproducible summation. IEEE TC, 64(7):2060–2070, July 2015.
  22. Accurate and efficient floating point summation. SIAM J. on Scientific Computing, 25(4):1214–1248, 2004.
  23. Fast and accurate floating point summation with application to computational geometry. Numerical Algorithms, 37(1-4):101–112, 2004.
  24. Alternative implementations of secure real numbers. In ACM Conference on Computer and Communications Security (CCS), pages 553–564, 2016.
  25. Improved primitives for MPC over mixed arithmetic-binary circuits. In Advances in Cryptology – CRYPTO, pages 823–852, 2020.
  26. Numerical behavior of NVIDIA tensor cores. PeerJ Computer Science, 7:e330, 2021.
  27. Laurent Fousse et al. MPFR: A multiple-precision binary floating-point library with correct rounding. ACM Transactions on Mathematical Software (TOMS), 2007.
  28. Processing encrypted floating point signals. In ACM Multimedia Workshop on Multimedia and Security, pages 103–108, 2011.
  29. GMPLib. GMP: the GNU multiple precision arithmetic library. https://gmplib.org/. Accessed 2015-12-16.
  30. David Goldberg. What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys, pages 5–48, March 1991.
  31. The GNU MPFR library. http://www.mpfr.org/. Accessed 2015-12-16.
  32. Dot-product engine as computing memory to accelerate machine learning algorithms. In 17th Int. Symp. on Quality Electronic Design (ISQED), pages 374–379, 2016.
  33. Leveraging NVIDIA Omniverse for in situ visualization. In Int. Conf. on High Performance Computing, pages 634–642, 2019.
  34. Secret sharing schemes realizing general access structures. In Globecom, pages 99–102, 1987.
  35. Accurate parallel floating-point accumulation. In 21st IEEE Symp. on Computer Arithmetic (ARITH), pages 153–162, April 2013.
  36. Secure floating point arithmetic and private satellite collision analysis. Int. Journal of Information Security, 14(6):531–548, 2015.
  37. Donald E. Knuth. The Art of Computer Programming, Volume 2 (3rd Ed.): Seminumerical Algorithms. Addison-Wesley, 1997.
  38. H. Leuprecht and W. Oberaigner. Parallel algorithms for the rounding exact summation of floating point numbers. Computing, 28(2):89–104, 1982.
  39. Michael A. Malcolm. On accurate floating-point summation. Communications of the ACM, 14(11):731–736, November 1971.
  40. P. Mohassel and P. Rindal. ABY3: A mixed protocol framework for machine learning. In ACM Conference on Computer and Communications Security (CCS), pages 35–52, 2018.
  41. Handbook of Floating-Point Arithmetic. Springer, 2009.
  42. Radford M. Neal. Fast exact summation using small and large superaccumulators. arXiv ePrint, abs/1505.05571, 2015.
  43. D.M. Priest. Algorithms for arbitrary precision floating point arithmetic. In 10th IEEE Symp. on Computer Arithmetic (ARITH), pages 132–143, Jun 1991.
  44. Secfloat: Accurate floating-point meets secure 2-party computation. In IEEE Symposium on Security and Privacy (S&P), pages 1553–1553, 2022.
  45. Jonathan Richard Shewchuk. Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete & Computational Geometry, 18(3):305–363, 1997.
  46. Accurate floating-point summation part i: Faithful rounding. SIAM J. on Scientific Computing, 31(1):189–224, 2008.
  47. Efficiency and accuracy improvements of secure floating-point addition over secret sharing. In Int. Workshop on Security, pages 77–94, 2020.
  48. Adi Shamir. How to share a secret. Comm. of the ACM, 22(11):612–613, 1979.
  49. Jonathan Richard Shewchuk. Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete & Computational Geometry, 18(3):305–363, 1997.
  50. Mikko Tommila. Apfloat for Java. http://www.apfloat.org/apfloat_java/.
  51. Benchmarks and performance analysis of decimal floating-point applications. In International Conference on Computer Design, pages 164–170, 2007.
  52. Correct rounding and a hybrid approach to exact floating-point summation. SIAM J. on Scientific Computing, 31(4):2981–3001, 2009.
  53. Algorithm 908: Online Exact Summation of Floating-Point Streams. ACM Transactions on Mathematical Software, pages 1–13, 2010.
Citations (1)

Summary

We haven't generated a summary for this paper yet.