Skip to main content
SpringerLink
Log in

Secure Multi-Party Computation for Elliptic Curves

  • Conference paper
Book cover Advances in Information and Computer Security (IWSEC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8639))

Included in the following conference series:

  • 852 Accesses

Abstract

In this paper, we propose the first multi-party computation protocols for scalar multiplication and other basic operations on elliptic curves, which achieve constant round complexity and linear communication complexity. The key idea is adopting point addition formula without conditional branch, i.e., Edwards curve.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Algesheimer, J., Camenisch, J.L., Shoup, V.: Efficient Computation Modulo a Shared Secret with Application to the Generation of Shared Safe-Prime Products. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 417–432. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Bar-Ilan, J., Beaver, D.: Non-Cryptographic Fault-Tolerant Computing in Constant Number of Rounds of Interaction. In: PODC 1989, pp. 201–209 (1989)

    Google Scholar 

  3. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation. In: STOC 1988, pp. 1–10 (1988)

    Google Scholar 

  4. Bernstein, D.J., Lange, T.: Faster Addition and Doubling on Elliptic Curves. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 29–50. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  5. Bernstein, D.J., Lange, T.: Inverted Edwards Coordinates. In: Boztaş, S., Lu, H.-F. (eds.) AAECC 2007. LNCS, vol. 4851, pp. 20–27. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Brier, E., Joye, M.: Weierstraß Elliptic Curves and Side-Channel Attacks. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 335–345. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Chaum, D., Crépeau, C., Damgård, I.: Multiparty Unconditionally Secure Protocols (Extended Abstract). In: STOC 1988, pp. 11–19 (1988)

    Google Scholar 

  8. Clavier, C., Joye, M.: Universal Exponentiation Algorithm. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 300–308. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Cramer, R., Fehr, S., Ishai, Y., Kushilevitz, E.: Efficient multi-party computation over rings. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 596–613. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally Secure Constant-Rounds Multi-party Computation for Equality, Comparison, Bits and Exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Edwards, H.M.: A Normal Form for Elliptic Curves. Bulletin of the American Mathematical Society 44, 393–422 (2007)

    Article  MATH  Google Scholar 

  12. Goldreich, O., Micali, S., Wigderson, A.: How to Play any Mental Game or A Completeness Theorem for Protocols with Honest Majority. In: STOC 1987, pp. 218–229 (1987)

    Google Scholar 

  13. Joye, M., Quisquater, J.-J.: Hessian Elliptic Curves and Side-Channel Attacks. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 402–410. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Liardet, P.-Y., Smart, N.P.: Preventing SPA/DPA in ECC Systems Using the Jacobi Form. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 391–401. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Ning, C., Xu, Q.: Multiparty Computation for Modulo Reduction without Bit-Decomposition and a Generalization to Bit-Decomposition. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 483–500. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  16. Ning, C., Xu, Q.: Constant-Rounds, Linear Multi-party Computation for Exponentiation and Modulo Reduction with Perfect Security. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 572–589. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Nishide, T., Ohta, K.: Multiparty Computation for Interval, Equality, and Comparison Without Bit-Decomposition Protocol. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 343–360. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Ohara, K., Ohta, K., Suzuki, K., Yoneyama, K.: Constant Rounds Almost Linear Complexity Multi-party Computation for Prefix Sum. In: Pointcheval, D., Vergnaud, D. (eds.) AFRICACRYPT. LNCS, vol. 8469, pp. 285–299. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  19. Toft, T.: Primitives and Applications for Multi-party Computation. Ph.D. thesis, University of Aarhus (2007)

    Google Scholar 

  20. Toft, T.: Constant-Rounds, Almost-Linear Bit-Decomposition of Secret Shared Values. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 357–371. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Wallace, C.S.: A Suggestion for a Fast Multipliers. IEEE Trans. on Electronic Comp. EC-13(1), 14–17 (1964)

    Article  Google Scholar 

  22. Yao, A.C.C.: Protocols for Secure Computations (Extended Abstract). In: FOCS 1982, pp. 160–164 (1982)

    Google Scholar 

  23. Yao, A.C.C.: How to Generate and Exchange Secrets (Extended Abstract). In: FOCS 1986, pp. 162–167 (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NTT Secure Platform Laboratories, 3-9-11 Midori-cho, Musashino-shi, Tokyo, 180-8585, Japan

    Koutarou Suzuki & Kazuki Yoneyama

Authors
  1. Koutarou Suzuki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kazuki Yoneyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Network Security Research Institute, National Institute of Information and Communications Technology (NICT), 4-2-1 Nukui-Kitamachi, 184-8795, Koganei, Tokyo, Japan

    Maki Yoshida

  2. College of Information Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, 525-8577, Kusatsu, Shiga, Japan

    Koichi Mouri

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Suzuki, K., Yoneyama, K. (2014). Secure Multi-Party Computation for Elliptic Curves. In: Yoshida, M., Mouri, K. (eds) Advances in Information and Computer Security. IWSEC 2014. Lecture Notes in Computer Science, vol 8639. Springer, Cham. https://doi.org/10.1007/978-3-319-09843-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-09843-2_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09842-5

  • Online ISBN: 978-3-319-09843-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation