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Secure Multi-Party Computation for Elliptic Curves

  • Koutarou Suzuki
  • Kazuki Yoneyama
Conference paper
  • 662 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8639)

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.

Keywords

multi-party computation elliptic curve scalar multiplication Edwards curve 

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References

  1. 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)CrossRefGoogle Scholar
  2. 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. 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. 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)CrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 7.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty Unconditionally Secure Protocols (Extended Abstract). In: STOC 1988, pp. 11–19 (1988)Google Scholar
  8. 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)CrossRefGoogle Scholar
  9. 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)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 11.
    Edwards, H.M.: A Normal Form for Elliptic Curves. Bulletin of the American Mathematical Society 44, 393–422 (2007)CrossRefzbMATHGoogle Scholar
  12. 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. 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)CrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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)CrossRefGoogle Scholar
  16. 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)CrossRefGoogle Scholar
  17. 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)CrossRefGoogle Scholar
  18. 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)CrossRefGoogle Scholar
  19. 19.
    Toft, T.: Primitives and Applications for Multi-party Computation. Ph.D. thesis, University of Aarhus (2007)Google Scholar
  20. 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)CrossRefGoogle Scholar
  21. 21.
    Wallace, C.S.: A Suggestion for a Fast Multipliers. IEEE Trans. on Electronic Comp. EC-13(1), 14–17 (1964)CrossRefGoogle Scholar
  22. 22.
    Yao, A.C.C.: Protocols for Secure Computations (Extended Abstract). In: FOCS 1982, pp. 160–164 (1982)Google Scholar
  23. 23.
    Yao, A.C.C.: How to Generate and Exchange Secrets (Extended Abstract). In: FOCS 1986, pp. 162–167 (1986)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Koutarou Suzuki
    • 1
  • Kazuki Yoneyama
    • 1
  1. 1.NTT Secure Platform LaboratoriesMusashino-shiJapan

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