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A Remark on Implementing the Weil Pairing

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Information Security and Cryptology (CISC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3822))

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Abstract

We propose an improved implementation of modified Weil pairings. By reduction of operations in the extension field to those in the base field, we can save some operations in the extension field when computing a modified Weil pairing. In particular, computing e ℓ (P,φ(P)) is the same as computing the Tate pairing without the final powering. So we can save about 50% of time for computing e ℓ (P,φ(P)) compared with the standard Miller’s algorithm.

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References

  1. Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354–368. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Barreto, P.S.L.M., Galbraith, S.D., O’hEigeartaigh, C., Scott, M.: “Efficient Pairing Computation on Supersingular Abelian Varieties,” Cryptology ePrint Archive, Report 2004/375

    Google Scholar 

  3. Available from http://planeta.terra.com.br/informatica/paulobarreto/pblounge html

  4. Blake, I., Seroussi, G., Smart, N.: Elliptic Curves in Cryptography. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  5. Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Charlap, L.S., Robbins, D.P.: An elementary introduction to elliptic curves, CRD Expository Report No. 31 (December 1988)

    Google Scholar 

  8. Charlap, L.S., Coley, R.: “An elementary introduction to elliptic curves II,” CCR Expository Report No. 34 (July 1990)

    Google Scholar 

  9. Cha, J.C., Cheon, J.H.: An identity-based signature from gap diffie-hellman groups. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 18–30. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Eisentrager, K., Lauter, K., Montgomery, P.L.: “Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation,” CT-RSA, pp. 343-354 (2003)

    Google Scholar 

  11. Eisentrager, K., Lauter, K., Montgomery, P.L.: Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves. In: ANTS 2004, pp.169-183 (2004)

    Google Scholar 

  12. Frey, G., Muller, M., Ruck, H.: The Tate Pairing and the Discrete Logarithm Applied to Elliptic Curve Cryptosystems. IEEE Transactions on Information Theory 45(5), 1717–1719 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Galbraith, S.D.: Supersingular curves in cryptography. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 495–513. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Galbraith, S.D., Harrison, K., Soldera, D.: Implementing the tate pairing. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 324–337. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. He, F.: Efficient identity based signature schemes based on pairings. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  16. Joux, A.: A one-round protocol for tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–394. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  17. Joux, A.: The weil and tate pairings as building blocks for public key cryptosystems. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 20–32. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. Kim, M., Kim, H., Kim, K.: A New Identification Scheme based on the Gap Diffie-Hellman Problem. In: 2002 Symposium on Cryptography and Information Security (SCIS 2002), Shirahama, Japan, January 29 – February 1, vol. 1/2, pp. 349–352 (2003)

    Google Scholar 

  19. Koblitz, N., Menezes, A.J.: Pairing-Based Cryptography at High Security Levels. Cryptology ePrint Archive, Report 2005/76

    Google Scholar 

  20. Menezes, A.J.: Elliptic Curve Public Key Cryptosystems. International Series in Engineering and Computer Science (1993)

    Google Scholar 

  21. Miller, V.: The Weil Pairing, and Its Efficient Calculation. Journal of Cryptology 17 (2004)

    Google Scholar 

  22. Paterson, K.G.: ID-based signatures from pairings on elliptic curves. Electronics Letters 38(18), 1025–1026 (2002)

    Article  Google Scholar 

  23. Silverman, J.H.: The Arithmetic of Elliptic Curves. In: Graduate Texts in Mathe- matics, vol. 106, Springer, Heidelberg (1986)

    Google Scholar 

  24. Solinas, J.: ID-based digital signature algorithms (2003), http://www.cacr.math.uwaterloo.ca/conferences/2003/ecc2003/solinas.pdf

  25. Verheul, E.: Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 195–210. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  26. Zhang, F., Safavi-Naini, R., Susilo, W.: ID-Based Chameleon Hashes from Bilinear Pairings. Cryptology ePrint Archive, Report 2003/208

    Google Scholar 

  27. Zhang, F., Safavi-Naini, R., Susilo, W.: An efficient signature scheme from bilinear pairings and its applications. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 277–290. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. ISaC and Department of Mathematical Sciences, Seoul National University, Korea

    Cheol Min Park & Myung Hwan Kim

  2. RSA Labs and Department of Computer Science, Columbia University, USA

    Moti Yung

Authors
  1. Cheol Min Park
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  2. Myung Hwan Kim
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  3. Moti Yung
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Editor information

Editors and Affiliations

  1. State Key Laboratory of Information Security, Institution of Software of Chinese Academy of Sciences, 100080, Beijing, China

    Dengguo Feng

  2. SKLOIS Lab, Institute of Software, Chinese Academy of Sciences, 100080, Beijing, P.R. China

    Dongdai Lin

  3. Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, NY 10027, New York, USA

    Moti Yung

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© 2005 Springer-Verlag Berlin Heidelberg

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Park, C.M., Kim, M.H., Yung, M. (2005). A Remark on Implementing the Weil Pairing. In: Feng, D., Lin, D., Yung, M. (eds) Information Security and Cryptology. CISC 2005. Lecture Notes in Computer Science, vol 3822. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11599548_27

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  • DOI: https://doi.org/10.1007/11599548_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30855-3

  • Online ISBN: 978-3-540-32424-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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