ETRI Journal

  • 제33권4호
  • /
  • Pages.656-659
  • /
  • 2011
  • /
  • 1225-6463(pISSN)
  • /
  • 2233-7326(eISSN)
한국전자통신연구원 (Electronics and Telecommunications Research Institute)
권호 표지
DOI QR코드

DOI QR Code

Pairing-Friendly Curves with Minimal Security Loss by Cheon's Algorithm

  • 투고 : 2010.09.08
  • 심사 : 2010.12.09
  • 발행 : 2011.08.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In ICISC 2007, Comuta and others showed that among the methods for constructing pairing-friendly curves, those using cyclotomic polynomials, that is, the Brezing-Weng method and the Freeman-Scott-Teske method, are affected by Cheon's algorithm. This paper proposes a method for searching parameters of pairing-friendly elliptic curves that induces minimal security loss by Cheon's algorithm. We also provide a sample set of parameters of BN-curves, FST-curves, and KSS-curves for pairing-based cryptography.

키워드

참고문헌

  1. J.H. Cheon, "Discrete Logarithm Problems with Auxiliary Inputs," J. Cryptology, vol. 23, no. 3, 2010, pp. 457-476. https://doi.org/10.1007/s00145-009-9047-0
  2. D. Sun, Elliptic Curves with the Minimized Security Loss of the Strong Diffie-Hellman Problem, Doctoral Dissertation, Seoul National University, 2007.
  3. A. Miyaji, M. Nakabayashi, and S. Takano, "New Explicit Conditions of Elliptic Curve Traces for FR-Reduction," IEICE Trans. Fundamentals, E84-A(5), 2001, pp.1234-1243.
  4. P.S.L.M. Barreto, B. Lynn, and M. Scott, "Constructing Elliptic Curves with Prescribed Embedding Degrees," Proc. SCN, LNCS, vol. 2576, 2002, pp. 263-273.
  5. F. Brezing, and A. Weng. "Elliptic Curves Suitable for Pairing Based Cryptography," Designs, Codes, Cryptography, vol. 37, no. 1, 2005, pp. 133-141. https://doi.org/10.1007/s10623-004-3808-4
  6. A. Comuta, M. Kawazoe, and T. Takahashi, "Pairing-Friendly Elliptic Curves with Small Security Loss by Cheon's Algorithm," Proc. ICISC, LNCS, vol. 4817, 2007, pp. 297-308.
  7. D. Freeman, "Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10," Proc. ANTS-VII, LNCS, vol. 4076, 2006, pp. 452-465.
  8. D. Freeman, M. Scott, and E. Teske, "A Taxonomy of Pairing- Friendly Elliptic Curves," J. Cryptology, vol. 23, no. 2, 2010, pp. 224-280. https://doi.org/10.1007/s00145-009-9048-z
  9. H.W. Lenstra Jr., "Factoring Integers with Elliptic Curves," Annals of Mathematics, vol. 126, no. 3, 1987, pp. 649-673. https://doi.org/10.2307/1971363
  10. A.O.L. Atkin and F. Morain, "Elliptic Curves and Primality Proving," Mathematics of Computation, vol. 61, 1993, pp. 29-68. https://doi.org/10.1090/S0025-5718-1993-1199989-X
  11. P.S.L.M. Barreto and M. Naehrig, "Pairing-Friendly Elliptic Curves of Prime Order," Proc. SAC, LNCS, vol. 3897, 2005, pp. 319-331.
  12. E. Kachisa, E. Schaefer, and M. Scott, "Constructing Brezing- Weng Pairing Friendly Elliptic Curves Using Elements in the Cyclotomic Field," Proc. Pairing, LNCS, vol. 5209, 2008, pp. 126-135.

피인용 문헌

  1. On the Final Exponentiation in Tate Pairing Computations vol.59, pp.6, 2011, https://doi.org/10.1109/tit.2013.2240763
  2. Simple and Provably Secure Anonymous Authenticated Key Exchange with a Binding Property vol.eb98, pp.1, 2011, https://doi.org/10.1587/transcom.e98.b.160
  3. Short Dynamic Group Signature Scheme Supporting Controllable Linkability vol.10, pp.6, 2015, https://doi.org/10.1109/tifs.2015.2390497
  4. Anonymity-Based Authenticated Key Agreement with Full Binding Property vol.18, pp.2, 2011, https://doi.org/10.1109/jcn.2016.000028