期刊论文详细信息
ETRI Journal
Scalar Multiplication on Elliptic Curves by Frobenius Expansions
关键词: cryptology;    public key cryptosystem;    elliptic curves;    Frobenius expansions;    Frobenius map;    scalar multiplications;    elliptic curve cryptosystems;   
Others  :  1184264
DOI  :  10.4218/etrij.99.0199.0102
PDF
【 摘 要 】

Koblitz has suggested to use "anomalous" elliptic curves defined over F2, which are non-supersingular and allow or efficient multiplication of a point by and integer, For these curves, Meier and Staffelbach gave a method to find a polynomial of the Froben

【 授权许可】

   

【 预 览 】
附件列表
Files Size Format View
20150520102126214.pdf 174KB PDF download
【 参考文献 】
  • [1]J.H. Cheon, S. Park, S. Park and D. Kim, "Two Efficient Algorithms for Arithmetic of Elliptic Curves Using Frobenius Map," Proc. of PKC'98, 1998, pp. 160-168.
  • [2]J. Guajardo, and C. Paar, "Efficient Algorithms for Elliptic Curve Cryptosystems," Proc. Crypto '97, Springer-Verlag, 1997, pp. 342-356.
  • [3]K. Koyama and Y. Tsuruoka, "Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method," Proc. Crypto'92, Springer-Verlag, 1993, pp. 43-56.
  • [4]N. Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, 1991.
  • [5]N. Koblitz, "CM Curves with Good Cryptographic Properties," Proc. Crypto '91, Springer-Verlag, 1992, pp. 279-287.
  • [6]N. Koblitz, "Elliptic Curve Cryptosystems," Math. of Comp., vol. 49, 1987, pp. 203-209.
  • [7]W. Meier and O. Staffelbach, "Efficient Multiplication on Certain Non-Supersingular Elliptic Curves," Proc. Crypto '92, Springer-Verlag, 1993, pp. 333-344.
  • [8]A. Menezes, Elliptic Curve Public Key Cryptosystems, Kluwer Academic Publishers, 1993.
  • [9]F. Morain and J. Olivos, "Speeding up the Computations on an Elliptic Curve Using Additions-Subtraction Chains," Inform. Theory. Appl., vol. 24, 1990, pp. 531-543.
  • [10]V. Müller, "Fast multiplication on elliptic curves over small fields of characteristic two," Journal of Cryptology, vol. 11, no. 4, 1998, pp. 219-234.
  • [11]T. Satoh and K. Araki, Fermat Quotient and the Polynomial Time Discrete Log Algorithm for Anomalous Elliptic Curves, preprint, 1997.
  • [12]R. Schoof, "Elliptic Curves over Finite Fields and the Computation of Square Roots mod p," Math. Comp., vol. 44, 1985, pp. 483-494.
  • [13]I.A. Semaev, "Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p," Mathematics of Computation, vol. 67, no. 221, pp. 353-356.
  • [14]J. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1992.
  • [15]N.P. Smart, "Discrete logarithm problem on elliptic curves of trace one," HP Laboratories Technical Report, (97-128), pp. 3pp.
  • [16]J. Solinas, "An Improved Algorithm for Arith-metic on a Family of Elliptic Curves," Proc. Crypto '97, Springer-Verlag, 1997, pp. 357-371.
  文献评价指标  
  下载次数:20次 浏览次数:38次