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 |
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【 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
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【 预 览 】
| Files | Size | Format | View |
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| 20150520102126214.pdf | 174KB |
【 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.
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