An addition algorithm in Jacobian of Cab curves

Discrete Applied Mathematics

Volumn 130, Issue 1, 2003, Pages 13-31

  Arita, Seigo ^a  

^a NEC CORPORATION   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ALGORITHMS; NONLINEAR EQUATIONS;

ELLIPTIC CURVES;

PUBLIC KEY CRYPTOGRAPHY;

EID: 0042969288     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(02)00586-3     Document Type: Conference Paper

References (12)

1. Cantor D.G. Computing in the Jacobian of a hyperelliptic curve. Math. Comput. 48(177):1987;95-101.
2. J. Chao, K. Matsuo, H. Kawashiro, S. Tsujii, Construction of Hyperelliptic Curves with CM and Its Application, Asiacrypt 2000, Advances in Cryptology, Lecture Notes in Computer Sciences, Vol. 1976, Springer, Berlin, 2000.
3. Cox D., Little J., O'Shea D. Ideals, Varieties, and Algorithms. 1992;Springer, Berlin.
4. Galbraith S.D., Paulus S.M., Smart N.P. Arithmetic on superelliptic curves. J. Cryptol. 12:1999;193-196.
5. Hartshorne R. Algebraic Geometry. 1977;Springer, Berlin.
6. Koblitz N. Hyperelliptic cryptosystems. J. Cryptogr. 1:1989;139-150.
7. N. Koblitz, A very easy way to generate curves over prime fields for hyperelliptic cryptosystems, Rump Talk, Crypto '97.
8. R. Matsumoto, The Cab curve - a generalization of the Weierstrass form to arbitrary plane curves, http://www.rmatsumoto.org/cab.html.
9. Miura S. Linear codes on affine algebraic curves. Trans. IEICE. J81-A(10):1998;1398-1421.
10. J.H. Silverman, The Arithmetic of Elliptic Curves, Springer, Berlin.
11. A.-M. Spallek, Kurven vom Geshlecht 2 und ihre Anwendung in Publick-Key-Kryptosystemen, Doctor Thesis, Universität GH Essen, 1994.
12. E.J. Volcheck, Computing in the Jacobian of a plane algebraic curve, ANTS-I, Lecture Notes in Computer Science, Vol. 877, Springer, Berlin, 1994, pp. 221-233.