Some Results For Computation Theory In Hyperelliptic Curves Type

Tran Duy Hung; Dao Viet Cuong; Ngo Tien Hung; Pham Tien Huy

doi:https://doi.org/10.14445/22315373/IJMTT-V67I10P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 10 | Year 2021 | Article Id. IJMTT-V67I10P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I10P506

Some Results For Computation Theory In Hyperelliptic Curves Type

Tran Duy Hung, Dao Viet Cuong, Ngo Tien Hung, Pham Tien Huy

Citation :

Tran Duy Hung, Dao Viet Cuong, Ngo Tien Hung, Pham Tien Huy, "Some Results For Computation Theory In Hyperelliptic Curves Type," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 10, pp. 67-71, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I10P506

Abstract

In this paper we consider a reduction algorithm and computation in the Jacobian of a hyperelliptic curve type as forms y2 = Pn(x), n≥3, which is generalized of a usual elliptic curve

Keywords

Cryptosystems, Elliptic curve, Hyperelliptic curve type.

References

[1] Andreas Enge: Elliptie eurves and their applieations to eryptography – an Introduction. Kluwer Academic Publishers, (1999).
[2] DavidG., Cantor: Computing in the Jacobian of a Hyperelliptic Curve. Math. Com., 48(177) (1987) 95-101.
[3] Martin Seysen., A Probabilistic Factorization Algorithm with Quadratic Forms of Negative Discriminant. Mathematics of Computation, 48(178) (1987) 757-780.
[4] Neal Koblitz: HyperellipticCryptosystem. J. Cryptology., 1 (1989)139-150
[5] N. Koblitz: Elliptic curve cryptosystems, Math. Comp., 48 (1987) 203-209
[6] Serge Lang: Introduction to Algebraic Geometry. Interscience, New York, (1958).
[7] W. Diffie and M. Hetlman: New directions in cryptography, IEEE Trans. Inform. Theory, 22 (1976) 644-654.