An Elliptic Curve over F_23

Authors

DOI:

https://doi.org/10.22481/intermaths.v3i2.11364

Keywords:

Elliptic curve, Finite field, Prime Field, Weierstrass equation, Characteristic of a field

Abstract

In this work we present  model of an elliptic curve defined over a prime field. In the first  sections, we do a preliminary study of the curves elliptic and finite fields, specially Galois fields, and is defined the addition operation on the elliptic curve (depending on the characteristic of the fieldin question). In the last section we present the model of an elliptic curve defined over the field F_23.

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Author Biography

Jaime Edmundo Apaza Rodriguez, Universidade Estadual Paulista (UNESP), Câmpus de Ilha Solteira-SP, Brasil

Possui graduação em Matemática pela Universidad Nacional de San Agustin Arequipa (1982), mestrado em Matemática pela Pontificia Universidad Católica Del Perú (1986) e doutorado em Matemática pela Pontifícia Universidade Católica do Rio de Janeiro (2002). Atualmente é professor assistente da Universidade Estadual Paulista Júlio de Mesquita Filho. Tem experiência na área de Matemática, com ênfase em Geometria Algébrica (Curvas Algébricas não-Singulares), Códigos de Goppa e Criptografia com curvas Elípticas. E-mail: jaime.rodriguez@unesp.br

References

J. A. Buchmann, “Introdução à Criptografia”, Berkeley, São Paulo, 2002.

N. Koblitz, “A Course in Number Theory and Cryptography”, Springer-Verlag, New York, 1994.

N. Koblitz, A. Menezes and S. Vanstone, “The State of Elliptic Curve Cryptography, Designs, Codes and Cryptography”, 19, 173-193 (2000).

K. Rabah, “Theory and Implementation of Elliptic Curve Cryptography”, Journal of Applied Sciences 5(4); 604-633, 2005.

N. Torii and K. Yokoyama, “Elliptic Curve Cryptosystem", Fujitsu Sci. Tech. J., 36, 2, pp. 140 - 146 (2000).

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Published

2022-12-31

How to Cite

Apaza Rodriguez, J. E. (2022). An Elliptic Curve over F_23. INTERMATHS, 3(2), 92-100. https://doi.org/10.22481/intermaths.v3i2.11364

Issue

Vol. 3 No. 2 (2022)

Section

Artigos

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Copyright (c) 2022 INTERMATHS

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