Revista Integración, temas de matemáticas.
Vol. 24 No. 1 (2006): Revista Integración, temas de matemáticas
Research and Innovation Articles

Criptografía usando curvas hiperelípticas

Alonso Sepúlveda Castellanos
Bolsista do Cnpq, Instituto de Matemática; Unicamp-Brasil.
Bio

Published 2006-05-17

Keywords

  • Criptografia,
  • Curvas Hiperelípticas,
  • Logaritmo Discreto

How to Cite

Sepúlveda Castellanos, A. (2006). Criptografía usando curvas hiperelípticas. Revista Integración, Temas De matemáticas, 24(1), 31–50. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/255

Abstract

In this work we present properties of the hiperelípticas curves and its Jacobianos, aiming at the implementation of criptossystems of public key. Also we show the algorithm of Singer to add points in the Jacobiana variety, important for effectiveness of criptossystems, and an algorithm to attack the problem of the discrete logarithms on these groups. The not tractably of this problem is essential for the security of criptossystems.

Downloads

Download data is not yet available.

References

[1]I. Blake, G. Seroussi, N. Smart. “ Elliptic Curves in Cryptgraphy”.LondonMathematical Society Lecture Note series,265, Cambrigde,1999.

[2]D. Cantor. “Computing in the jacobian of a hiperelliptic curve”.Math.Comp.48, 95–101,1987.

[3]W. Fulton.Algebric Curves. Benjamin, New York,1969

.[4]N. Koblitz. “Hyperelliptic cryptosystems”.Journal Criptology 1, 139–150,1989.

[5]N. Koblitz.Algebraic Aspects of Cryptography. Springer-Verlag, Berlin-Heidelberg-New York,1998.

[6]H. Stichtenoth.Algebraic Function Fields and Codes. Springer-Verlag,Berlin, Heidelberg,1993.

[7] N. Thériault. “Index Calculus attack for hyperellíptic curves os small genus”,2003. (http://www.math.toronto.edu/ganita/publications.html)