Research and Innovation Articles
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)
[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)