Generación de curvas elípticas con buenas propiedades criptográficas sobre campos primos

Autores/as

  • Yessica Caridad Castaño Sainz Instituto de Criptografía, Universidad de la Habana, La Habana
  • Claudia Espinosa Contreras Empresa de Tecnologías para la Defensa (XETID)
  • Huber Martínez Rodríguez Departamento de Matemática, Facultad de Ciencias Informáticas, Universidad de Ciego de Ávila https://orcid.org/0000-0002-2452-7574

Palabras clave:

parámetros de definición de curvas elípticas, requisitos de seguridad, requisitos técnicos

Resumen

En este trabajo se presentan las funcionalidades del paquete implementado en SAGE, ECDP Generator, el cual permite generar parámetros de definición de curvas elípticas utilizando los métodos pseudoaleatorio y pseudoaleatorio verificable para las formas de Weierstrass, Edwards y torcida de Edwards y evaluar la seguridad de diferentes juegos de parámetros. Para ello se analizaron los requisitos de seguridad que una curva elíptica debe satisfacer para ser utilizada en sistemas criptográficos teniendo en cuenta los requisitos adoptados por los diferentes estándares y las discusiones sobre la estandarización de nuevas curvas elı ́pticas. Se analizan requisitos técnicos que propician implementaciones eficientes y en el caso de la forma de Edwards (torcida de Edwards) completitud en las operaciones de grupo. Se presentan algoritmos para verificar las condiciones del discriminante y el número de clases que constituyen las restricciones más complejas.

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Publicado

2024-03-26 — Actualizado el 2019-06-27

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Cómo citar

[1]
Castaño Sainz, Y.C. et al. 2019. Generación de curvas elípticas con buenas propiedades criptográficas sobre campos primos. Ciencias matemáticas. 33, 1 (jun. 2019), 18–27.

Número

Vol. 33 Núm. 1: Junio, 2019

Sección

Artículo Original

Licencia

Derechos de autor 2019 Ciencias Matemáticas

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