Elgamal
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El algoritmo ElGamal se basa en el trabajo de Diffie-Hellman de 1976 sobre criptografía de clave pública. Fue descrito por Taher ElGamal en 1984 y puede usarse para generar firmas digitales, cifrar o descifrar mensajes. Se utiliza en software como GNU Privacy Guard y versiones recientes de PGP. El esquema involucra que Alicia elija números primos P y G, así como una clave privada A, para generar su clave pública. Bruno luego puede cifrar un mensaje eligiendo un número aleatorio y aplicando operaciones módulo
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Elgamal
- 1. ELGAMAL PRESENTADO POR: SERGIO ANDRES MURILLO TORRES
- 2. • Basado en la idea de Whitfield Diffie y Martin Hellman en 1976 “EL ALGORITMO DISCRETO”. • DESCRITO POR Taher ElGamal en 1984 • puede ser utilizado tanto para generar firmas digitales, cifrar o descifrar.
- 3. • se usa en software GNU Privacy Guard, versiones recientes de PGP, y otros sistemas criptográficos • uso libre sin patente
- 4. EJEMPLO Para generar la clave, Alicia escoge un número primo P cualquiera tal que P-1 tenga un factor primo grande (esto se pide para que el problema del logaritmo discreto sea difícil ). Además elige dos números aleatorios G (el generador) y A (que actuará como clave privada) tal que Alicia calcula el valor de . La clave pública será (G, P, K) , mientras que el valor de A lo mantendrá en secreto. .
- 5. Cifrado Supongamos que Bruno tiene un texto claro que quiere enviar cifrado a Alicia. Lo primero por hacer es convertir este texto en un entero entre y , obteniendo un (esto no es parte del cifrado, sino que es una manera de codificar estándar, conocida por todos). Luego Bruno escoge arbitrariamente un número (que mantendrá secreto) para finalmente calcular:
- 6. El mensaje cifrado final corresponde a la tupla
- 7. Descifrado[editar] Para descifrar se tiene que realizar el siguiente cálculo: donde representa el inverso de módulo P (que, utilizando el Pequeño teorema de Fermat puede calcularse como ). Veamos por qué esto da como resultado : Vale observar que para calcular el descifrado, es necesario conocer , que es justamente la clave privada de Alicia.