Reto Top Coder #1

Inspirado en el conocido sistema de cifrado RSA ( se propuso el siguiente enunciado a resolver:


Una conocida tienda online desea implementar un método seguro para compras por internet y para ello se asoció con una entidad financiera que provee dispositivos que generan códigos cada minuto. Los códigos están sincronizados con un servidor y asociados a la cuenta de cada usuario. Los códigos están conformados por algunos dígitos constantes, otros variables, son únicos por usuario y tienen las siguientes características:

    • Son códigos de 8 o 10 dígitos.
    • El producto de las 02 primeras cifras (números aleatorios) es igual al 3er y 4to dígito (00,01,02…81).
    • La 5ta cifra es igual a la cantidad de vocales distintas de su primer nombre.
    • La 6ta cifra es un número equivalente a la última letra del 2do apellido según la siguiente tabla:























































    • La sumatoria de las cifras de la fecha de nacimiento del usuario es igual a los últimos dígitos del código.


Nombre usuario: Alberto Rodrigo Bertelo Mansilla
Fecha Nacimiento (>=18 años): 29/09/1995

1er aleatorio = 2
2do aleatorio = 9
# vocales distintas 1er nombre = 3
última letra = a = 0
sumatoria (2+9+0+9+1+9+9+5) = 44

Método de encriptación:

m = Número a encriptar
c = Número encriptado

p = númer primo #1
q = número primo #2
n = p*q
f(n) = (p-1)*(q-1)
e = número sin divisores comunes con f(n) y que divida a f(n) + 1 sin residuo.
d = ( f(n)+1 ) / e
c= m^emodn (Número encriptado)
m=c^dmodn (Número desencrptado)

Entonces: p= 311, q= 23 , n = 253 , f(n) = 220 , e= 13 , d= 221/ 13 = 17, y el número a encriptar es 44,

c = 44^13mod253 = 88
m = 88^17mod253 = 44

Código: 29183088

A través del Website los usuarios generan sus datos de acceso (nombre de usuario y contraseña), se les envía un correo electrónico de confirmación y se activa la cuenta. La Base de Datos contiene datos de usuarios, productos, compra (clave utilizada, lugar y fecha de compra, entre otros). Finalmente, la tienda sólo permite compras entre las 7am y 12am, fuera de ese periodo devuelve un mensaje de error.

El reto Top Coder consiste en:

a) Programar el algoritmo para la creación y validación de códigos.
b) Generar todas las combinaciones posibles.

Para hacerlo utilizar la lista de usuarios:

Usuario Fecha de Nacimiento
Alberto Rodrigo Bertelo Mansilla 29/09/1995
Alvaro Andrés Gonzáles Porras 1988-03-22
Bertha Luz Linares Coya 1990/08/11
Cinthia Yolanda Salas Núñez 1988-03-12
Donald Darío Robles Maldonado 1995-05-05
Aldo Franco Barrenechea 1986-09-23
Roberto Carlos Zurdo Izquierdo 01/12/1978
Carmen Molina Esparta 1986-09-23
Silvana María Morote Zavala 1983-02-09
Alex Tercio Coronado 1980-11-08
Diego Rodrigo Novoa Alpes 1982-10-14


Solución en Python Descargar

Los ganadores Jorge Suárez y Angel Ortiz :


Solución en PHP Descargar

Para ejecutar el script utilizar lo siguiente:

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