RSA

For this week, the homework is to implement the RSA, I followed the next steps:

(the names of my variables are different than those we saw in class because I based the variable names on the book "Discrete Mathematics, Richard Johonsonbaugh"
)

• Create 3 scripts, one that generate public and private keys, another that is client.py and one for the server.py.

• For keys first generate a list of primes where I chose the p and q
• After, the n in my program is part of the public key. I chose the prime number as n. I noticed that phi is not a multiple of n.
• Immediately implements the Euclidean algorithm to get the s(private key)
• and finally create two key files, one public.txt and one private.txt
• I create the client.py and server.py and follow the next steps:

RSA:

	#!/usr/bin/python
	import random
	def genera_primos():
	"""hago una lista de los primero 10 numeros primos
	para despues de ahi elegir p,q, y n
	"""
	numero = 2
	total = 0
	primos = list()
	while total <= 10:
	div = 0
	cont = 1
	while cont <= numero:
	res = numero % cont
	if res == 0:
	div = div + 1
	cont = cont + 1
	if div <= 2:
	total = total + 1
	primos.append(numero)
	numero = numero + 1
	return primos
	def escoge_p_q():
	"""eligo p y q al azar decidi que no se repitieran
	"""
	primos = genera_primos()
	p = random.choice(primos)
	primos.remove(p)
	q = random.choice(primos)
	return p, q
	def escoge_n(o):
	"""escogo n al azar de la lista de numeros primos
	la escogo prima para que pueda cumplir mas facil las caracteristicas
	de ser coprima con o=(p-1)(q-1)
	"""
	primos = genera_primos()
	n = random.choice(primos)
	if o%n == 0 or n>o:
	return escoge_n(o)
	return n
	def euclides(n, o):
	"""en esta funcion obtengo la s,
	que hace que (s*n mod o) sea igual a 1
	"""
	a = n
	b = o
	s, t, s1, t1 = 1, 0, 0, 1
	while b != 0:
	q = a/b
	r = a%b
	a, s, t, b, s1, t1 = b, s1, t1, r, s-(s1*q), t-t1*q
	s = s%o
	return s
	def escribo_clave_publica():
	usuarios = ['cecy', 'lupita', 'pedrito']
	f = open("claves_publicas.txt", "w")
	datos = {}
	for i in usuarios:
	p, q = escoge_p_q()
	print "La p y la q son:"
	print p, q
	z = p * q
	print "La z es:"
	print z
	o = (p-1)*(q-1)
	print "La o es:"
	print o
	n = escoge_n(o)
	print "La n es:"
	print n
	clave_publica = z, n
	print "La clave publica es:"
	print clave_publica
	f.write(""+str(i)+", "+str(n) + ", "+str(z)+"\n")
	datos[i] = [p, q, z, o, n]
	f.close()
	return datos
	def escribo_clave_privada(datos):
	usuarios = ['cecy', 'lupita', 'pedrito']
	f = open("claves_privadas.txt", "w")
	for i in datos:
	numeros = datos[i]
	print numeros
	p = numeros[0]
	q = numeros[1]
	z = numeros[2]
	o = numeros[3]
	n = numeros[4]
	s = euclides(n, o)
	print "La s encontrada es:"
	print s
	x = int(random.random()*100)
	print "la x es:"
	print x
	f.write(""+str(i)+", "+str(s) + ", "+str(z)+"\n")
	def main():
	datos = escribo_clave_publica()
	print datos
	escribo_clave_privada(datos)
	main()

view raw gistfile1.py hosted with ❤ by GitHub

Server:

	#!/usr/bin/python
	import socket
	import random
	def f(x):
	y = x*29
	return y
	def leer_claves():
	f = open("claves_publicas.txt")
	usuarios = {}
	for l in f.readlines():
	linea = l.split("\n")[0]
	linea = linea.split(",")
	#print linea
	usuarios[linea[0]] = [linea[1], linea[2]]
	return usuarios
	def main():
	usuarios = leer_claves()
	socket_1 = socket.socket()
	socket_1.bind(("localhost", 9999))
	print "Servidor iniciado"
	socket_1.listen(1)
	socket_2, addr = socket_1.accept()
	x = int(random.random()*100)
	socket_2.send(str(x))
	datos = socket_2.recv(512)
	datos = datos.split(",")
	print datos
	usuario = datos[0]
	r = int(datos[1])
	if usuario in usuarios:
	print usuario
	clave = usuarios[usuario]
	n = clave[0]
	z = clave[1]
	y = (int(r)**int(n))%int(z)
	if f(x) == y:
	print "Bienvenido al sistema"
	else:
	print "Algo esta mal con las igualdades"
	else:
	print "Algo esta mal con el nombre"
	socket_1.close()
	socket_2.close()
	main()

view raw gistfile1.py hosted with ❤ by GitHub

Client:

	#!/usr/bin/python
	import socket
	def leer_claves():
	f = open("claves_privadas.txt")
	usuarios = {}
	for l in f.readlines():
	linea = l.split("\n")[0]
	linea = linea.split(",")
	usuarios[linea[0]] = [linea[1], linea[2]]
	return usuarios
	def f(x):
	y = x*29
	return y
	def main():
	usuarios = leer_claves()
	socket_c = socket.socket()
	socket_c.connect(("localhost", 9999))
	print "Servidor iniciado"
	x = socket_c.recv(512)
	x = int(x)
	y = f(x)
	usuario = raw_input("Usuario: ")
	print usuario
	if usuario not in usuarios:
	print "Algo esta mal"
	socket_c.close()
	return
	datos = usuarios[usuario]
	s = int(datos[0])
	z = int(datos[1])
	r = (y**s)%z
	enviar = ""+usuario+","+str(r)
	socket_c.send(enviar)
	socket_c.close()
	main()

view raw gistfile1.py hosted with ❤ by GitHub

Corrects users and keys:

Incorrect user:

Extra points