RSA Authentication

For this week, we had to do the following:

•  Implement RSA authentication in Python for a client-server system with sockets.

Key generation

RSA involves a public key and a private key. The public key can be known to everyone and is used for encrypting messages. Messages encrypted with the public key can only be decrypted using the private key. 

So, the algorithm is:

    * Generate n = p × q, where both p and q are prime.
    * (e, n) is the public key; c = m^e mod n.
    * e is to be relatively prime with ɸ(n)
    * (d, n) is the private key; m = c^d mod n.
          o Requirement: e × d ≣ 1 mod ɸ(n) (or in other words d needs to be the inverse multiplicative of e);
    * ɸ(n) = (p - 1) × (q - 1).
    * m^(e×d)≣ m mod n due to Euler’s theorem.

 

These are the results

These are the results.

Code RSAKeys: 

	import math
	import random
	from random import randint
	def t_primo(num):
	for i in range(2,num):
	if num % i == 0:
	return False
	return True
	def mcd(phi_n, e): #obtener el facor comun de phi
	if phi_n % e == 0:
	return e
	else:
	return mcd(e, phi_n%e)
	def gcde(e,phi_n):
	a, A = 0, 1
	c, C = 1, 0
	while phi_n:
	coct = e // phi_n
	e, phi_n = phi_n, e%phi_n
	a, A = A - coct * a, a
	c, C = C - coct * c, c
	return(A, C, e)
	def inverso(e, phi_n):
	a, c, gcd = gcde(e,phi_n)
	if gcd == 1:
	return (a+phi_n)%phi_n
	else:
	return 0
	def g_primo():
	while True:
	num = randint(50,100)
	if t_primo(num):
	break
	return num
	def crear_e(phi_n):
	e = g_primo()
	#print e
	if(mcd(phi_n, e) == 1):
	return e
	else:
	crear_e(phi_n)
	def claves(user1,d,e,n):
	a= str(user1)+" "+str(e) +" "+str(n)+"\n"
	b= str(user1)+" "+str(d) +" "+str(n)+"\n"
	arch=open("Server_keys.txt","a")
	arch.write(a)
	arch.close
	us= str(user1)+ ".txt"
	arch2=open(us,"a")
	arch2.write(b)
	arch2.close
	def main():
	user1=raw_input("Nombre de usuario:")
	#clave=claves(user1,d,e,n)
	p = g_primo()
	q = g_primo()
	print p
	print q
	n = p*q
	print n
	phi_n =(p-1)*(q-1)
	print phi_n
	e = crear_e(phi_n)
	print e
	d = inverso(e, phi_n)
	print d
	clave=claves(user1,d,e,n)
	print clave
	main()

view raw gistfile1.py hosted with ❤ by GitHub

Server:

	import socket
	import random
	import socket,sys,pickle
	from math import sqrt
	#if __name__ == '__main__':
	def bArchivo(usuario):
	file = open("Server_keys.txt", "r")
	for linea in archivo.readlines():
	if len(linea)==0:
	continue
	lin = linea.split()
	if lin[0] == usuario:
	dato1=[int(lin[1]), int(lin[2])]
	return dato1
	else:
	linea += 1
	return False
	file.close()
	return False
	def fun(x):
	x =(x*sqrt(3)+7)
	return x
	def main():
	# Se prepara el servidor
	server = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
	server.bind(("", 8000))
	server.listen(1)
	print "Esperando clientes..."
	# bucle para atender clientes
	while 1:
	# Se espera a un cliente
	socket_cliente, datos_cliente = server.accept()
	# Se escribe su informacion
	print "conectado "+str(datos_cliente)
	x=randint(1,1000)
	usuario=socket_cliente.recv(1000)
	socket_cliente.send(str(x))
	seguir = True
	while seguir:
	# Espera por datos
	peticion = socket_cliente.recv(1000)
	if dato1 == False:
	dato1= bArchivo(peticion)
	print "no identificado"
	socket_s.close()
	client_socket.close()
	e = dato1[0]
	n = dato1[1]
	y = (int(request)**e)%n
	# Contestacion a "hola"
	if fun (x) == y:
	#print str(datos_cliente)+ " envia hola: contesto"
	socket_cliente.send("hola")
	else:
	socket_client.send("fail")
	socket_client.close()
	main()

view raw gistfile1.py hosted with ❤ by GitHub

Cliente: 
 Here I have a difficult with of server, this is the code but it hasn´function

	import socket
	from math import sqrt
	def bArchivo(usuario):
	file = open("Server_keys.txt", "r")
	for linea in archivo.readlines():
	if len(linea)==0:
	continue
	lin = linea.split()
	if lin[0] == usuario:
	dato1=[int(lin[1]), int(lin[2])]
	return dato1
	else:
	linea += 1
	#return False
	file.close()
	return False
	def fun(x):
	x =(x*sqrt(3)+7)
	return x
	def main():
	server = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
	server.bind(("", 8000))
	server.listen(1)
	print " clientes..."
	socket_cliente, datos_cliente = server.accept()
	# Se escribe su informacion
	print "conectado cliente "+str(datos_cliente)
	#x=randint(1,1000)
	socket_cliente.send(str(x)) peticion = socket_cliente.recv(1000)
	print Client
	rx = int(x)
	y = funcion(rx)
	usuario = raw_input("usuario:")
	dato1= bArchivo(request)
	if dato1 == False
	print no eres
	d=dato1[0]
	n=dato1[1]
	r =str(pow(y,d) %n)
	#print str(datos_cliente)+ " envia adios: contesto y desconecto"
	socket_cliente.send(usuario)
	socket_cliente.send(r)
	socket_cliente.close()
	main()

view raw gistfile1.py hosted with ❤ by GitHub