fixed inconsistance with prime numbers

encode.py

@@ -9,134 +9,123 @@
 '''
 Calcula o totiente do numero primo
 '''
-def totient(number): 
+def totient(number):
     if(prime(number)):
         return number-1
     else:
         return False
 
-    
+
 '''
 Verifica se um numero gerado é primo
 '''
-# it isnt the best method to compute prime numbers
-def prime(n): # check if the number is prime
+# fairly good method to check if a number is prime
+def prime(n):  # check if the number is prime
     if (n <= 1):
         return False
     if (n <= 3):
         return True
 
-    if (n%2 == 0 or n%3 == 0):
+    if (n % 2 == 0 or n % 3 == 0):
         return False
 
     i = 5
     while(i * i <= n):
-        if (n%i == 0 or n%(i+2) == 0):
-           return False
-        i+=6
+        if (n % i == 0 or n % (i+2) == 0):
+            return False
+        i += 6
     return True
 
 
-
 '''
 Gera um numero aleatório E, sasfazendo as condições
 '''
-def generate_E(num): 
-    def mdc(n1,n2):
+def generate_E(num):
+    def mdc(n1, n2):
         rest = 1
         while(n2 != 0):
-            rest = n1%n2
+            rest = n1 % n2
             n1 = n2
             n2 = rest
         return n1
 
     while True:
-        e = random.randrange(2,num) 
-        if(mdc(num,e) == 1):
+        e = random.randrange(2, num)
+        if(mdc(num, e) == 1):
             return e
 
-        
+
 '''
 Gera um numero primo aleatório
 '''
-def generate_prime(): # generate the prime number - p e q
-    while True: # 2**2048 is the RSA standart keys
-        x=random.randrange(1,100) # define the range of the primes
-        if(prime(x)==True):
-            return x
-'''
-Função modular entre dois números
-'''
-def mod(a,b): # mod function
-    if(a<b):
-        return a
-    else:
-        c=a%b
-        return c
+def generate_primes():  # generate the primes numbers - p and q
+    while True:  # 2**2048 is the RSA standart keys
+        x = random.randrange(11, 101, 2)  # this third param is the step (only odd numbers are accounted)
+        y = random.randrange(11, 101, 2)  # it starts at twelve so the lower primes don't mess up
+        if(prime(x) and prime(y) and x != y):  # x can't be equal to y, otherwise the algorithm won't work
+            return (x, y)
+
 
-
-
 '''
 Cifra um texto
 '''
-def cipher(words,e,n): # get the words and compute the cipher
+def cipher(words, e, n):  # get the words and compute the cipher
     tam = len(words)
     i = 0
     lista = []
     while(i < tam):
         letter = words[i]
         k = ord(letter)
         k = k**e
-        d = mod(k,n)
+        d = k % n
         lista.append(d)
         i += 1
     return lista
 
+
 '''
 Descriptografa um texto criptografado
 '''
-def descifra(cifra,n,d):
+def descifra(cifra, n, d):
     lista = []
     i = 0
     tamanho = len(cifra)
     # texto=cifra ^ d mod n
     while i < tamanho:
         result = cifra[i]**d
-        texto = mod(result,n)
+        texto = result % n
         letra = chr(texto)
         lista.append(letra)
         i += 1
-    return lista
+    return "".join(lista)
 
 
 '''
 Calcula a chave privada
 '''
-def calculate_private_key(toti,e):
+def calculate_private_key(toti, e):
     d = 0
-    while(mod(d*e,toti)!=1):
+    while(d*e % toti != 1):
         d += 1
     return d
 
 
 
-
-## MAIN
-if __name__=='__main__':
+# MAIN
+if __name__ == '__main__':
     text = input("Insert message: ")
-    p = generate_prime() # generates random P
-    q = generate_prime() # generates random Q
-    n = p*q # compute N
-    y = totient(p) # compute the totient of P
-    x = totient(q) # compute the totient of Q
-    totient_de_N = x*y # compute the totient of N
-    e = generate_E(totient_de_N) # generate E
+    p, q = generate_primes()  # generates random primes
+    n = p*q  # compute N
+    y = totient(p)  # compute the totient of P
+    x = totient(q)  # compute the totient of Q
+    totient_de_N = x*y  # compute the totient of N
+    e = generate_E(totient_de_N)  # generate E
     public_key = (n, e)
 
     print('Your public key:', public_key)
-    text_cipher = cipher(text,e,n)
+    text_cipher = cipher(text, e, n)
     print('Your encrypted message:', text_cipher)
-    d = calculate_private_key(totient_de_N,e)
+    d = calculate_private_key(totient_de_N, e)
     print('Your private key is:', d)
-    original_text = descifra(text_cipher,n,d)
-    print('your original message:', original_text)
+    original_text = descifra(text_cipher, n, d)
+    print('your original message:', original_text)