Encryption Software Status

python/RSA.py

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+import random
+import math
+import time
+
+def rabinMiller(n,t,kn):
+  assert t >= 1 and 0 <= kn <= 1
+  if n<=3:
+    if n>1:
+      return True
+    return False
+  elif n%2==0:
+    return False
+  RANDOM=random.SystemRandom()
+  r=n1=n-1
+  s=0
+  while (r%2)>0:
+    s+=1
+    r//=2
+  s1=s-1
+  for i in range(t):
+    if i==0 and kn==1:
+      a=2
+    else:
+      a=RANDOM.randint(2,n-2)    
+    y=pow(a,r,n)
+    if y!=1 and y!=n1:
+      j=1
+      while j<=s1 and y!=n1:
+        y=(y*y)%n
+        if y==1:
+          return False      
+        j+=1
+      if y!=n1:
+        return False
+  return True
+
+def xgcd(b, n): #computes the gcd(b,n) using the extended euclidian algoritm
+    x0, x1, y0, y1 = 1, 0, 0, 1 #x0 and y0 are the last values of x and y, x1 and y1 are the current values of x and y
+    while n != 0: #after going through the loop, n is the remainder of b/n
+        q, b, n = b // n, n, b % n #q equals the integer part of b/n, b is set equal to n, and n is equal to b%n
+        x0, x1 = x1, x0 - q * x1 #store the current x val in x0, then set the current x val to the last x value minus q times the current x val
+        y0, y1 = y1, y0 - q * y1 #same thing as above, but for y; Start next loop with n as the new b and the remainder of b/n as the new n
+    return  b, x0, y0 #return coefficents of bx + ny = gcd(b,n) and returns gcd(b, n)
+
+def mulinv(b, n): #computes the multiplicative inverse of a number mod n
+    g, x, _ = xgcd(b, n)
+    if g == 1:
+        return x % n
+
+def gen_primes(lower,upper): #generates two random primes in a range from lower to upper
+    candidate1 = random.randint(lower,upper)
+    candidate2 = random.randint(lower,upper)
+    #if it is not prime, regenerate it until it is
+    while not rabinMiller(candidate1,5,0) or not rabinMiller(candidate2,5,0) or candidate1 == candidate2:        
+        if not rabinMiller(candidate1,5,0) or candidate1 == candidate2:
+            candidate1 = random.randint(lower,upper)
+        elif not rabinMiller(candidate2,5,0) or candidate1 == candidate2:
+            candidate2 = random.randint(lower,upper)
+    return candidate1, candidate2
+
+def gen_rsa_primes(lower,upper,e):
+  p,q = gen_primes(lower,upper)
+  while not is_coprime(e,totient(p,q)):
+    p,q = gen_primes(lower,upper)
+  return p,q
+
+def is_coprime(p,q):
+    return p%q != 0 and q%p != 0
+
+def totient(p,q): #computes the totient of the product of the two prime inputs, the totient is the number of numbers coprime to that product
+    assert rabinMiller(p,5,0) and rabinMiller(q,5,0), "inputs must be prime"
+    return (p-1)*(q-1)
+
+def gen_keys(p,q,e): #generates public and private keypairs
+    tot = totient(p,q)
+    n = p*q
+
+    assert e > 1 and e < tot, "public key is not within correct domain"
+    assert is_coprime(e,tot), "public key and totient are not coprime"
+
+    d = mulinv(e,tot)
+    return (e,n),(d,n)
+
+#message input must be number (convert text to ascii numbers)
+#public key input is a tuple of (public exponent, n)
+def encrypt(public_key,message):
+    if type(message) == str:
+        ciphertext = []
+        for char in message:
+            ciphertext.append(encrypt(public_key,ord(char)))
+    else:
+        assert message > 1 and message < public_key[1],"seed is too small"
+        ciphertext = pow(message,public_key[0],public_key[1])
+
+    return ciphertext
+
+#same format as encrypt
+def decrypt(private_key,ciphertext):
+    if type(ciphertext) == list:
+        plaintext = []
+        for char in ciphertext:
+            plaintext.append(chr(decrypt(private_key,char)))
+        plaintext = "".join(plaintext)
+    else:
+        plaintext = pow(ciphertext,private_key[0],private_key[1])
+
+    return plaintext
+
+#some brief tests to make sure it is working
+t1,t2 = gen_rsa_primes(1,100,3)
+assert rabinMiller(13,5,0),"is_prime did't correctly check if it was a prime"
+assert rabinMiller(t1,5,0) and rabinMiller(t2,5,0), "gen_rsa_primes didn't generate a pair of primes"
+assert is_coprime(totient(t1,t2),3), "gen_rsa_primes did not generate coprime primes"
+assert totient(11,13) == 120, "totient is broken somehow"
+assert is_coprime(12,13), "is_coprime does not correctly check for coprimes"
+
+message = "abcdefghijklmnopqrstuvwxyz"
+#message = 123
+e = 2
+start = time.clock()
+p,q = gen_rsa_primes(pow(2,1024),pow(2,1025),e)
+finish = time.clock() - start
+public,private = gen_keys(p,q,e)
+#public = (7,2534665157)
+#private = (1810402843,2534665157)
+
+#p,q = gen_rsa_primes(10000,15000,e)
+#public,private = gen_keys(p,q,e)
+
+print(public)
+print(private)
+
+print(message)
+cipher = encrypt(public,message)
+print(cipher)
+plain = decrypt(private,cipher)
+print(plain)
+print(finish)