Sage Codes

def randomPrimes (pbit , qbit) :
  # Choosing large primes
  # 512 <= pbit <= 1024 and multiple of 64
  p = random_prime ( 2^pbit , proof=True , lbound=2^(pbit-1) )
  q = random_prime ( 2^qbit , proof=True , lbound=2^(qbit-1) )
  # q must be prime divisor of p
  if is_prime(p) and is_prime(q) : return p,q
  else : randomPrimes(640,160)
  #   The algorithm parameters (p, q, g) may be shared between different users of the system. 
def integers (p , q) :
# The signer selects a random secret integer k
  h = Integer ( 1 , p-1 )
  # h is any integer 1 < h < (p-1) 
  g = ( ( h ^ ( (p-1) / q ) ) % p)
  k = randint ( 0 , q )
  return h,g,k
  # Creating a new per-message key
  #   Parameters x and k are used for signature generation only, and must be kept secret.
  #   Parameter k must be regenerated for each signature
def private_key (q) : # Generate a private key
  # The private key is used in the signature generation process 
  x = randint ( 1 , q+1 )
  return x
def public_key (x , g , p) : # Generate a public key
  # The public key is used in the signature verification process
  y = ( g^x ) % p
  return y
def getMessage () : 
  # Read the file to sign 
  myFile = open ( "/home/EmreOvunc/Desktop/Message.txt" , "r" )
  # Opens file with name of "Text.txt"
  Message = myFile.read() 
  print "<<< Message >>>\n\n" , Message , "\n<<< End of The Message >>>\n"
  myFile.close()
  return Message
  # Read text file and print it and then return message
  def signature_signing (p , q , g , k , Message , x) : 
  # Computes signature pair
  r = ( ( g^k ) % p ) % q
  s = ( ( k^1 ) * ( hash ( Message ) + x * r ) ) % q
  signed_document(s)
  # Signature = ( r , s ) 
  return s,r 
def signed_document(s) :
  # Write file to signed document
  signedFile = open ( "/home/EmreOvunc/Desktop/Sign.txt" , "w+")
  signedFile.write(str(s))
  signedFile.close()
  def signature_verification (s , r , Message , p , q , publicKey , g) :  
  w = ( s^-1 ) % q
  u1 = ( hash ( Message ) * w ) % q
  # Convert message to hash value
  u2 = ( r*w ) % q
  v = ( ( (g^u1) * ((publicKey)^u2) ) % p ) % q
  if v==r : print "The signature is verified !"
  else: print "The signature is not verified!"
  # if v = r, then the signature is verified and the verifier can have high confidence that the 
  #received 
  #    DSA is similar to the ElGamal signature scheme
def main () : 
  p,q = randomPrimes (640,160)
  h,g,k = integers (p,q)
  privateKey = private_key (q)
  publicKey = public_key (privateKey,g,p)
  messageI = getMessage ()
  s,r = signature_signing (p,q,g,k,messageI,privateKey)
  signature_verification (s,r,messageI,p,q,publicKey,g)
main ()