python - PythonRSAアルゴリズムの修正

Question

私はユークリッドアルゴリズムと乗法逆数の前のスレッドの質問をしていましたが、それは完全なコードを投稿して厳密な質問をする方が良いことを理解しました：私はpython rsa実装を行っており、間違った結果を出力しているので修正する必要があります。

コード：

import fractions  #gcd

def generateRSAKeys(p, q):
    "Generate RSA Public and Private Keys from prime numbers p & q"

    n = p * q #is used as the modulus for both the public and private keys
    etf = (p - 1) * (q - 1) #Euler's totient function.  etf   

    # Generate a number e so that gcd(n, e) = 1, start with e = 3
    e = 3

    while 1:
        if fractions.gcd(e, etf) == 1 and 1<e and e<etf: 
            break  
        else: 
            e = e + 1 

    #e is released as the public key exponent.
    # start with a number d = etf/e will be atleast 1


    #e*d == 1%etf  #multiplicative inverse of etf   
    d = (e**(etf-2)) % etf 

    # Return a tuple of public and private keys 
    return ((n,e), (n,d))           

    #http://en.wikipedia.org/wiki/RSA_%28algorithm%29

if __name__ == "__main__":

    print "RSA Encryption algorithm...."
    p = long(raw_input("Enter the value of p (prime number):"))
    q = long(raw_input("Enter the value of q (prime number):"))

    print "Generating public and private keys...."
    (publickey, privatekey) = generateRSAKeys(p, q)

    print "Public Key (n, e) =", publickey
    print "Private Key (n, d) =", privatekey

    n, e = publickey
    n, d = privatekey

    m = 34 #some message

    print "0<m<n m=", m
    print "0<m<n n=" , n
    #then computes ciphertext c
    c = (m**e)%n
    print "Encrypted number using public key =", c
    #recovering
    m = (c**d)%n
    print "Decrypted (Original) number using private key =", m