(HARD) Given a public key exponent and the "totient," the result of multiplying (prime1-1)*(prime2-1) from the two primes used to create the public key, discover the private key exponent. The private key is the smallest number x such that (publicKey * x) % totient == 1.

The public key exponent is available to anyone, as is the modulus (prime1*prime2), but the totient number is kept secret as are the two primes themselves.

This problem is based on, and helps to construct, the simplified public key encryption algorithm found at https://en.wikibooks.org/wiki/Cryptography/A_Basic_Public_Key_Example