Cracking simple RSA when just the ciphertext and one public key is known
Running RSA backwards would imply cracking the key (determining the private key) and you could brute force that by factoring.  You could generate all possible prime's of the requisite size until you could generate the known public key.  Or perhaps there are other approaches that are more mathematical, that could factor for the primes, which would also be a form of brute force, as currently factoring is thought to be a NP-hard problem.