Factoring is the underlying, presumably hard problem upon which several public-key cryptosystems are based, including RSA. Factoring an RSA modulus would allow an attacker to figure out the private key; thus, anyone who can factor the modulus can decrypt messages and forge signatures. The security of RSA depends on the factoring problem being difficult and the presence of no other types of attack. Unfortunately, it has not been proven that factoring must be difficult, and there remains a possibility that a quick and easy factoring method might be discovered , although factoring researchers consider this possibility remote.