If we are being strictly mathematical, we have no proof that one-way functions exist, nor any real evidence that they can be constructed. B. Scheneier, Wiley 1996. The NSA has mandated 512 bits to 1024 bits for their Digital Signature Standard far less than I recommend for long term security. B. Scheneier, Wiley 1996. When the first quantum factoring devices are built, the security of public key cryptosystems will vanish.
Criminals steal passwords from the sick and dead and scout classified systems without.