The whole point of public key encryption is you cannot generate a public key from a private key, and vice versa.
Toshi
Where did you get an idea like that?
Public keys can always be generated from a private key (although apparently you need some tool other than openssl).
This doesn't sound right.
AFAIK a public-key encryption algorithm relies on two keys: a private key and a public key.
Messages encoded using the private key can be decoded using the public key, and vice versa.
Therefore, PKE can be used for authentication because one can prove one owns the private key matching a certain public key without disclosing the private key itself.
If a private key corresponding to a public key can be generated arbitrarily, then this allows impersonation.
Toshi