Why in this paper private (public) keys are used to encrypt (decrypt) messages?

Question

I'm reading this paper, at page 5 you can find:

We apply a public key cryptographic algorithm in this work, similar to the one used by Digital Signature. To simplify the description, we use PBA to represent this public key algorithm. Its encryption and decryption can be described with the following formats: PBA.encrypt ( m , k ) for encrypting a message m with the public key k, and PBA. decrypt ( m , k ) for decrypting a message m with the private key k.

This seems a classic public key approach. However, all over the paper, the encrypt method is called using private key, while decrypt by using public key. Isn't it the opposite?

Example:

The proxy credential is sent directly, while the random message CA_Rand and the user session are encrypted with the private key MN_Prv that was generated in Phase II: MN_Rand = PBA . encrypt ( CA_Rand , MN_Prv ) MN_U _Session = PBA . encrypt ( U _Session , MN_Prv )

Is that an error (very frequent error!) or am I missing something?

Answer 1

As commenters have said, technically you can use either the public or private key for either capacity; the distinction helps prevent you from accidentally distributing both publicly at some point, which would be a catastrophic failure.

PGP provides good examples of reasons to do it both ways. If I want to send you a sensitive message, I will encrypt it with your public key, which means that you will decrypt it with your private key. However, if I want to prove that an email comes from me, I can "sign" the message, which involves encrypting some data with my private key; anyone who has my public key can decrypt it, which allows them to verify that the person sending the message had access to my private key (and presumably then is me).