I was studying a little about PGP. I am a total newbie at it.

But there are so many similarities to PGP and Bitcoin. Is it possible to encrypt a message using my public key, and decrypt it using my private key? Like PGP does. It would be something very nice to do, as Bitcoin clients are much more common and widespread than PGP related software (also easier to use).

I would like to be able to encrypt my messages using bitcoin key pairs. It would be really useful.

Maybe in future Bitcoin signatures could even replace PGP signatures? Is there any discussion about this? Or is it technically impossible ? I searched but couldn't find any.