First, you're describing RSA signatures. "Encrypt X with your private key" means "X^D mod N" which is how RSA signatures work. In the context of RSA-based cryptosystems, it's clearer to just say "signed".
Second, the ghsign library uses the `RSA-SHA1` signer, which runs the message through SHA1 before signing it. The reason it does this is because "textbook" RSA (i.e. RSA on arbitrary messages) is vulnerable to chosen-plaintext attacks.
First, you're describing RSA signatures. "Encrypt X with your private key" means "X^D mod N" which is how RSA signatures work. In the context of RSA-based cryptosystems, it's clearer to just say "signed".
Second, the ghsign library uses the `RSA-SHA1` signer, which runs the message through SHA1 before signing it. The reason it does this is because "textbook" RSA (i.e. RSA on arbitrary messages) is vulnerable to chosen-plaintext attacks.