My understanding (albeit limited) of asymmetric public key cryptography is that the public key is designed to be shared with one and all, while the private key is kept private.
Suppose I store my local machine's public key on a remote web server, and encrypted information (by my private key) I send to this server is intercepted by another party that also possesses my public key. Does this not mean they can also decrypt my encrypted information?
If yes, does this mean I should only share the public key with the one party - in this case the server - which goes against my understanding of what a public key is for? Can I have different key pairs on my local machine for different applications?