If they want to respond, then they encode the message with your public key and you can read it with your private key. To send an encrypted message to someone you lock the message with their public key and when they get it, they can unlock it with their private key.
The two keys work together so that you need both to decrypt anything. Your private key is the part of the encryption that you never share with anyone under any circumstance. Your public key is the part of the encryption that you make public. Anyone who wants to play creates a public key and a private key. The principle behind GPG encryption is easy.
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