Digital signing. Public-key cryptography / asymmetric cryptography.
In this example the message is only signed and not encrypted. 1) Alice signs a message with her private key. 

2) Bob can verify that Alice send the message and that the message has not been modified. For verification the public key of Alice must be used.
Combined changed the image https://en.wikipedia.org/wiki/File:Public_key_encryption.svg from encryption to signing.
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