What is Cryptography?

Signatures

Cryptographic signatures use asymmetric cryptography to provide a strong assurance that a signed message is authentic and has not been tampered with. While a cryptographic signature uses a private key, it is a different function than encryption. A signed message does not need to be encrypted. 

The first thing Alice will do is make her public key just that, public. She can share it on social media, add it to a key server, post it on her website, etc. She then composes a message to Bob and uses her corresponding private key to sign that message creating a digital signature. Then she can transmit the message and signature to Bob. 

Once Bob has received that message, he can run the message, signature, and Alice's public key through a signature validation function that will tell him if Alice's public key is part of the key pair that was used to create the signature from the message received. If Bob is able to validate the signature then he can be reasonably assured that the message was indeed signed by Alice and that the message has not been altered in any way. 

We can already see how digital signatures are a necessary security component in Bitcoin. They are used in Bitcoin to sign transactions, which prevents fraud by preventing anyone from forging a transaction or altering transaction data.