Elliptic curve

https://en.wikipedia.org/wiki/Elliptic_curve

The curve is used for "digital signatures".

Alice will be sending a message to Bob. Alice digitally signs her message, then sends the message and the signature to Bob. Bob is able to know that (1) the message really came from Alice, (2) nothing was added/removed/changed in the message between Alice and Bob.

This is important for Bitcoin.

When Bob sends Bitcoin to Alice, his wallet digitally signs, then broadcasts the transaction to all of the Bitcoin nodes, saying, "Owner of address 'B' sends 0.75 BTC to address 'A'." Digital signatures allow the other nodes to know (1) that message was actually sent by the owner of address 'B', and (2) the message has not been altered in any way.