A cryptographic signature is a mathematical scheme that is used to verify the authenticity and integrity of a message or a piece of data. It is a way of signing a message with a digital key, which can be used to verify that the message was indeed sent by the person who claims to have sent it. Cryptographic signatures are an essential part of many cryptographic protocols, and they are used in a wide range of applications, including secure communication, digital signatures, and blockchain technology. To create a cryptographic signature, a sender uses a secret key to generate a unique "signature" for the message. The signature is then attached to the message, and it can be verified by anyone who has the corresponding public key. This allows recipients to verify that the message was indeed sent by the owner of the secret key, and that it has not been tampered with.