Digital signatures

Another important cryptographic technique used in Bitcoin are digital signatures. They are used for authentication of the origin of transactions on the blockchain. They enable the receiver to verify that the transaction received was originally sent by the sender using his or her private key. This process again includes mathematical calculations. Surprise, surprise!

Basically, the digital signature is generated out of the sender's private key being processed through a digital signature algorithm. The resulting code output is then attached to the signed message and acts like a signature. It designates the sender of the message. Each transaction will have a different digital signature, which is generated through the digital signature algorithm to increase security. It is impossible to generate a valid signature for a party without knowing that party's private key.

Please note that, we use the words transaction and message interchangeably, because transactions on the blockchain are basically messages broadcasted through the network. When you send cryptocurrency to another person, you are basically sending them a message.

Furthermore, digitally signed transaction messages are unforgeable, meaning they cannot be intercepted and modified or reproduced while in transit.

Digital signatures are also non-reusable and they cannot be separated from a transaction message and used for a different message given that the algorithm creates a new signature for each transaction.

To conclude the topic, let's put these cryptographic solutions into the words of the great Satoshi himself:

"We define an electronic coin as a chain of digital signatures. Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin. A payee can verify the signatures to verify the chain of ownership."