Digital signatures are a fundamental security mechanism used to verify blockchain transactions and prove that a transaction was authorized by the legitimate owner of a cryptocurrency or digital asset. They use public-key cryptography, which involves a private key and a corresponding public key.

When a user creates a blockchain transaction, such as sending cryptocurrency to another wallet, the transaction information is processed using the sender's private key to create a unique digital signature. The private key remains secret and is not shared with the blockchain network. The transaction, along with the signature and the sender's public key or related verification information, is then broadcast to the network.

Blockchain nodes use the sender's public key to verify the digital signature. The verification process checks whether the signature was created using the corresponding private key and whether the transaction data has been altered since it was signed. If the signature is valid, nodes can confirm that the transaction was authorized by the holder of the private key and that the signed information remains intact.

Digital signatures also provide authentication and integrity. Authentication helps establish that the transaction was authorized by the appropriate key holder, while integrity ensures that important transaction details have not been changed during transmission.

Importantly, digital signatures do not reveal the user's private key. Instead, they allow anyone with the appropriate public information to verify that a valid signature exists. This makes unauthorised modification of transactions extremely difficult without access to the private key.

Overall, digital signatures help blockchain networks securely authorise transactions, protect data integrity, and reduce the risk of fraudulent or unauthorised transfers.