How do digital signatures work and what do they provide?

A digital signature is created by hashing a message and then encrypting the hash with the sender's private key. The recipient decrypts the signature using the sender's public key and compares the resulting hash to a fresh hash of the received message. If they match, the signature is valid. Digital signatures provide three security services: integrity because any modification changes the hash, authentication because only the sender's private key could have created the signature, and non-repudiation because the sender cannot deny signing since only they possess the private key.