What cryptographic function combines two functions to authenticate a sender and prove the integrity of a message?

The correct response focuses on the role of digital signatures in cryptography. A digital signature effectively combines two cryptographic functions: hashing and asymmetric encryption.

When a sender wants to authenticate a message, they first create a hash of that message using a hashing algorithm. This hash uniquely represents the message and ensures its integrity—any alteration of the message results in a different hash value. The sender then encrypts this hash with their private key, forming the digital signature.

This dual function serves two key purposes. First, by encrypting the hash with the sender's private key, the signature serves as proof of authenticity, confirming that the message was indeed sent by the holder of that private key. Second, the recipient can perform a verification process. They can hash the received message themselves and decrypt the sender's digital signature with the sender’s public key. If both hash values match, it confirms that the message was not altered during transmission, thus ensuring its integrity.

This combination of both authenticity and integrity is what makes digital signatures a vital technology in secure communications and transactions, such as in email, software distribution, and financial exchanges. This distinguishes it from the other options, which do not perform this dual function of authenticity and integrity verification in the same manner as digital