Hashing and digital signatures provide data integrity and non-repudiation. Which describes how?

• A. Hashing hides data; signatures encrypt with symmetric key; ensures speed.
• B. Hashing creates fixed-size digest; digital signatures sign the hash with a private key; recipient verifies with public key; ensures integrity and non-repudiation.
• C. Hashing creates fixed-size digest; digital signatures use a public key to decrypt the hash.
• D. Hashing reversibly encodes data; digital signatures provide confidentiality.

Answer: (B)

The important idea is that a hash creates a compact, fixed-size representation of the message, and a digital signature signs that representation with the sender’s private key so others can verify it with the public key. Because the hash is tightly tied to the exact content, even a tiny change in the message yields a completely different digest. When the recipient uses the sender’s public key to verify the signature, they confirm two things at once: the digest produced from the received message matches the signed digest, proving the content hasn’t been altered (integrity), and that the signature could only have been created with the sender’s private key, tying the message to the sender and enabling non-repudiation. In practice, signing the hash rather than the whole message keeps the process efficient while delivering the desired guarantees.

Why the other ideas don’t fit: hashing isn’t about hiding data, and signatures aren’t used for confidentiality in this context. Private-key signing is not about decrypting the hash with a public key to reveal the original data; rather, the signature verifies that the signer possessed the private key. Finally, hashing isn’t reversible, so saying hashing reversibly encodes data and that signatures provide confidentiality isn’t accurate.