How is a MAC computed and verified, and what keys are involved?

A MAC is computed as $\text{MAC} = h(K_G, m)$ using a shared generation key, and verified by recomputing with the verification key $K_V = K_G$.

Generation (by Alice):

$$\text{MAC} = h(K_G, m)$$

Alice sends both $m$ (plaintext) and the MAC.

Verification (by Bob):

$$h(K_V, m) \stackrel{?}{=} \text{received MAC}$$

Bob recomputes the MAC using his key $K_V$ and checks if it matches.

Key relationship: $K_G = K_V$ (symmetric — same shared secret)

What MAC provides:

• Data integrity — modification is detected
• Data authenticity — only someone with the key could have generated the MAC
• Insertion protection — a forged message won't have a valid MAC

What MAC does NOT provide:

• Non-repudiation — since $K_G = K_V$, Bob could have created the MAC himself. Alice can deny sending it.

Go deeper:

• HMAC — the hash-based MAC used in practice.