Challenge-Response Authentication

security

Definition

Challenge-Response Method

A challenge-response method is an authentication protocol in which the server sends a challenge $C$ to the user, who then computes a response $R$ by applying a cryptographic operation to $C$ using a shared secret.

Conceptually similar to a one-time password generator, but the one-time password depends on server-generated data rather than on time alone.

Protocol

Challenge

The authentication server sends a challenge $C$ to the user.

• $C$ must include a randomly generated component to prevent replay attacks.
• $C$ can partially depend on the operation to be authorised.

Response

The user performs a cryptographic operation on $C$ to compute the response $R$.

• The response is usually computed by an authenticator app installed on the user’s smartphone or PC.
• The ability to compute $R$ proves possession of the required secret or cryptographic key.

Variations

Hash-Based

The response is computed by hashing the challenge together with a shared secret $S_X$:

$$R=h(C\Vert S_X)$$

Symmetric Encryption

The response is the encryption of the challenge under a shared secret key $K_X$:

$$R=\mathrm{Enc}(K_X,C)$$

Signature-Based

The response is a digital signature on the challenge using the user’s private key ${SK}_X$:

$$R=\mathrm{Sign}({SK}_X,C)$$

Security

Replay Resistance

Because the challenge contains a fresh random component, an attacker who intercepts a previous response cannot reuse it.

Proof of Possession

The response demonstrates that the user holds the secret key, without transmitting the key itself.