Consider the following two authentication schemes. In both cases the server knows a public key of the client (for a signature system in the first and an encryption system in the second case).

### Scheme A

Server presents a randomly generated plaintext to the client, and asks the client to sign the message. The server can verify the signature using the public key.

### Scheme B

Server randomly generates a plaintext, encrypts the message using the client's public key, and asks the client to decrypt and send back the plaintext. The server can verify that the plaintext matches the one it generated.

---

The second scenario feels less secure than the first scenario, but I cannot quite put my finger on why.

Is there any effective difference between the two authentication schemes?