GATE CS 2013 Q.13 (CS Q.13): Application Layer: DNS, HTTP, SMTP, FTP

Using public key cryptography, X adds a digital signature $\sigma$ to message $M$ , encrypts $\langle M, \sigma \rangle$ , and sends it to Y, where it is decrypted. Which one of the following sequences of keys is used for the operations?

Encryption: X’s private key followed by Y’s private key; Decryption: X’s public key followed by Y’s public key

Encryption: X’s private key followed by Y’s public key; Decryption: X’s public key followed by Y’s private key

Encryption: X’s public key followed by Y’s private key; Decryption: Y’s public key followed by X’s private key

Encryption: X’s private key followed by Y’s public key; Decryption: Y’s private key followed by X’s public key

Official answer and solution

Official answer: D
From: Official GATE 2013 answer key

Solution

Differentiate between the key requirements for digital signatures (authenticity/non-repudiation) and public-key encryption (confidentiality).

Sender X wants to sign message $M$ to ensure authenticity:
- Only X has X's private key.
- Therefore, X signs using X's private key to produce signature $\sigma$ .
Sender X wants to send $\langle M, \sigma \rangle$ confidentially to receiver Y:
- To ensure only Y can read the package, X encrypts $\langle M, \sigma \rangle$ using recipient Y's public key.
Upon receiving the ciphertext, receiver Y performs decryption:
- Y decrypts the ciphertext using Y's private key to recover $\langle M, \sigma \rangle$ .
Receiver Y verifies the digital signature $\sigma$ :
- Y uses sender X's public key to verify that the message indeed came from X.

Therefore:

Encryption sequence: X's private key followed by Y's public key.
Decryption sequence: Y's private key followed by X's public key.

This matches option D.

Final answer

Option (D)

Common trap

Confusing the order of decryption at the receiver: the outer layer (encrypted with Y's public key) must first be peeled off with Y's private key before the signature can be verified with X's public key.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2013 Computer Science and Information Technology (CS)
Question: 13 of 65, printed as CS Q.13
Section: Computer Science and Information Technology

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