GATE CS 2016 Set 1 Q.62 (CS Q.52): Application Layer: DNS, HTTP, SMTP, FTP

Consider that $B$ wants to send a message $m$ that is digitally signed to $A$ . Let the pair of private and public keys for $A$ and $B$ be denoted by $K_x^-$ and $K_x^+$ for $x = A, B$ , respectively. Let $K_x(m)$ represent the operation of encrypting $m$ with a key $K_x$ and $H(m)$ represent the message digest. Which one of the following indicates the CORRECT way of sending the message $m$ along with the digital signature to $A$ ?

$\{m, K_B^+(H(m))\}$

$\{m, K_B^-(H(m))\}$

$\{m, K_A^-(H(m))\}$

$\{m, K_A^+(m)\}$

Official answer and solution

Official answer: B
From: Official GATE 2016 answer key

Solution

Recall the fundamental mechanism of digital signatures using public key cryptography and cryptographic hash functions.

Key definitions:

$K_x^-$ : Private key of entity $x$ (known only to $x$ ).
$K_x^+$ : Public key of entity $x$ (known to everyone).
$H(m)$ : Cryptographic hash / message digest of message $m$ .

Digital Signature Generation:

A digital signature provides non-repudiation and authentication of the sender $B$ .
Only the sender $B$ possesses $K_B^-$ .
Therefore, the signature is created by encrypting the message digest $H(m)$ with $B$ 's private key: $\text{Signature} = K_B^-(H(m))$ .

Transmission:

Sender $B$ sends the plaintext message $m$ along with the digital signature: $\{m, K_B^-(H(m))\}$ .

Verification by Receiver $A$ :

$A$ computes $H(m)$ directly from $m$ .
$A$ decrypts $K_B^-(H(m))$ using $B$ 's public key $K_B^+$ to obtain the sent digest.
If both digests match, $A$ confirms that the message came from $B$ and was not altered.

This corresponds to option B.

Final answer

Common trap

Confusing encryption for confidentiality (which uses the receiver's public key $K_A^+$ ) with digital signing for authentication (which uses the sender's private key $K_B^-$ ).

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

Source

Paper: GATE 2016 Computer Science and Information Technology (CS) Session 1
Question: 62 of 65, printed as CS Q.52
Section: Computer Science and Information Technology

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