GATE CSE 2016 | Set 1 | Question: 52

Question

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 $A$?

• A. $\left\{m, {K_{B}}^+(H(m))\right\}$
• B. $\left\{m, {K_{B}}^-(H(m))\right\}$
• C. $\left\{m, {K_{A}}^-(H(m))\right\}$
• D. $\left\{m, {K_{A}}^+(m)\right\}$

Comments

I am not able to find this question in go pdf

Answer 1

B wants to send message $'m'$ to A.
Private keys are denoted by $K^{-}_{(x)}$ and public keys by $K^{+}_{(x)}$.
In digital signature, the private key of the sender is used to encrypt the message and its public key is used to decrypt.
So, $\{m, K^{-}_{(B)}(H(m))\}$ must be the correct way of sending the message.

The answer is option B.

Comments

I get part where you have to send digital signature over the hash of message, but shouldn't the proper representation go like { K_A⁺(m), K_B^-(H(m)) }. Why is the message itself going unencrypted in all options?

 

EDIT:

Well, encryption of the message m wasn't a requirement for the question. 

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What is the difference between this question and the question in the link given below?
https://gateoverflow.in/1435/gate2013-13

Please help

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@arjun Sir what is the reason of sending private key of b to receiver.

Answer 2

While digitally signing a document, the sender uses his private key, ${K_b}^-$ to computer ${K_b}^-(m)$.

It is unusual that sender is using his private key (which is generally used for decrypting a message), but sender's goal is not to scramble the contents of the document, but rather to sign a document in a manner that is verifiable and nonforgeable.

One concern with signing data by encryption is that encryption and decryption are conceptually expensive. A more efficient approach is to introduce hash functions into digital signature. Using hash function, Sender signs the hash of the message rather than message itself, thus sender calculates ${K_b}^-(H(m))$.

So the answer is $\left \{ {m, {K_b}^-(H(m))} \right \}$

Comments

@Mk Utkarsh

Why not taking $K_{B}^{+}$? Is it because we donot require public key for B?

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@srestha

Coz then to decrypt it, the receiver will require sender's private key. And no one ever transmitts its private key, otherwise how will it be private!

Answer 3

Option B is CORRECT bcoz Sender generates the digital signature using his own private key and verifies using sender's public key.

Answer 4

In digital signature -->

(1) Private key of sender is used to encrypt the message.

(2) Public Key of sender is used to decrypt the message

Answer 5

COMMENT BELOW IF YOU HAVE ANY DOUBT