Tag: Diffie Hellman Decryption

Diffie Hellman Key Exchange | Asymmetric Encryption

Asymmetric Encryption-

 

Before you go through this article, make sure that you have gone through the previous article on Asymmetric Key Cryptography.

 

In asymmetric encryption,

  • Sender and receiver use different keys to encrypt and decrypt the message.
  • The famous asymmetric encryption algorithms are-

 

 

In this article, we will discuss about Diffie Hellman Key Exchange Algorithm.

 

Symmetric Key Cryptography-

 

In symmetric key cryptography,

  • Both sender and receiver use a common secret key to encrypt and decrypt the message.
  • The major issue is exchanging the secret key between the sender and the receiver.
  • Attackers might intrude and know the secret key while exchanging it.

 

Read More- Symmetric Key Cryptography

 

Diffie Hellman Key Exchange-

 

As the name suggests,

  • This algorithm is used to exchange the secret key between the sender and the receiver.
  • This algorithm facilitates the exchange of secret key without actually transmitting it.

 

Diffie Hellman Key Exchange Algorithm-

 

Let-

  • Private key of the sender = Xs
  • Public key of the sender = Ys
  • Private key of the receiver = Xr
  • Public key of the receiver = Yr

 

Using Diffie Hellman Algorithm, the key is exchanged in the following steps-

 

Step-01:

 

  • One of the parties choose two numbers ‘a’ and ‘n’ and exchange with the other party.
  • ‘a’ is the primitive root of prime number ‘n’.
  • After this exchange, both the parties know the value of ‘a’ and ‘n’.

 

Step-02:

 

  • Both the parties already know their own private key.
  • Both the parties calculate the value of their public key and exchange with each other.

 

Sender calculate its public key as-

Ys = aXs mod n

Receiver calculate its public key as-

Yr = aXr mod n

 

Step-03:

 

  • Both the parties receive public key of each other.
  • Now, both the parties calculate the value of secret key.

 

Sender calculates secret key as-

Secret key = (Yr)Xs mod n

Receiver calculates secret key as-

Secret key = (Ys)Xr mod n

 

Finally, both the parties obtain the same value of secret key.

 

PRACTICE PROBLEMS BASED ON DIFFIE HELLMAN KEY EXCHANGE-

 

Problem-01:

 

Suppose that two parties A and B wish to set up a common secret key (D-H key) between themselves using the Diffie Hellman key exchange technique. They agree on 7 as the modulus and 3 as the primitive root. Party A chooses 2 and party B chooses 5 as their respective secrets. Their D-H key is-

  1. 3
  2. 4
  3. 5
  4. 6

 

Solution-

 

Given-

  • n = 7
  • a = 3
  • Private key of A = 2
  • Private key of B = 5

 

Step-01:

 

Both the parties calculate the value of their public key and exchange with each other.

 

Public key of A

= 3private key of A mod 7

= 32 mod 7

= 2

 

Public key of B

= 3private key of B mod 7

= 35 mod 7

= 5

 

Step-02:

 

Both the parties calculate the value of secret key at their respective side.

 

Secret key obtained by A

= 5private key of A mod 7

= 52 mod 7

= 4

 

Secret key obtained by B

= 2private key of B mod 7

= 25 mod 7

= 4

 

Finally, both the parties obtain the same value of secret key.

The value of common secret key = 4.

Thus, Option (B) is correct.

 

Problem-02:

 

In a Diffie-Hellman Key Exchange, Alice and Bob have chosen prime value q = 17 and primitive root = 5. If Alice’s secret key is 4 and Bob’s secret key is 6, what is the secret key they exchanged?

  1. 16
  2. 17
  3. 18
  4. 19

 

Solution-

 

Given-

  • n = 17
  • a = 5
  • Private key of Alice = 4
  • Private key of Bob = 6

 

Step-01:

 

Both Alice and Bob calculate the value of their public key and exchange with each other.

 

Public key of Alice

= 5private key of Alice mod 17

= 54 mod 17

= 13

 

Public key of Bob

= 5private key of Bob mod 17

= 56 mod 17

= 2

 

Step-02:

 

Both the parties calculate the value of secret key at their respective side.

 

Secret key obtained by Alice

= 2private key of Alice mod 7

= 24 mod 17

= 16

 

Secret key obtained by Bob

= 13private key of Bob mod 7

= 136 mod 17

= 16

 

Finally, both the parties obtain the same value of secret key.

The value of common secret key = 16.

Thus, Option (A) is correct.

 

To gain better understanding about Diffie Hellman Key Exchange Algorithm,

Watch this Video Lecture

 

Next Article- Digital Signatures

 

Get more notes and other study material of Computer Networks.

Watch video lectures by visiting our YouTube channel LearnVidFun.