Mastering Cryptography: Unraveling the Enigma of Encryption

Welcome, cryptography enthusiasts and students seeking help with cryptography assignment! At ProgrammingHomeworkHelp.com, we understand the intricate world of cryptographic techniques and the challenges they pose. Today, we delve into a couple of master-level cryptography questions, accompanied by comprehensive solutions crafted by our expert. Let's embark on a journey to decode the mysteries of encryption. Visit at https://www.programminghom...

Question 1: Caesar Cipher Reinvented
One of the oldest and simplest forms of encryption, the Caesar Cipher, involves shifting each letter in the plaintext by a fixed number of positions down the alphabet. Now, let's revamp this classic technique.

Given the plaintext: "HELLO WORLD," we want to encrypt it using a Caesar Cipher with a variable shift determined by the letters' positions in the plaintext. The shift is calculated as follows:

For the first letter 'H,' the shift is 7.
For the second letter 'E,' the shift is 4.
For the third letter 'L,' the shift is 11.
And so on.

Solution:

To encrypt "HELLO WORLD" using the modified Caesar Cipher, we apply the respective shifts to each letter:

H (shift by 7): O
E (shift by 4): I
L (shift by 11): W
L (shift by 11): W
O (shift by 14): Y
W (shift by 23): P
O (shift by 15): Z
R (shift by 18): F
L (shift by 12): X
D (shift by 4): H
The encrypted text is "OIWWY PZFHX."

Question 2: Diffie-Hellman Key Exchange

The Diffie-Hellman key exchange protocol facilitates secure communication over an insecure channel. Suppose Alice and Bob wish to establish a shared secret key using Diffie-Hellman.

Given:

Alice's public key (g^a mod p) is 13^5 mod 17.
Bob's public key (g^b mod p) is 13^3 mod 17.
The shared prime number (p) is 17.
The shared base (g) is 13.
Determine the shared secret key using the Diffie-Hellman key exchange protocol.

Solution:

Alice computes her shared secret key:
Alice's shared key = (Bob's public key)^a mod p
= (13^3)^5 mod 17
= 2^5 mod 17
= 32 mod 17
= 15

Bob computes his shared secret key:
Bob's shared key = (Alice's public key)^b mod p
= (13^5)^3 mod 17
= 6^3 mod 17
= 216 mod 17
= 15

The shared secret key for both Alice and Bob is 15.

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