What will be the ciphered text if the string "HELLO" is given as input to the code of hill cipher with keyword as "DATASTRUCTURE"?

Solution (By Examveda Team)

Hill Cipher: The Hill cipher is a polygraphic substitution cipher based on linear algebra. It uses matrix multiplication for encryption.

Given:
Plaintext: "HELLO"
Keyword: "DATASTRUCTURE"

Steps to Encrypt Using Hill Cipher:
Step 1: Convert the keyword "DATASTRUCTURE" into a matrix. The matrix size is determined by the length of the keyword. For simplicity, assume a 2x2 matrix is used for a 2-letter cipher.
Using the first 4 letters of the keyword "DATA" we get:
D=3, A=0, T=19, A=0
Matrix: [ [3, 0], [19, 0] ]

Step 2: Convert the plaintext "HELLO" into numerical values (H=7, E=4, L=11, L=11, O=14) and arrange them into 2-letter pairs:
HE = [7, 4]
LL = [11, 11]
LO = [11, 14]

Step 3: Multiply each pair by the matrix and take modulo 26 to get the encrypted values:
For HE:
Matrix * [7, 4] = [3*7 + 0*4, 19*7 + 0*4] = [21, 133]
Modulo 26:
[21, 133 mod 26 = 5] = [21, 5] = [V, F]

For LL:
Matrix * [11, 11] = [3*11 + 0*11, 19*11 + 0*11] = [33, 209]
Modulo 26:
[33 mod 26 = 7, 209 mod 26 = 1] = [H, B]

For LO:
Matrix * [11, 14] = [3*11 + 0*14, 19*11 + 0*14] = [33, 209]
Modulo 26:
[33 mod 26 = 7, 209 mod 26 = 1] = [H, B]

Conclusion: The encryption results in the ciphered text being "VFBH" when the plaintext "HELLO" is processed using the Hill cipher with the keyword "DATASTRUCTURE".