Miscellaneous On Data Structures - Study Mode

Explanation

Solution: 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".