Final answer:
To find the encryption matrix of a 2x2 Hill cipher, we need to reverse the encryption process. Set up two equations using matrix multiplication and solve for the values of the encryption matrix.
Step-by-step explanation:
To find the encryption matrix of a 2x2 Hill cipher, we need to reverse the encryption process. In this case, the plaintext "SOLVED" was encrypted to the ciphertext "GEZXDS".
First, convert both the plaintext and ciphertext to their respective numerical values using the alphabetical order, where A=0, B=1, C=2, and so on. The plaintext letters correspond to the matrix S=18, O=14, L=11, V=21, E=4, and D=3, and the ciphertext letters correspond to the matrix G=6, E=4, Z=25, X=23, D=3, and S=18.
Next, we set up two equations using matrix multiplication to represent the encryption:
Encryption:
[ a b ] [ 18 ] = [ 6 ]
[ c d ] [ 14 ] [ 4 ]
[ 11 ] [25 ]
[ 21 ] [23 ]
[ 4 ] [ 3 ]
[ 3 ] [ 18 ]
Since the matrix size is 2x2, we can solve this system of equations to find the values of a, b, c, and d. This involves finding the inverse of the matrix [18, 14, 11, 21]. The inverse matrix is [7, 9, 15, 1].
So, the encryption matrix of the 2x2 Hill cipher is [7, 9, 15, 1].