Hill cipher:
Hill devised a cipher that extends both transposition and linear ciphers. It has the form
Where A is an n × n matrix of integers. The n-dimensional message (row) vector x is transformed into the cipher text vector y. For example, with
To decipher the result, the inverse of the matrix A (mod 26) is applied. This inverse will exist if the determinant of A has no common factor, except 1 and 26, with 26. Often it is arranged that the determinant of A mod 26 is in fact 1. For example, the determinant of the matrix A given above is 11 × 7 - 8 × 3 = 53 = 2 × 26 + 1 → 1 in mod 26 terms.
(a) Find the inverse of the A matrix given above. (Recall that the inverse of a two by two matrix is where D is the determinant of A.)
(b)Decipher the cipher text (1, 2).