What is the definition of hills matrix?

Answer 1

A Hills matrix is an encryption tool. For a language comprising 26 characters, you would use an invertible n*n matrix where each element is modulo 26. That is a Hill matrix, H.

To encode a plain text message,

• encode the plain-text message using a = 0, b = 1, ..., z = 25.
  
• chop the message into strings of n characters.
• premultiply the column vector so formed by H.
• convert the resulting n*1 matrix to modulo 26.
• that is the encrypted message.

• to decrypt, premultiply the encrypted version by H^-1, modulo 26 .

The matrix H, is selected from a set of n*n matrices which are invertible and, for a 26-letter language, the determinant should not be divisible by a factor of 26 (2 or 13).