Hill Cipher
Assume that we intercept a number of items, as follows: The following text was sent: "What do you get when you take the dot product of a vector and a mountain climber?" A string of coded numbers was replied: -4, 17, 1, 14, 0, 19, 7, -5, 7, -2, -3, 6, 3, 6, 11, -9, -13, 31, 19, -19, -17, 35, 5, -5, 16, -13, -11, 23, -17, 35, 19, -19. The end of the last word of the decoded message is: "arS _". The fact that a 2x2 decoding matrix was used in the Hill Cipher will be investigated to see if the rest of the message can be decoded. We'll set up two matrix vector equations for the decoding matrix using the intercepted part of the message, either by hand or in Maple, and annotate as below: Define the decoding matrix using generic variables:
[~17 -17] decodes to the vector corresponding to "ar" via [35 35] [18 19]. Now we set up the next part of the string decoding to the vector corresponding to "s -19". You can create the vector from the standard digitized alphabet (space is 0, a is 1) as well as the matrix vector equation and annotate the linear algebra like I did just above, but for this part of the message.