Applications of Matrices & Determinants (cryptogram prob

[johnst22]

I have a cryptogram that was encoded with a 2 x 2 matrix.

The encoding key is numbered 0 through 26 with 0 being a space (denoted by an underscore "_") and 1 - 26 being letters beginning at "A". I have the following encrypted message.

8 21 -15 -10 -13 -13 5 10 5 25 5 19 -1 6 20 40 -18 -18 1 16

The last word of the message has been decoded for me and is _RON.

How in the heck do I decrypt the remainder of the message without the matrix? I am not looking for the solution but a nudge in the right direction.

Thanks in advance and please try not to be too harsh.

 

[JakeD]

Re: Applications of Matrices & Determinants (cryptogram

I have a cryptogram that was encoded with a 2 x 2 matrix....

What does it mean to be encoded by a 2 x 2 matrix with some encoding key? It sounds like given the information, you can solve for the matrix and encoding key.

 

[johnst22]

Re: Applications of Matrices & Determinants (cryptogram

What does it mean to be encoded by a 2 x 2 matrix with some encoding key? It sounds like given the information, you can solve for the matrix and encoding key.

I'm not sure I understand your reply.

I don't have to solve for the encoding key. It's given, the encoding key is as follows

0 = "_" (space)
1 = A
2 = B
3 = C
.
.
.
26 = Z

I know that I need to figure out what the 2 x 2 matrix is but my problem is I don't know where to start to achieve that. Any tips?

Thanks.

 

[stapel]

I think the process for this sort of exercise is that a text message was converted to a numeric message through alpha-numeric substitution. (That's the "1 = A", etc, stuff.)

Then the numbers were coding by multiplying the string (?) by a 2-by-2 matrix. (Or were the numbers put into two strings, so you'd have an 2-by-n matrix...?)

To undo the multiplication, one would customarily find the inverse of the coding matrix, and multiply the coded message by that. Since you don't have the message, I guess you'll have to work from the known part of the message.

What is the numerical value for "_RON"? How would this look in a uncoded matrix? Whatever your coding matrix A is, you know that "0 18 15 14" is coded to become whichever of the four numbers corresponds to this part of the message. (I don't have the specifics of the configuration, but naturally it cannot be a single line during the multiplication.) So set up the matrix equation, and solve for the coding matrix.

Then find its inverse, and so forth.

Eliz.

 

[johnst22]

Thanks so much for that response. Thanks to you I got it!

The message is "Meet me tonight Ron."

With your help I found the encoding matrix was A^-1 = [-1 -2] [1 1] (2 x 2) using Gauss-Jordan Elimination.

I then grouped the encoded string in 2 x 2 matrices and multipled each matrix by the A^-1 To get the decoded string.

Thanks for the nudge, I really appreciate it!