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problem:simple_matrix_encryption

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problem:simple_matrix_encryption [2013/08/16 17:21]
bmwoodruff created 		problem:simple_matrix_encryption [2013/08/16 17:29] (current)
bmwoodruff [$\LaTeX$ version]
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 ==== Problem ==== ==== Problem ====
 Consider the matrix  Consider the matrix 
-$A = +$A = \begin{bmatrix} 2&1&-1\\ 5&2&-3\\ 0&2&1\end{bmatrix}$.   
-\begin{bmatrix} +Joe decides to send a message to Sam by encrypting the message with the matrix $A$. He first takes his message and converts it to numbers by replacing A with 1, B with 2, C with 3, and so on till replacing Z with 26.  He uses a 0 for spaces.  After replacing the letters with numbers, he breaks the message up into chunks of 3 letters.  He then multiplies each chunk of 3 by the matrix $A$, resulting in a coded message. For example, to send the message "good job ben" he firsts converts the letters to the numbers and places them in a large matrix $M$ (top to bottom, left to right) 
- 2&1&-1\\ +
- 5&2&-3\\ +
- 0&2&1 +
-\end{bmatrix} +
-$.   +
-Joe decides to send a message to Sam by encrypting the message with the matrix $A$. He first takes his message and converts it to numbers by replacing A with 1, B with 2, C with 3, and so on till replacing Z with 26.  He uses a 0 for spaces.  After replacing the letters with numbers, he breaks the message up into chunks of 3 letters.  He then multiplies each chunk of 3 by the matrix $A$, resulting in a coded message. For example, to send the message ``good job ben'' he firsts converts the letters to the numbers and places them in a large matrix $M$ (top to bottom, left to right) +
 $$ $$
 \left[ \left[
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 $ to Sam. Sam uses the inverse of $A$ to decode the message.  $ to Sam. Sam uses the inverse of $A$ to decode the message. 
   - Find the inverse of $A$.    - Find the inverse of $A$. 
-  - Use $A^{-1}$ to decode $[[ 14,  20,  45],[ -2, -10,  10],[ 32,  79,   4],[ -5, -22,  24]]$ and show the message is ``good job ben''.+  - Use $A^{-1}$ to decode $[[ 14,  20,  45],[ -2, -10,  10],[ 32,  79,   4],[ -5, -22,  24]]$ and show the message is "good job ben."
   - Decode the message $[[39, 89, 22],[20, 48,  4],[39, 88, 33]]$.   - Decode the message $[[39, 89, 22],[20, 48,  4],[39, 88, 33]]$.
  
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 ==== $\LaTeX$ version ==== ==== $\LaTeX$ version ====
 <file tex problem.simple_matrix_encryption.tex> <file tex problem.simple_matrix_encryption.tex>
-%%%%% 
-% DEPENDENCIES 
-% RequiredPackages: \usepackage{tikz} 
-% RequiredMacros: \DeclareMathOperator{\aut}{Aut}  
-%%%%% 
 %Encryption using matrices (and inverses to decode things). %Encryption using matrices (and inverses to decode things).
 \begin{problem} \begin{problem}
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   *    * 
  
-{{tag>problem}}+{{tag>problem ben needsreview rben}}
problem/simple_matrix_encryption.1376688115.txt.gz · Last modified: 2013/08/16 17:21 by bmwoodruff

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