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Matrix decoding is a method used in cryptography to decode messages that have been encoded using matrix multiplication. This technique involves using the inverse of the encoding matrix to retrieve the original message.
Example: Decoding a Message
Let's decode a message that was encoded using the matrix ( A = \begin{bmatrix} 1 & 2 \ 1 & 3 \end{bmatrix} ).
Encoded Message
[ \begin{bmatrix} 21 & 26 \ 37 & 53 \ 45 & 54 \ 74 & 101 \ 53 & 69 \end{bmatrix} ]
Decoding Steps
Find the Inverse of Matrix ( A ): [ A^{-1} = \begin{bmatrix} 3 & -2 \ -1 & 1 \end{bmatrix} ]
Multiply Each Encoded Matrix by ( A^{-1} ): [ A^{-1} \begin{bmatrix} 21 \ 26 \end{bmatrix} = \begin{bmatrix} 11 \ 5 \end{bmatrix} ] [ A^{-1} \begin{bmatrix} 37 \ 53 \end{bmatrix} = \begin{bmatrix} 5 \ 16 \end{bmatrix} ] [ A^{-1} \begin{bmatrix} 45 \ 54 \end{bmatrix} = \begin{bmatrix} 27 \ 9 \end{bmatrix} ] [ A^{-1} \begin{bmatrix} 74 \ 101 \end{bmatrix} = \begin{bmatrix} 20 \ 27 \end{bmatrix} ] [ A^{-1} \begin{bmatrix} 53 \ 69 \end{bmatrix} = \begin{bmatrix} 21 \ 16 \end{bmatrix} ]
Convert Numbers Back to Letters: [ [11,5] = KE, [5,16] = EP, [27,9] = -I, [20,27] = T-, [21,16] = UP]
2.5: Application of Matrices in Cryptography
Jul 18, 2022 · Some modern methods make use of matrices as part of the encryption and decryption process; other fields of mathematics such as number …
Abstract: This paper includes encoding and decoding using nonhomogeneous matrix method AM =X. Where A is encoding Matrix and in M is message matrix. X is unknown message. Index Terms - …
Cryptography with Matrices: Encoding & Decoding …
Learn cryptography using matrices! This worksheet covers encoding/decoding messages with 2x2 & 3x3 matrices, alphabet assignments, and matrix inverses.
We will soon see that the encoding and decoding can be done much more efficiently than this, using some simple linear algebra.
Newer and more complicated methods have evolved, such as cryptography using matrices which changes the alphabets to numbers and use several matrix operations to encode the messages sent. …
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AlexEspinoza2005/Matrix-Message-Encoding - GitHub
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