Question

A criptografia é o estudo dos princípios e técnicas 20 pontos

Answer 1

Vamos utilizar (M*C) * C^(-1)= M

Sabemos que  ==>P =M*C , então

P * C⁻¹= M    ...Queremos M , temos que encontrar  a inversa de C ==> C⁻¹

$P = \left[\begin{array}{ccc}12&47&-23\\17&58&-34\\1&6&-2\end{array}\right]$

$C = \left[\begin{array}{ccc}2&7&-5\\0&1&0\\-1&-5&3\end{array}\right]$

$\left[\begin{array}{ccc}2&7&-5\\0&1&0\\-1&-5&3\end{array}\right] * \left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right] =\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

2a+7d-5g=1

2b+7e-5h=0

2c+7f-5i=0

0a+1d-0g=1

0b+1e-0h=0

0c+1f-0i=0

-a-5d+3g=1

-b-5e+3h=0

-c-5f+3i=0

Resolvendo este sistema :

 

$C^{-1} =\left[\begin{array}{ccc}3&4&5\\0&1&0\\1&3&2\end{array}\right]$

M=P * C⁻¹

$M =\left[\begin{array}{ccc}12&47&-23\\17&58&-34\\1&6&-2\end{array}\right] * \left[\begin{array}{ccc}3&4&5\\0&1&0\\1&3&2\end{array}\right]\\M =\left[\begin{array}{ccc}9&14&6\\15&18&13\\1&4&1\end{array}\right]$

Fazendo a conversão na tabela

$M = \left[\begin{array}{ccc}I&N&F\\O&R&M\\A&D&A\end{array}\right]$

M = INFORMADA  é a mensagem