# Le cryptosystème Kyber
## STA Flashback
$$
\begin{align}
&a = 4X^2 + 7X + 1 \\
&b = 3X^2 + 2
\end{align}
$$
### a)
- $a+b = 7X^2 + 7X + 3$
- $a \cdot b = 12X^4 + 8X^2 + 21X^3 + 14X + 3X^2 + 2 = 12X^4 + 21X^3 + 11X^2 + 14X + 2$
### b)
$X^3 = -1, \, X^4 = -X$
- $a+b = 7X^2 + 7X + 3$
- $a\cdot b = -12X -21 + 11X^2 + 14X + 2 = 11X^2 + 2X -19$
### c)
$X^3 = -1, \, X^4 = -X$
- $a+b = 7X^2 + 7X + 3$
- $a\cdot b = 2X^2 + 2X + 8$

## Kyber
### a)