diff options
Diffstat (limited to 'CHIFR')
| -rw-r--r-- | CHIFR/TD/TD5 - Kyber.md | 24 |
1 files changed, 24 insertions, 0 deletions
diff --git a/CHIFR/TD/TD5 - Kyber.md b/CHIFR/TD/TD5 - Kyber.md index 26859b5..63947a8 100644 --- a/CHIFR/TD/TD5 - Kyber.md +++ b/CHIFR/TD/TD5 - Kyber.md @@ -20,3 +20,27 @@ $X^3 = -1, \, X^4 = -X$ ## Kyber ### a) +$R_{7,5} = \mathbb{Z}/7 \mathbb{Z}[X]/(X^5 + 1)$ +Donc $X^5 = -1, \, X^6 = -X, \, X^7 = -X^2$ +$$ +\begin{align} +t &= a \cdot s + e \\ +&= (X^4 + 3X^2 + 6X + 2) \cdot (X^3 - X - 1) + X^3 \\ +&= -X^2 + 1 -X^4 -3 - 3X^3 - 3X^2 + 6X^4 - 6X^2 - 6X + 2X^3 - 2X - 2 + X^3\\ +&= 5X^4 + 4X^2 + 6X + 3 +\end{align} +$$ +### b) +$$ +\begin{align} +m' &= v - s\cdot u \\ +&= 5 + 5X + X^2 + 2X^3 + 2X^4 - (-1 -X + X^3) \cdot (6 + 4X + 5X^2 + 4X^3 + 4X^4) \\ +&= 5 + 5X + X^2 + 2X^3 + 2X^4 - (-6 - 4X - 5X^2 - 4X^3 - 4X^4 -6X - 4X^2 - 5X^3 -4X^4 + 4 + 6X^3 + 4X^4 - 5 - 4X - 4X^2) \\ +&= 5 + 5X + X^2 + 2X^3 + 2X^4 - (X^2 - 3X^3 +3X^4) \\ +&= 5 + 5X + 5X^3 + 6X^4 \\ +m &= 1 + X + X^3 +\end{align} +$$ + +## 1-3 +### a) |