From 5406f106126b8053f7433c3abb036f04c8da8d8b Mon Sep 17 00:00:00 2001
From: marcellus <msimon_fr@hotmail.com>
Date: Sat, 24 May 2025 15:37:07 +0200
Subject: update: Saturday 6 May, 15:37:07 from IUseArchBTW

---
 CHIFR/TD/TD5 - Kyber.md | 24 ++++++++++++++++++++++++
 IQC/CM1.md              |  1 +
 2 files changed, 25 insertions(+)
 create mode 100644 IQC/CM1.md

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)
diff --git a/IQC/CM1.md b/IQC/CM1.md
new file mode 100644
index 0000000..3567b47
--- /dev/null
+++ b/IQC/CM1.md
@@ -0,0 +1 @@
+$10010 \to \ket{10010}$
-- 
cgit v1.2.3