From baaeb3612a490a1a67045c1d2f6f53911bac27dc Mon Sep 17 00:00:00 2001
From: Andre Henriques <andr3h3nriqu3s@gmail.com>
Date: Fri, 3 Nov 2023 17:24:24 +0000
Subject: [PATCH] Fix cw.tex

---
 cw/cw.tex | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/cw/cw.tex b/cw/cw.tex
index c189a4e..b03bcc6 100644
--- a/cw/cw.tex
+++ b/cw/cw.tex
@@ -159,6 +159,35 @@
 	The plaintext is $(4, 3)$ and the $r=(4,9)$
 
 	C:
+	$$\begin{cases}
+		30548=1975t_1 + 7548t_2\\
+		6642=438t_1 + 1627t_2\\
+	\end{cases}= \begin{cases}
+		t_1 = \frac{432220}{92699}\\
+		t_2 = \frac{262074}{92699}\\
+	\end{cases}=\begin{cases}
+		t_1 \approx 4.66\\
+		t_2 \approx 2.83\\
+	\end{cases}=\begin{cases}
+		t_1 \approx 5\\
+		t_2 \approx 3\\
+	\end{cases}
+	$$	
+
+	$$v'=5(1975,438) + 3(7548, 1627)=(32519, 7071)$$
+
+	
+	$$
+	w = v'\times m' + r\iff
+		m'= (32519, 7071)\times\begin{pmatrix}
+			1975 & 438\\
+			7548 & 1627\\
+		\end{pmatrix}^{-1}\iff
+		m'=(5,3)
+	$$
+
+	Using $u_1$ and $u_2$ we do not dectypt correctly $m\ne m'$
+	
 
 	\subsection*{7.2}
 	No he should not.