Fix small errors

cw/cw.tex

@@ -116,7 +116,7 @@
 			I used factorization to obtain the private key. After obtaining the private key, I can decrypt the cipher text and obtain "handlebars''
 
 		\subsection*{3.3}
-			I used the general number sieve to factorize\cite{cadonfs} to factorize the public modulus and obtained:
+			I used the general number sieve\cite{cadonfs} to factorize the public modulus and obtained:
 			$$p=112546167358047505471958486197519319605436748416824057782825895564365669780011$$
 			and
 			$$q=65802972772386034028625679514602920156340140357656235951559577501150333990623$$
@@ -253,9 +253,9 @@
 
 				which means that
 
-				$$(((m^{r_{a\text{ alice}}})^{r_{a\text{ bob}}})^{r_{b\text{ alice}}})^{r_{b\text{ bob}}} = m (\text{mod } p)$$
+				$$(((m^{r_{a1}})^{r_{b1}})^{r_{a2}})^{r_{b2}} = m (\text{mod } p)$$
 
-				in this case, $r_a$ from Alice cancels $r_b$ from Alice, and $r_a$ from Bob cancels $r_b$ from Bob.
+				in this case, $r_{a1}$ from Alice cancels $r_{a2}$ from Alice, and $r_{b1}$ from Bob cancels $r_{b2}$ from Bob.
 
 			\subsubsection*{6.3.2}
 				To send an encrypted message using this system between 2 people, i.e. Alice and Bob:
@@ -303,9 +303,13 @@
 	
 			$$=\frac{\sqrt{92699}}{9427678922^{\frac{1}{4}}}\approx0.977094\approx0.98$$
 
+			The Hadamard ration for the private bias is $0.98$
+
 			$$H(U)=(\frac{det(L)}{\|u1\|\times\|u2\|})^\frac{1}{n}=(\frac{92699}{\sqrt{u1_1^2 + u1_2^2}\times\sqrt{u2_1^2 + u2_2^2}})^\frac{1}{2}=$$
 			$$=\frac{\sqrt{92699}}{243990681350077^{\frac{1}{4}}}\approx0.0770361\approx0.077$$
 
+			The Hadamard ration for the public bias is $0.077$
+
 			B:
 			$$w = (30548, 6642)$$
 			$$\begin{cases}