Fix cw.tex

cw/cw.tex

@@ -57,7 +57,23 @@
 	$$H(m')=E(K, IV \oplus m') = C_2$$
 	And if there the hashing function was not collision resistant that would imply
 	$$C_1=C_2\Rightarrow D(C_1)=D(C_2) \Rightarrow m=m'$$
-	and since $m !=m'$ the hash function is collision resistant, for messages with 1 block.
+	and since $m\ne m'$ the hash function is collision resistant, for messages with 1 block.
+
+	For if the block size is bigger than one we can say
+	$$H(m)=E(m)_{\text{Last Block}}$$
+	$$E(m)=E(K, m)$$
+	$$\exists a,b,c,d : m = a||b \and m' = c||d$$
+	where a,b,c,d are the size of one block
+	$$H(m)=E(b \oplus E(a \oplus IV)) = C_1$$
+	$$H(m')=E(d \oplus E(c \oplus IV)) = C_2$$
+	since it's possible to have: 
+	$$b \oplus E(a \oplus IV) = d \oplus E(c \oplus IV)$$
+	with:
+	$$a \ne b \ne c \ne d$$
+	therefore
+	$$H(m)=H(m') \and m\ne m'$$
+
+