update typo and structures

pages/CSE442T/index.md

@@ -32,10 +32,24 @@ Many definitions to remember. They are long and tedious.
 
 For example, I have to read the book to understand the definition of "hybrid argument". It was given as follows:
 
-
-
+>Let $X^0_n,X^1_n,\dots,X^m_n$ are ensembles indexed from $1,..,m$
+> If $\mathcal{D}$ distinguishes $X_n^0$ and $X_n^m$ by $\mu(n)$, then $\exists i,1\leq i\leq m$ where $X_{n}^{i-1}$ and $X_n^i$ are distinguished by $\mathcal{D}$ by $\frac{\mu(n)}{m}$
 
 I'm having a hard time to recover them without reading the book.
 
 The lecturer's explanation is good but you'd better always pay attention in class or you'll having a hard time to catch up with the proof.
 
+### Notations used in this course
+
+The notations used in this course is very complicated. However, since we need to defined those concepts mathematically, we have to use those notations. Here are some notations I changed or emphasized for better readability at least for myself.
+
+- I changed all the element in set to lowercase letters. I don't know why K is capitalized in the book.
+- I changed the message space notation $\mathcal{M}$ to $M$, and key space notation $\mathcal{K}$ to $K$ for better readability.
+- All the $\mathcal{A}$ denotes a algorithm. For example, $\mathcal{A}$ is the adversary algorithm, and $\mathcal{D}$ is the distinguisher algorithm.
+- As always, $[1,n]$ denotes the set of integers from 1 to n.
+- $P[A]$ denotes the probability of event $A$.
+- $\{0,1\}^n$ denotes the set of all binary strings of length $n$.
+- $1^n$ denotes the string of length $n$ with all bits being 1.
+- $0^n$ denotes the string of length $n$ with all bits being 0.
+- $;$ means and, $:$ means given that.
+- $\Pi_n$ denotes the set of all primes less than $2^n$.