update typo and structures

pages/CSE442T/CSE442T_L16.md

@@ -1,6 +1,6 @@
 # Lecture 16
 
-## Continue on PRG
+## Chapter 3: Indistinguishability and Pseudorandomness
 
 PRG exists $\implies$ Pseudorandom function family exists.
 
@@ -49,13 +49,13 @@ Pseudo random function familiy exists $\implies$
 
 Mult-message secure encryption exists.
 
-## Public key cryptography
+### Public key cryptography
 
 1970s.
 
 The goal was to agree/share a key without meeting in advance
 
-### Diffie-Helmann Key exchange
+#### Diffie-Helmann Key exchange
 
 A and B create a secret key together without meeting.
 
@@ -75,7 +75,7 @@ And Alice do $(g^b)^a$ where Bob do $(g^a)^b$.
 
 With $g^a,g^b$ no one can compute $g^{ab}$.
 
-### Public key encryption scheme
+#### Public key encryption scheme
 
 Ideas: The recipient Bob distributes opened Bob-locks
 
@@ -90,12 +90,12 @@ Public-key encryption scheme:
 
 Let $A, E$ knows $pk$ not $sk$ and $B$ knows $pk,sk$.
 
-Adversary can now encypt any message $m$ with the public key.
+Adversary can now encrypt any message $m$ with the public key.
 
 - Perfect secrecy impossible
-- Randomness necessary 
+- Randomness necessary
 
-Security of public key
+#### Security of public key
 
 $\forall n.u.p.p.t D,\exists \epsilon(n)$ such that $\forall n,m_0,m_1\in \{0,1\}^n$
 
@@ -113,7 +113,9 @@ We will achieve security in sending a single bit $0,1$
 
 Time for trapdoor permutation. (EX. RSA)
 
-Encryption Scheme: Given family of trapdoor permutation $\{f_i\}$ with hardcore bit $h(i)$
+#### Encryption Scheme via Trapdoor Permutation
+
+Given family of trapdoor permutation $\{f_i\}$ with hardcore bit $h(i)$
 
 $Gen(1^n):(f_i,f_i^{-1})$, where $f_i^{-1}$ uses trapdoor permutation of $t$