Tidy up

docs/lectures/cryptography/02_randomness.md

@@ -20,9 +20,7 @@ d_{s_i} (y_i) \equiv (x_i + 0\cdot s_i \space (mod\space 2) \\
 d_{s_i} (y_i) \equiv x_i
 $$
 
-Note: 2 % 2 is 0, its like **xor**-ing twice.
-
- 
+Note: 2 % 2 is 0; it's like **xor**-ing twice.
 
 #### Security of XOR
 
@@ -44,12 +42,12 @@ The security of a stream cipher depends entirely on the nature of the key stream
 ##### True Randomness
 
 - True randomness is impossible to recreate except by chance
-  - coin flips
+    - coin flips
 - Computer systems often use hardware sources for randomness
-  - Thermal or other noise
-  - Radioactive decay
-  - Clock drift
-  - Random timings of interrupts
+    - Thermal or other noise
+    - Radioactive decay
+    - Clock drift
+    - Random timings of interrupts
 
 ##### Pseudo Randomness
 
@@ -58,7 +56,7 @@ The security of a stream cipher depends entirely on the nature of the key stream
 
 ###### Linear Congruential Generator
 
-Cs `rand()` function, this is a PRNG
+C's `rand()` function is a PRNG
 
 $$
 s_0 = 12345 \\
@@ -76,7 +74,7 @@ $$
 
 #### Unconditional Security
 
-A crypto-system is **unconditional security** is unconditionally or information-theoretically secure if it cannot be broken, even with infinite computational resources.
+A cryptosystem has **unconditional security**: it is unconditionally or information-theoretically secure if it cannot be broken, even with infinite computational resources.
 
 **Perfect Secrecy**: The cipher-text should reveal no information about the plain text
 
@@ -84,7 +82,7 @@ $\forall_{m_0, m_1} \in M$ where $|m_0| = |m_1|$ and $\forall_c \in C$
 
 $Pr[E(k,m_0) = c] = Pr[E(k,m_1) = c]$
 
-The probability that $m_0$ encrypts to $c$ is the same as the probability of $m_1$ also encrypted to $c$
+The probability that $m_0$ encrypts to $c$ is the same as the probability of $m_1$ also being encrypted to $c$
 
 ## One Time Pad
 
@@ -134,7 +132,7 @@ $$
 
 #### Crib Dragging
 
-This involves guessing $M_1$, this can be a common message such as `HTTP` request.
+This involves guessing $M_1$; this can be a common message such as an `HTTP` request.
 
 This can be automated by checking $M_1$ over different parts of $M_2$.
 
@@ -145,14 +143,14 @@ This can be automated by checking $M_1$ over different parts of $M_2$.
 
 - Numbers used once or *nonces* are vital for stream cipher security
 - Instead of always using a unique key, the security requirement is you always use a unique (key + nonce) pair
-- Nonces are not secret, they are public random seed for a key stream
+- Nonces are not secret; they are public random seeds for a key stream
 
-### Could we use a LCG?
+### Could we use an LCG?
 
 - LCG - Linear congruential generators
 - Seed using some key, then
-  - $s_{i+1} \equiv A \cdot s_i + B \space (mod \space 2)$
-  - $s_i, A, B$ are $log_2m$ bits long
+    - $s_{i+1} \equiv A \cdot s_i + B \space (mod \space 2)$
+    - $s_i, A, B$ are $log_2m$ bits long
 - This is trivial to break
-  - Given known plaintext $x_1, x_2, x_3$
-  - Calculate corresponding key $s_1, s_2, s_3$
+    - Given known plaintext $x_1, x_2, x_3$
+    - Calculate corresponding key $s_1, s_2, s_3$