Tidy up

docs/lectures/cryptography/03_stream_ciphers.md

@@ -2,23 +2,23 @@
 
 ### Pseudo-randomness
 
-- TRNGs - true Random Number Generator
-  - Not feasible at scale
-- PRNGs - Pseudo Random Number Generator
-- CSPRNGs - Cryptographically Secure Pseudo Random Number Generator
+- TRNGs - True Random Number Generators
+    - Not feasible at scale
+- PRNGs - Pseudo-random Number Generators
+- CSPRNGs - Cryptographically Secure Pseudo-random Number Generators
 
 #### LFSRs
 
-- A Linear-feedback Shift Register us a register if buts whose positions shift to the right
+- A linear-feedback shift register is a register of bits whose positions shift to the right
 - Usually comprised of flip-flops, the last bit represents the output
 
 (Where the squares at the bottom are flip-flops)
 
 - If initialised to `000`, nothing happens as $0\oplus0 = 0$.
-  - Therefore, we have $2^n-1$ states
-  - Statistical randomness
+    - Therefore, we have $2^n-1$ states
+    - Statistical randomness
 - To add more randomness to the setup, we can add another (more) `xor` gate
-  - However, we have fewer states
+    - However, we have fewer states
 
 $$
 s_m \equiv s_{m-1}p_{m-1} + ... + s_1p_1 + s_0p_0\space (mod \space 2)\\
@@ -27,11 +27,11 @@ $$
 
 - We usually represent m-bit LFSRs using polynomials of degree m.
 - In general $P(x)=x^m + p_{m-1}x^{m-1} + ... + p_1x + p_0$
-- LFSRs that have primitive polynoimials produce sequences of maximum length
-- There are many and are easily computed
-  - $x^5 + x^2 + 1$ has 31 states
-  - $x^{10} + x^3 + 1$ has 1023
-  - $x^{85}+x^8+x^2+x+1$ has $10^{26}$ states
+- LFSRs that have primitive polynomials produce sequences of maximum length
+- There are many, and they are easily computed
+    - $x^5 + x^2 + 1$ has 31 states
+    - $x^{10} + x^3 + 1$ has 1023
+    - $x^{85}+x^8+x^2+x+1$ has $10^{26}$ states
 
 ##### Attacking LFSRs
 
@@ -55,31 +55,31 @@ $s_{2m+1} \equiv s_{2m-1}p_{m} + ... + s_mp_1 + s_{m-1}p_0$
 
 - LFSRs are much more cryptographically secure if we combine more than one together in a non-linear way.
 
-Trivium is 3 LFSR in a row
+Trivium is 3 LFSRs in a row
 
 - Feedback between each with non-linear AND gates
 - Initialises the LFSR with an 80-bit key and 80-bit random value
 
 ### ChaCha20
 
-- ChaCha is a stream cipher written by Daniel Berstein
+- ChaCha is a stream cipher written by Daniel Bernstein
 - A modification of a previous cipher, Salsa
 - Very lightweight, using only `add`, `xor` and rotate operations
 - One of two ciphers in `TLS 1.3`
 - Dashes represent bit length
 - Constants are not secret
 - The block number can skip to anywhere
-  - Suppose someone skips ahead on a video stream, the cipher can skip unlike other synchronous stream ciphers
+    - Suppose someone skips ahead on a video stream, the cipher can skip unlike other synchronous stream ciphers
 - Works well on low power devices, due to simplicity of encryption
 - Once the input and the mixed words are added together it is hard to know what the starting thing was
-  - e.g. what two numbers have i added to make 100
+    - e.g. what two numbers have I added to make 100
 
 ChaCha performs **20** rounds
 
 - Alternates column and diagonal rounds
-  - Each round is 4 quarter rounds
+    - Each round is 4 quarter rounds
 
 #### Vulnerabilities
 
 - Stream ciphers like ChaCha give us *confidentiality*, but *not integrity*
-- Running a stream cipher by itself is not sufficient
+- Running a stream cipher by itself is not sufficient