Tidy up

docs/lectures/security/03_cryptography.md

@@ -2,8 +2,8 @@
 
 - Symmetric encryption gives us confidentiality
 - Implemented using block ciphers or stream ciphers
-  - Lightweight and fast
-  - Used for general communication
+    - Lightweight and fast
+    - Used for general communication
 
 ![1644517237.png](img/1644517237.png)
 
@@ -12,7 +12,7 @@
 - Stream ciphers use an initial seed key to generate an infinite keystream of random looking bits
 - The message and keystream are usually combined using an `xor` ($\oplus$) which is reversible if applied twice
 
-- How ever using the same keystream to encrypt two messages makes messages easy to break
+- However, using the same keystream to encrypt two messages makes messages easy to break
 - A random *number used once* nonce is added as an additional seed
 - The nonce is not a secret, it simply ensures the keystream is new
 
@@ -33,7 +33,7 @@
 #### Block Ciphers
 
 - Block ciphers use a key to encrypt a fixed size block of plain text into a *fixed-sized block* of cipher-text
-  - Changing and permuting the bits of the block depending on the key
+    - Changing and permuting the bits of the block depending on the key
 - Different lengths of messages can be handled by splitting the message up, and padding
 
 ##### SP-Network
@@ -68,28 +68,28 @@
 ### Attack Models
 
 1. Brute force
-   - Weakest attack, guessing the key
-   - If the key is $2^{128}$, on a super computer would take $10^9$ years
+    - Weakest attack, guessing the key
+    - If the key is $2^{128}$, on a supercomputer it would take $10^9$ years
 2. Cipher text only
-   - Static analysis on the cipher text, frequency analysis etc
-   - e.g. looking at the enginma machine and recognising a letter cannot be itself
+    - Static analysis on the cipher text, frequency analysis etc
+    - e.g. looking at the Enigma machine and recognising a letter cannot be itself
 3. Known plaintext
-   - Where you know some plaintext and the corresponding ciphertext
-   - e.g. Enigma being broken using “heil hitler”
+    - Where you know some plaintext and the corresponding ciphertext
+    - e.g. Enigma being broken using “heil hitler”
 4. Chosen plaintext
-   - Seeing if certain plain-texts takes the algorithm longer/shorter
+    - Seeing if certain plain-texts take the algorithm longer/shorter
 5. Chosen ciphertext
 6. Related-key attack
-   - Get the same message encrypted in different keys
-   - More of a theoretical attack
+    - Get the same message encrypted in different keys
+    - More of a theoretical attack
 
 Modern algorithms are expected to overcome these attacks trivially
 
 ## Asymmetric Encryption
 
 - Two keys, a public & private key
-- Public-key asymmetric cryptography hinges upon the premuse that:
-  - It is computationally infeasible to calculate a private key from a public key
+- Public-key asymmetric cryptography hinges upon the premise that:
+    - It is computationally infeasible to calculate a private key from a public key
 - In practice this is achieved through intractable mathematical problems
 
 #### Key Exchange
@@ -104,17 +104,16 @@ It is extremely easy to go from a -> A but extremely difficult to go backwards.
 
 #### Public key Encryption
 
-- Client encrypts message with servers public key, now only the server’s private key can be used to read it.
+- Client encrypts message with the server’s public key; now only the server’s private key can be used to read it.
 - The authenticity of signatures generated by the private key can be verified by the public key
 
 ![1644519300.png](img/1644519300.png)
 
 ##### Public key Algorithms
 
-| Algorithm      | Key Exchange | Encryption | Digital Signitures | Mathematical Problem  | Elliptic Curves | Typical Key Size |
+| Algorithm      | Key Exchange | Encryption | Digital Signatures | Mathematical Problem  | Elliptic Curves | Typical Key Size |
 | :------------- | :----------: | :--------: | :----------------: | --------------------- | :-------------: | ---------------- |
-| Diffie-Hellmen |      ✅       |     ❌      |         ❌          | Discrete Logs         |        ✅        | 256              |
+| Diffie-Hellman |      ✅       |     ❌      |         ❌          | Discrete Logs         |        ✅        | 256              |
 | `RSA`          |      ❌       |     ✅      |         ✅          | Integer Factorisation |        ❌        | 2048/4096        |
 | `Elgamal`      |      ❌       |     ✅      |         ✅          | Discrete Logs         |        ✅        | 2048             |
 | `DSA`          |      ❌       |     ❌      |         ✅          | Discrete Logs         |        ✅        | 256              |
-