Tidy up

docs/lectures/cryptography/08_block_cipher_modes.md

@@ -5,23 +5,25 @@
 - Most messages don’t come in convenient 128-bit block lengths
 - We’ll need to run a block cipher repeatedly on consecutive blocks
 - Why not use stream ciphers?
-  - Historically stream ciphgers have proven harder to implement
+    - Historically, stream ciphers have proven harder to implement
 
 ##### Padding
 
 - ECB and some other modes require message length to be a multiple of the block size
 - Public Key Cryptography Standards `PKCS7` is a common padding scheme:
-  1. Padding bytes are always added to the plaintext **before it is encrypted**
-  2. Each padding byte has a *value equal to the total number of padding bytes* that are added
-  3. The total number of padding bytes is **atleast one**
+    1. Padding bytes are always added to the plaintext **before it is encrypted**
+    2. Each padding byte has a *value equal to the total number of padding bytes* that are added
+    3. The total number of padding bytes is **at least one**
+
 - ![1646749511.png](img/1646749511.png)
+
 - Note in this example there are 7 `7`s and 16 `16`s
-- Note the bottom left example there is 1 `1`. This could be interpreted as 1 bytes of padding or some plaintext. This is why every block must contain at least one padding byte
+- Note that in the bottom-left example there is 1 `1`. This could be interpreted as 1 byte of padding or some plaintext. This is why every block must contain at least one padding byte
 
 ### Electronic Code Book Mode (ECB)
 
 - Just encrypt each block one after another
-- This is quick as can be easily parallelised
+- This is quick as it can be easily parallelised
 
 ![1646749909.png](img/1646749909.png)
 
@@ -44,7 +46,7 @@
 ### Deterministic vs Probabilistic Encryption
 
 - An encryption scheme is **deterministic** if some plaintext is mapped to a fixed ciphertext if the key is unchanged
-- ECB is deterministic, but most modern modes of operation of **probabilistic**
+- ECB is deterministic, but most modern modes of operation are **probabilistic**
 - Probabilistic encryption schemes add randomness to the encryption process to achieve a non-deterministic generation of the ciphertext
 
 ![1646750428.png](img/1646750428.png)
@@ -55,9 +57,9 @@
 
 - `XOR` the output of each cipher block with the next input
 - $IV$ - **Initialisation Vector**
-  - The initial random seed that randomises the whole stream
-  - If you encrypted the same plaintext later it will be different
-  - An attacker will be unable to tell if $y_1$ and $y_2$ are the same message but with different $IV$ or different messages with different $IV$
+    - The initial random seed that randomises the whole stream
+    - If you encrypted the same plaintext later it will be different
+    - An attacker will be unable to tell if $y_1$ and $y_2$ are the same message but with different $IV$ or different messages with different $IV$
 
 ![1646750496.png](img/1646750496.png)
 
@@ -79,29 +81,31 @@ x_i = d_k(y_i) \oplus y_{i-1}
 $$
 
 - If we lost $y_1$ we would be unable to decrypt $y_2$
-  - We would be able to decrypt $y_3$ though
+    - We would be able to decrypt $y_3$ though
 
 ##### Weaknesses
 
-- CBC was the primary method of encryption for many  years
-  - Now it is less common
+- CBC was the primary method of encryption for many years
+    - Now it is less common
+
 - ![1646750960.png](img/1646750960.png)
+
 - If you flip the first bit in $y_2$, the same bit is flipped for $x_3$
-  - Changing $y_2$ means $x_2$ no longer decrypts properly
+    - Changing $y_2$ means $x_2$ no longer decrypts properly
 
 ### Padding Oracles
 
-- Here, an **oracle** is a system we can query and it will tell us if, once decrypt, some text has **valid padding**
+- Here, an **oracle** is a system we can query and it will tell us if, once decrypted, some text has **valid padding**
 - A system is unlikely to tell you directly, but it might give away some clue
-- Image an example `api` that receives a CBC encrypted authorisation token
+- Imagine an example `api` that receives a CBC-encrypted authorisation token
 
 ![1646751224.png](img/1646751224.png)
 
 #### Padding Oracle Attacks
 
-- Lets look at a single decryption block in CBC
+- Let's look at a single decryption block in CBC
 - The attack is essentially the same for multiple blocks, just one at a time
-  - You attack the last block, which contains the padding
+    - You attack the last block, which contains the padding
 
 > The general strategy is to manipulate bits in the IV to find valid padding and recover $z_i$
 
@@ -116,22 +120,22 @@ $$
 ### Counter Mode (CTR)
 
 - Encrypt a nonce + counter and use this to mask the plaintext with `XOR`
-  - This is very easily parallelised
-  - Each block is encrypted differently, avoiding the issues with ECB mode
+    - This is very easily parallelised
+    - Each block is encrypted differently, avoiding the issues with ECB mode
 
 ![1646751954.png](img/1646751954.png)
 
 - We are now using our block cipher as a stream cipher
-  - The keystream generation (AES) is run through blocks
+    - The keystream generation (AES) is run through blocks
 - Decrypting is super easy, just the reverse
 
 ### Galois Counter Mode
 
 - Extends counter mode to add authenticity
-  - The sender definitely sent that message and it hasn’t been modified
-- Very similar to ocunter mode, but **adds authentication tag**
-  - Uses multiplication in a Galois Finite field $GF(2^{128})$ modulo $x^{128} + x^7 + x^2 + x + 1$
-- Extremely parallelsiable
+    - The sender definitely sent that message and it hasn’t been modified
+- Very similar to counter mode, but **adds an authentication tag**
+    - Uses multiplication in a Galois Finite field $GF(2^{128})$ modulo $x^{128} + x^7 + x^2 + x + 1$
+- Extremely parallelisable
 - Robust to message modification
 - Is now standard in `TLS1.3`