Add the rest of university notes

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+# Symmetric Cryptography
+
+- Symmetric encryption gives us confidentiality
+- Implemented using block ciphers or stream ciphers
+  - Lightweight and fast
+  - Used for general communication
+
+![1644517237.png](img/1644517237.png)
+
+### Stream Cipher
+
+- 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
+- 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
+
+##### Pros and Cons
+
+✅ Encrypting long continuous streams, possibly of unknown length
+
+✅ Extremely fast with low memory footprint, ideal for low-power battery devices
+
+✅ If designed well, can seek to any location in the stream
+
+❌ The keystream must appear statistically random
+
+❌ You must **never** reuse a key & nonce
+
+❌ Stream ciphers do not protect the cipher-text
+
+#### 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
+- Different lengths of messages can be handled by splitting the message up, and padding
+
+##### SP-Network
+
+- Repeated substitution and permutation
+
+![1644517216.png](img/1644517216.png)
+
+- This round will be run multiple times (around 10-15 times)
+
+###### Key Mixing
+
+- Mixing in the key prevents attackers from reversing the process
+
+![1644517396.png](img/1644517396.png)
+
+- To decrypt, reverse the process
+
+#### Symmetric Algorithms
+
+- `DES` was used from 1970s to 2000s
+- `3DES` (using DES 3 times) is sometimes found in legacy systems
+- `AES` and `ChaCha20` are the only two ciphers used in `TLS 1.3`
+
+| Algorithm  | Cipher type | Design       | Block Size (bits) | Speed     | Memory Footprint | Safe Implementation Difficulty | Key Sizes |
+| ---------- | ----------- | ------------ | ----------------- | --------- | ---------------- | ------------------------------ | --------- |
+| `DES`      | Block       | `Feistel`    | 64                | Fast      | Low              | Easy                           | 56        |
+| `3DES`     | Block       | `Feistel`    | 64                | Slow      | Low              | Easy                           | 112       |
+| `AES`      | Block       | `SP-Network` | 128               | very fast | medium           | Hard                           | 128/192   |
+| `ChaCha20` | Stream      | add-xor-rot  | N/A               | Very fast | very low         | Easy                           | 256       |
+
+### 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
+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
+3. Known plaintext
+   - 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
+5. Chosen ciphertext
+6. Related-key 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
+- In practice this is achieved through intractable mathematical problems
+
+#### Key Exchange
+
+- Diffie-Hellman key exchange allows two parties to mathematically agree a shared secret over an insecure channel
+
+![1644518533.png](img/1644518533.png)
+
+It is extremely easy to go from a -> A but extremely difficult to go backwards.
+
+- Encryption performed by the **public** key can only be decrypted by the corresponding **private** key
+
+#### Public key Encryption
+
+- Client encrypts message with servers 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 |
+| :------------- | :----------: | :--------: | :----------------: | --------------------- | :-------------: | ---------------- |
+| Diffie-Hellmen |      ✅       |     ❌      |         ❌          | Discrete Logs         |        ✅        | 256              |
+| `RSA`          |      ❌       |     ✅      |         ✅          | Integer Factorisation |        ❌        | 2048/4096        |
+| `Elgamal`      |      ❌       |     ✅      |         ✅          | Discrete Logs         |        ✅        | 2048             |
+| `DSA`          |      ❌       |     ❌      |         ✅          | Discrete Logs         |        ✅        | 256              |
+