notes/docs/lectures/security/03_cryptography.md

Symmetric Cryptography

• Symmetric encryption gives us confidentiality
• Implemented using block ciphers or stream ciphers
  • Lightweight and fast
  • Used for general communication

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

• 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

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

• This round will be run multiple times (around 10-15 times)

Key Mixing

• Mixing in the key prevents attackers from reversing the process

• 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 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 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”
4. Chosen plaintext
   • 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

Modern algorithms are expected to overcome these attacks trivially

Asymmetric Encryption

• Two keys, a public & private 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

• Diffie-Hellman key exchange allows two parties to mathematically agree a shared secret over an insecure channel

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 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

Public key Algorithms

Algorithm	Key Exchange	Encryption	Digital Signatures	Mathematical Problem	Elliptic Curves	Typical Key Size
Diffie-Hellman	✅	❌	❌	Discrete Logs	✅	256
RSA	❌	✅	✅	Integer Factorisation	❌	2048/4096
Elgamal	❌	✅	✅	Discrete Logs	✅	2048
DSA	❌	❌	✅	Discrete Logs	✅	256