Security and Cryptography

• Entropy

  • Entropy is a measure of randomness.

• Hash functions

  • A cryptographic hash function maps data of arbitrary size to a fixed size, and has some special properties.
  • hash(value: array<byte>) -> vector<byte, N> (for some fixed N)
  • Applications:
    • Git, for content-addressed storage.
    • A short summary of the contents of a file.
    • Commitment schemes.

• Key derivation functions

  • Applications:
    • Producing keys from passphrases for use in other cryptographic algorithms
    • Storing login credentials.

• Symmetric cryptography

  • keygen() -> key  (this function is randomized)
    
    encrypt(plaintext: array<byte>, key) -> array<byte>  (the ciphertext)
    decrypt(ciphertext: array<byte>, key) -> array<byte>  (the plaintext)
    

  • Applications:

    • Encrypting files for storage in an untrusted cloud service.

• Asymmetric cryptography

  • keygen() -> (public key, private key)  (this function is randomized)
    
    encrypt(plaintext: array<byte>, public key) -> array<byte>  (the ciphertext)
    decrypt(ciphertext: array<byte>, private key) -> array<byte>  (the plaintext)
    
    sign(message: array<byte>, private key) -> array<byte>  (the signature)
    verify(message: array<byte>, signature: array<byte>, public key) -> bool  (whether or not the signature is valid)
    

  • Applications

    • PGP email encryption.
    • Private messaging.
    • Signing software.

  • Key Distribution

• Case Studies

  • Password managers
    • KeePassXC, pass, and 1Password
  • Two-factor authentication (2FA)
  • Full disk encryption
  • Private messaging
    • Signal or Keybase
  • SSH
    • ssh-keygen
    • stored in the .ssh/authorized_keys file

• Resouces

  • Cryptographic Right Answers: answers “what crypto should I use for X?” for many common X.