• Caesar Cipher - Simple modulo rotation of each letter
  • ABCD ->3-> DEFG
• Monoalphabetic substitution cipher
  • ABAB ->XY-> XYXY
• Transposition cipher
  • HELLO ->2-> LOHEL
• Vigenere cipher
  • HELLO ->SECRET-> ZINCS
• One-time pad / Vernam cipher
  • OP.

Feedback Ciphers

When the key is not long enough to encipher the entire plaintext message, we can use extra data as the key

Plaintext Feedback

Uses the plain text as extra letters for the key.

Ciphertext feedback

Uses the cipher result as extra letters for the key,

External Source

… eh.

Analysing / Breaking Ciphers

Kasiski’s Method

Kasiski’s method helps to find a key length / period.

Read: Index of Coincidence

$P_C(m) ~= I_c(m) = \Sum (f_i ; 2 ) / (n ; 2) = (\Sum f_i^2 - n) / (n^2 - n) $

((Sum of the square of each frequency) - #elems) / (#elems^2 - #elems)

So the number of pairs is ¹⁄₂ n (n-1) I_c

Cipher Mechanisms

• Stream ciphers - One symbol at a time
• Block ciphers - Groups of symbols at a time
• Product ciphers - Cipher output is re-enciphered again

One way functions:

• Given $x$, easy to find $f(x)$.
• With only $f(x)$, hard to find $x$

One way hash functions:

• Function is a one-way function
• Takes a message of any length and maps to a fixed length
• Given x, hard to find x’ where f(x) = f(x’)

One way trapdoor function:

• Function is a one-way function
• Given f(x) and some extra information, easy to find x

Symmetric Cryptography

Same key used to encrypt and decrypt

Diffie-Hellman can be used to private share a secret with a recipient, which can then be used to generate a secret.

(Diffie-Hellman is for key exchange, not secure communication)

Asymmetric Cryptography

One key (public key) for encrypting, one key (private key) for decrypting.

Only the owner has the private key, whilst anyone can hold the public key.

• RSA
• McEliece Encryption (1978)

Digital Signatures

Read: Signing

Sign by encrypting with private key. Receiver decrypts with public key.