More Encryption

• Keys
  • Most encryption algorithms rely on a key.
    • Noted as K in the symbolic representation.
    • This is a parameter to the algorithm used to form the encrypted message.
    • By changing the key, the message is encrypted differently.
  • C = E(K,P), P = D(K, C)
    • Since a single key is used for both encryption and decryption this is called a symmetric key, single-key or secret key encryption
    • If the algorithm is well known, then this key must be kept secret for the encryption to hold.
  • Consider the Playfair cipher.
    • One version
    • Build an encryption key
      • Start with a keyword
      • Remove duplicate letters, for this case i=j.
      • Form a square by writing the letters down in rows of 5.
      • Fill in the remaining square with unused letters in order
    • Example: Keyword Edinboro -> edinbor

      • e	d	i/j	n	b
        o	r	a	c	f
        g	h	k	l	m
        p	q	s	t	u
        v	w	x	y	z

    • Rules for encryption/decryption
      • Take the plaintext and split it into letter pairs
        • If a pair contains the same letter insert an x
        • If the last letter is not paired, add an x.
      • Find the letters in the table
        • If they are in the same row, shift each letter to the right by one, wrapping to the right if necessary
        • If they are in the same column, shift each letter down by one, wrapping to the top if necessary
        • Otherwise the letters form a square. Find the alternative corners of the square and use the letter on the same row for substation.
      • Example plaintext: the attack is at dawn

        Letter Pairs:     th ea tt ac ki sa td aw n
        Split Duplicates: th ea tx ta ck is at da wn
                          th -> ql
                          ea -> io
                          tx -> sy
                          ta -> sc 
                          ck -> al
                          is -> ax
                          at -> cs
                          da -> ir
                          wn -> yd
        ciphertext qliosyscalaxcsiryd

    • How would you decode?
    • Encrypt "Send More Monkeys" with the keyword "Fun Times"
    • Answer
      ASUGELOBELIGAWGN
    • Decode "PFYIATMETALCQW" with the keyword "crypto"
    • Answer
      ciphers are fun
    • Here is an app to do this.
• Other systems employ two keys
  • One key for encryption $K_e$ and one for decryption $K_d$
  • $C = E(K_e, P)$ and $P = D(K_d, C)$
  • In this case, this is called asymmetric encryption
  • These will become extremely valuable soon.
• Symmetric vs asymmetric
  • Symmetric systems are frequently used for a longer term message exchanges
    • Users somehow swap a valid key
    • Then communicate encrypting and decrypting with this key.
    • Think exchanging a key, build a playfair cypher then sending messages back and forth using this table.
    • The key needs to be private.
    • And key exchange is a real problem.
  • Asymmetric systems usually conist of a public key and a private key
    • We will look at these in more deatil later but
    • $K_{pub}$ and $K_{priv}$ are the keys in this system.
    • $P = D(K_{pub}, E(K_{priv}, P))$
      • I can encrypt a message with my private key, and you can decript it with my public key
      • You since I am the only person who knows my private key, I am the only person who could have created this message.
    • $P = D(K_{priv}, E(K_{pub}, P))$
      • I can decrypte a message with my private key that you encrypted with my public key.
      • I am the only person who can do this.
  • We can use a puiblic key/private key system to ecchange symmetric keys.
  • And other things.
  • The main problem is validating my public key.
  • These are done by key-distribution services.
  • And key management is a problem.
• A system with no key is a keyless cipher.
• Another way to look at computer based ciphers is block vs stream
  • A stream cipher encrypts a minimal amount of information.
    • Think caeser, each letter is encrypted independently.
    • No padding is needed.
  • A block cipher, on the other hand must encrypt a fixed size or block of the plain text.
    • Think playfair
    • You need a minimum of two letters.
    • If you don't have sufficient characters, you must pad.
  • Many modern ciphers use block sizes of 64, 128, 256, ...
    • sha-256 are an example of this.