Codemaking and Codebreaking

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Codemaking and Codebreaking

• Dan Cox
• Trevelyan College

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Bit of lingo

• Plaintext the readable message that is to be
  encrypted for secrecy.
• Ciphertext the result of encrypting the
  plaintext. This is unreadable.
• Code substitution at the level of words or
  phrases.
• Cipher substitution at the level of letters.
• Cryptography used generally to describe the
  science of codes and ciphers and anything related
  to them.
• Key the information that defines how messages
  are encrypted and decrypted.

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Few examples

• Example of a code
• apples attack at dawn
• ____________
• Example of a cipher
• WUDJXL ES GORN
• attack at dawn

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How does it work?
Sender
Receiver
Key Plaintext
Ciphertext (unreadable)
Use key to change ciphertext back into
Plaintext (readable)
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The Caesar Shift

• Plaintext
• alphabet a b c d e f g h i j k l m n o p q
  r s t u v w x y z
• Ciphertext
• alphabet S T U V W X Y Z A B C D E F G H I J
  K L M N O P Q R
• Plaintext what do you think of it so far?
• Ciphertext OZSL VG QGM LZAFC GX AL KG XSJ?

Shift of 8 places
s gets encrypted as a K
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Monoalphabetic Cipher

• Plaintext alphabet
• a b c d e f g h i j k l m n o p q r s t u v w x y
  z
• Ciphertext alphabet
• V I F L H G B X T O N Z A E P C R S U J K W Y D M
  Q
• Number of possible ciphertext alphabets
  26x25x24xx3x2x1 26!
• which is roughly 4.03x1026
• i.e. 403,000,000,000,000,000,000,000,000

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Frequency analysis
E T A O I N S H R D L U . . .
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Excerpt from A Void by Georges Perec,
translated into English by Gilbert Adair

• Noon rings out. A wasp, making an ominous sound,
  a sound akin to a klaxon or a tocsin, flits
  about. Augustus, who has had a bad night, sits up
  blinking and purblind. Oh what was that word (is
  his thought) that ran through my brain all night,
  that idiotic word that, hard as I'd try to pun it
  down, was always just an inch or two out of my
  grasp - fowl or foul or Vow or Voyal? - a word
  which, by association, brought into play an
  incongruous mass and magma of nouns, idioms,
  slogans and sayings, a confusing, amorphous
  outpouring which I sought in vain to control or
  turn off but which wound around my mind a
  whirlwind of a cord, a whiplash of a cord, a cord
  that would split again and again, would knit
  again and again, of words without communication
  or any possibility of combination, words without
  pronunciation, signification or transcription but
  out of which, notwithstanding, was brought forth
  a flux, a continuous, compact and lucid flow an
  intuition, a vacillating frisson of illumination
  as if caught in a flash of lightning or in a mist
  abruptly rising to unshroud an obvious sign - but
  a sign, alas, that would last an instant only to
  vanish for good.

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The Navajo Code Talkers

• One way to say Navy in Navajo code would be
• tsah (Needle), wol-la-chee (Ant), ah-keh-di-
  glini (Victor), tsah-ah-dzoh (Yucca).
• The receiver would translate these Navajo words
  into English and take the first letter of each
  word
• Needle
• Ant
• Victor
• Yucca
• and get the result Navy.

There were about 400 Navajo Code Talkers during
World War 2
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The problem of Key exchange
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One-way function Yx (mod P). Alicia and Bob agree
on Y7 and P11, so the function is 7x (mod 11).
Alicia
Bob

• Alicia chooses a number A and keeps it secret.
  Let A3.
• She puts xA into the one-way function and gets
  the answer 2.
• Alicia labels this result a and sends a2 to Bob.
• Alicia then takes Bobs value for ß and works out
  ßA(mod 11), which is found to equal 9.

• Bob chooses a number B and keeps it secret. Let
  B6.
• He puts xB into the one-way function and gets
  the answer 4.
• Bob labels this result ß and sends ß4 to Alicia.
• Bob then takes Alicias value for a and works out
  aB(mod 11), which is found to equal 9.

Alicia and Bob have ended up with the same
number, 9. This is now the Key!
American Standard Code for Information
Interchange (ASCII) assigns a 7-digit
binary number to each letter of the alphabet.
E.g. A 1000001, S 1010011
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Public Key Cryptography

• Public (encryption) Key Bob uses Alicias Public
  Key to encrypt a message to her
• Private (decryption) Key only Alicia knows this
  and so only she can decrypt Bobs message
• Needs a function thats only reversible if
  certain information about it is known, i.e. a
  function thats practically one-way.

Whitfield Diffie
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RSA (as opposed to ARS)

• Two massive primes are randomly chosen this is
  the Private Key.
• The product of these primes is the Public Key.
• Only known method of finding the two prime
  factors of the product is to check all
  possibilities one by one.
• This is not practical, as the time taken to do
  this would be longer than the age of the
  universe.

So RSA is virtually unbreakable.
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A political cross-roads
Or
Either

• Give everyone access to the strongest encryption
  products (such as RSA) so all communication is
  secure.
• Advantages
• e-commerce will be secure, and the Internet will
  grow.
• peoples rights to privacy can be guaranteed.
• Disadvantages
• criminals will also be able to communicate
  securely

• Put controls on the use of encryption products
  like RSA
• Advantages
• law-enforcement agencies can still use
  wire-tapping.
• National Security secret intelligence can
  still be gathered.
• Disadvantages
• would jeopardise e-commerce and the security of
  the Internet.
• some people argue that we have a right to
  personal privacy, this would contravene that.

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Thank you