Chaos, Communication and Consciousness Module PH19510

Lecture 10 Cryptography - The Science of Secret Writing

Overview of Lecture

 Ways of keeping information secret  Steganography  Ceasar’s cipher  The Vigenere square  Mechanical Cryptography

The Code Book

 Simon Singh  Fourth Estate  ISBN    1-85702-889-9 £9.99

http://www.simonsingh.com

Ways of keeping information secret  Steganography 

steganos

– covered 

graphein

– to write  Hidden Message  Crytopgraphy 

kryptos

– hidden 

graphein

– to write  Hidden Meaning

Steganography

      Ancient Greece – write message on shaved head of slave, allow hair to grow back Ancient China – write message on fine silk, roll into ball, cover in wax, swallow 1 st century AD. – Invisible ink from variety of organic fluids 16 th Century Italy – Write on shell of egg in alum solution. Message appears on egg inside when boiled.

2 nd World war – Microfilm, text shrunk to full stop size.

Now: Hide inside music file/image ?

Cryptography

 2 main options  Substitution  Letters retain position  Identity of letters substituted  Transposition  Letters retain identity  Position of letters scrambled

Transposition ciphers

 Re-arrange letters of message  Need pre-arranged method, otherwise one long anagram (possibly many solutions)  eg. Rail fence code  Scytale

General Cipher Process

Plain Text Key Algorithm Cipher Text Key Algorithm Plain Text

Encryption Decryption

Substitution Cipher

 Algorithm  substitute letters  Key  cipher alphabet

A I Q P F C W O H J T N U L B M E V S G Z D X K Y R Simple cipher alphabet based of pairs of letters Plain Text Cipher Text

a t t a c k t h e c a s t  l e a t d a w n L K K L S T K D P S L C K A P L K H L G Y

Caesar Cipher

 Shift alphabet along by n places  n is key  eg n=3 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  D E F G H I J K L M N O P Q R S T U V W X Y Z A B C

Monoalphabet Substitution Ciphers  How many different cipher alphabets ?

 26 × 25 × 24 × ….. × 1 = 26! ≈ 4 x 10 26  Seems difficult to break  Good until ≈ 850AD

Cryptanalysis - Code breaking

  Al-Kindi 800 – 873 AD  Analysis of text  frequency of letters  double letters (ee, oo, mm, tt …)  adjacent letters  single letter words  common words

The Renaissance – Code makers trying to stay ahead  Addition to ciphers to make frequency analysis more difficult:  Nulls – meaningless symbols or letters  Misspellings – DISTAWT PHREKWENCYS  Code words/symbols for common words

Mary Queen of Scots

     Plot to assassinate Queen Elizabeth Messages hidden in bung of barrel –

steganography

Substitution cipher  Nulls  Codewords Broken by Walsingham Mary executed 1587

Le chiffre indéchiffrable

The Vigen ère Cipher   Belaso 1553 Vigen ère C19 th  Polyalphabetic substitution  Key word/phrase Key: PlainText: thelordoftherings CipherText:

Cracking le chiffre indéchiffrable

 Look for repeated groups in cipher text

Example:

IPKAWXSWLIPKGQTVA  Result of repeat of key with same plaintext  Distance between repeats is multiple of key length  Possible to guess length of key  Split problem into several monoalphabet ciphers  Apply frequency analysis to each in turn

Making the Vigen ère cipher unbreakable  Security increases with key length  Unbreakable if key:  truly random (radioactive decay, electronic noise, quantum effect)  doesn’t repeat  One-time pad  But … key distribution problem

Mechanical Encryption

 Automate encryption process  Freedom from mistakes  Possible to use complicated algorithms  Speed

The Enigma Machine

      Patented 1921 by Arthur Scherbius Used in WWII Input via Keyboard Output via Lamps Plugboard  fixed substitution Lamps Rotors  substitution  changes every character Plugboard Rotors Keys

The Enigma rotors

    Rotor    26 way substitution 3 rotors Reflector Rotors advance every keystroke & change substitutions Middle Rotor advances for every complete turn of Right Ditto for left rotor & reflector

The Enigma Keys

 Arrangement of rotors  3 rotors,  6 possible arrangements  Total  17,576x6x 100,391,791,500 ≈10 16 ≈53 bits =6  Start position for rotors  3 rotors, 26 start positions=26x26x26=17,576  Plugboard  swap 6 from 26 =100,391,791,500

Day Keys & Message Keys

  Don’t send too much information with same key Generate ‘random’ key for each message  Message Key  Use day key (from codebook) to encrypt message key, put at start of message.

 Encrypt rest of message with message key  Day key only used to encrypt message keys

Bletchley Park & ULTRA

 UK codebreakers  Station X  Bletchley Park  Alan Turing  Product known as ULTRA  Shortened WWII by 2 years

Cracking Enigma

 Captured/stolen machines & codebooks  Known/guessed plaintext (Cribs)  weather station reports in fixed format  ‘planted’ information  Operator & Systematic weaknesses  ‘easy’ message keys (‘cillies’)  Message key sent twice  Restrictions on plugboard & rotor settings

Cracking Enigma #2

 Look for loops in crib/ciphertext  Separate effect of plugboard & rotors  Use machine to test possibilities bombe

Review of Lecture

 Ways of keeping information secret  Steganography  Ceasar’s cipher  The Vigenere square  Mechanical Cryptography  The Enigma Machine