Chaos, Communication and Consciousness Module PH19510

Chaos, Communication and ConsciousnessModule PH19510

Lecture 10Cryptography - 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 1st century AD. – Invisible ink from variety of organic

fluids 16th Century Italy – Write on shell of egg in alum solution.

Message appears on egg inside when boiled. 2nd 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

TranspositionLetters retain identityPosition 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

PlainText Algorithm Cipher

Text Algorithm PlainText

Key

Key

Encryption Decryption

Substitution Cipher

Algorithm substitute letters Key cipher alphabet

A I Q P F C WO H J T N UL B M E V S G Z D X K Y R

Simple cipher alphabet based of pairs of letters

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

Plain Text

Cipher Text

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 1026

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 lettersMisspellings – DISTAWT PHREKWENCYSCode 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 Vigenère Cipher Belaso 1553 Vigenère C19th

Polyalphabetic substitution

Key word/phrase

Key:PlainText:

CipherText:

PIGPIGPIGPIGPIGPIGPIthelordoftherings

IIPIPKAWXSWLIPKGQTVA

Cracking le chiffre indéchiffrable

Look for repeated groups in cipher textExample: 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 Vigenère 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 Rotors

substitution changes every

character Plugboard

Rotors

KeysLamps

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 rotors3 rotors, 6 possible arrangements =6

Start position for rotors3 rotors, 26 start positions=26x26x26=17,576

Plugboardswap 6 from 26 =100,391,791,500

Total17,576x6x 100,391,791,500≈1016 ≈53 bits

Day Keys & Message Keys

Don’t send too much information with same key

Generate ‘random’ key for each messageMessage 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 twiceRestrictions 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