Cryptography the early days

1
Cryptography - the early days

• One of the first ciphers is due to Julius Ceasar
• Every letter of the alphabet was shifted up 3
  places
• So attack at dawn became dwwdfn dw gdzq
• Then there was the simple substitution cipher
• abcdefghijklmnopqrstuvwxyz
• ?
• qwertyuioplkjhgfdsazxcvbnm

2
Substitution

• However substitution falls to frequency analysis
• Most common letter in English are ETAINSHRDLU.
• The longer the ciphertext, the easier to break
• Mary Queen of Scotts lost her head by going on
  and on..

3
The Zimmerman Telegram

• In WWI, the Germans were worried about America
  entering the War after they introduced
  unrestricted submarine warfare..
• So they tried to do a deal with the Mexicans,
  encouraging them to invade the US if the US
  should attack Germany.
• The British broke their codes and exposed the
  whole deal.

4
The one-time pad - I

• This system is unbreakable!
• This uses XOR function. Note that CP?R and PC
  ?R.
• R must be truly random, and available to both

R
R
C
P
P
5
One Time Pad Enigma

• Its fatal to re-use a one-time pad
• Meet the Rosenbergs!
• In WWII the Germans used the Enigma rotor
  machine.
• After the war they were astonished that the
  Poles/British/Americans had broken it.
• To do so, they had to invent the Computer!

6
Tossing a coin over the phone!

• Bob picks up the phone book and opens it at
  random at page 273
• He asks Alice to guess whether or not the number
  following the number 676 2700 is odd or even
• Alice guesses odd (wrong its 836 1770 !)
• Bob tells her the page number and the name
  associated with 676 2700
• Alice checks that the number following is even

7
One-way function

• A phone book is an example of an important
  construction - the one-way function
• yf(x).
• Given x find y - easy
• Given y find x - very very hard.
• Integer factorization is a kind of one-way
  function
• What are the factors of 1111111111111111110 ?

8
Key exchange - Merkles Puzzles

• Alice creates 1,000,000 puzzles, each of which
  takes 1 minute to solve. The solution is the
  puzzle number and a cryptographic key.
• She sends them in random order to Bob.
• He picks one at random and solves it. He shouts
  back the puzzle number to Alice - its number
  176,982!. She retrieves it from an ordered list.
  
• They both have the same cryptographic key. But
  how does an eavesdropper determine their key?

9
A match-making Protocol

• Alice Bob are out on a blind date with friend
  Michael. At the end of the evening each wants to
  know if the other fancies them without
  revealing their own feelings.
• Michael offers to help. He produces 5 playing
  cards, 3 spades and 2 hearts. He gives a spade
  and heart to Alice same to Bob. He puts the
  remaining spade face-down on the table. Alice
  Bob are invited to place their cards face down on
  top of this one
• Bob puts his 2 cards down, heart on top if he
  fancies Alice. Alice puts her two cards down
  heart on bottom if she fancies Bob

10
Match-making - II
Top

• They fancy each-other
• Bob fancies Alice, but she doesnt fancy him
• Alice fancies Bob, but he doesnt fancy her.
• Neither fancies the other...

Bottom
11
Match-Making - III

• Note that the last three cases are
  indistinguishable if the cards are considered in
  a circle
• So Michael cuts the cards randomly and lays them
  face up on the table. Only if the two hearts are
  side-by-side do they fancy each-other. Otherwise
  - no hard feelings!