Solitaire

1
Solitaire

• Aaron Styx
• (some material from Bruce Schneiers Solitare
  paper. See References)

2
Overview

• History
• Basics
• The Key
• The Key stream
• Encryption
• Decryption
• Cryptanalysis

3
Solitaire Background

• Bruce Schneier
• Paper/pencil cipher
• Pontifex
• Cryptonomicon Neal Stephenson

4
Solitaire Basics

• Uses standard deck of 52 cards 2 jokers
• Strong Security
• Dont re-use key
• (A K) (B K) A B No Key Needed!
• Stream Cipher
• Output-feedback mode
• Also called key-generator
• Plain text converted to numbers ? added to key
  stream ? converted back to letters
• Can only use letters
• No spaces
• No punctuation

5
Stream Cipher

• Also called State Cipher
• Data encrypted one character at a time
• Uses pseudorandom key stream
• Successive elements of key stream are generated
  automatically based on some initial state

6
The Solitaire Key Stream

• Initial ordering of deck is used as key
• Key / key stream
• 54! (2.31x1071) possible orderings
• Unique jokers
• Call them A and B

7
Key Stream cont.

• Step 1
• Move Joker A down 1 card
• If Joker A is on the bottom of the deck, move it
  just below the top card.
• Step 2
• Move Joker B down 2 cards
• If Joker B is bottom card, move it to 3rd from
  top
• If Joker B is second to bottom, move it just
  below the top card

8
Key Stream cont.

• Example (from Shneiers paper)
• Before step 1 A 7 2 B 9 4 1
• After step 2 7 A 2 9 4 B 1
• Another Example
• Before step 1 3 A B 8 9 6
• After step 2 3 A 8 B 9 6
• Order matters!

9
Key Stream cont.

• Step 3 Triple Cut
• Joker locations determine where you cut
• Swap top cards with bottom cards
• Before Cut Top P1 (J)P2(J) P3
• After Cut Top P3 (J)P2(J) P1
• Jokers dont move
• Move empty packets regardless

10
Key Stream cont.

• Example
• Before cut B 5 8 7 1 A 3 9
• After cut 3 9 B 5 8 7 1 A
• Deck can remain unchanged

11
Key Stream cont.

• Suits have order
• Sheepshead order ? ? ? ?
• Bridge order ? ? ? ?
• Or any other order. Be consistent
• Schneier uses bridge order
• ? 1-13
• ? 14 26
• ? 27 39
• ? 40 - 52

12
Key Stream cont.

• Step 4 Count Cut
• Convert bottom card to a number 1..53
• Both Jokers 53
• Example A? 1, 9? 35 (w/ bridge ordering)
• Count into the deck the number of cards
  corresponding to the bottom card
• Cut the deck, leaving the bottom card on the
  bottom of the deck
• Why?

13
Key Stream cont.

• Example
• Before cut 8 4 75 3 2 61 9
• With the 3 being the 9th card from the top
• After cut 3 2 6 1 8 4 75 9

14
Key Stream cont.

• Step 5 Getting an output card
• Look at top card ? convert to number
• Count down through deck that number of cards
• Card after last card counted is output card
• Convert to number, but only want 1 26
• Ace-clubs King-diamonds 1 26
• Ace-hearts King-spades 1 26
• Number corresponds to letter of alphabet 1A,
  2B, etc
• This number/letter is the first in the Key Stream

15
Key Stream cont.

• Step 5 does not modify the deck order!
• Steps 1 5 are repeated for every character in
  the plain text
• Dont re-key the deck after getting each Key
  Stream number

16
Putting it all together Encryption

• Split plain text into 5 character groups w/o
  spaces
• Generate the same number of key stream letters as
  characters in the plain text
• Convert both plain text and key stream into
  numbers
• Add plain text to key stream and mod 26
• Result is encrypted text

17
Decryption

• To decrypt, generate the same key stream by using
  the original keyed deck
• The original deck is the private key
• Simply subtract the key stream from the encrypted
  text

18
Considerations

• Randomly shuffled deck is best
• Receiver must also know what this order is
• Still have key distribution problem
• No Mistakes!
• Studies of the method show that Solitaire has a
  bias
• Can be done on computer as well