Solitaire (cipher)

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The Solitaire cryptographic algorithm was designed by Bruce Schneier "to allow field agents to communicate securely without having to rely on electronics or having to carry incriminating tools",[1] at the request of Neal Stephenson for use in his novel Cryptonomicon. It was designed to be a manual cryptosystem calculated with an ordinary deck of playing cards. In Cryptonomicon, this algorithm was originally called Pontifex to hide the fact that it involved playing cards.

One of the motivations behind Solitaire's creation is that in totalitarian environments, a deck of cards is far more affordable (and less incriminating) than a personal computer with an array of cryptological utilities. However, as Schneier warns in the appendix of Cryptonomicon, just about everyone with an interest in cryptanalysis will know about this algorithm.

Cryptanalysis by Paul Crowley in 1999 shows that the probability that two successive outputs from the cipher are the same is not 1/26 as it should be, but closer to 1/22.5.[2]

Contents

[edit] Encryption and decryption

The algorithm generates a stream of values which are combined with the message to encrypt and decrypt it. Each value of the keystream is to be used for one value of the message, thus the keystream will need to be the same length as the message.

  1. Remove all punctuation and convert the characters to the same case.
  2. Convert all the characters to their natural numerical values, A = 1, B = 2, etc, Z = 26.
  3. To encrypt a message, add each keystream value to its corresponding character in the plaintext, rolling over back to 1 if the resulting value exceeds 26. To decrypt, subtract each keystream value from its corresponding character in the ciphertext, rolling back up to 26 if the resulting value should be lower than 1.

[edit] Algorithm

This algorithm assumes that the user has a deck of cards and two jokers. For simplicity's sake, only two suits will be used in this example. Each card will be assigned a numerical value: the first suit of cards will be numbered from 1 to 13 (Ace through King) and the second suit will be numbered 14 through 26 in the same manner. The jokers will be assigned the values of 27 and 28. Thus, a 5 from the first suit would have the value 5 in our combined deck, the value 1 in the second suit would have the value 14 in the combined deck.

The deck will be assumed to be a circular array, meaning that should a card ever need to advance below the bottom card in the deck, it will simply rotate back to the top (in other words, the first card follows the last card).

  1. Arrange the deck of cards according to a specific key. This is the most important part as anyone who knows the deck's starting value can easily generate the same values from it. How the deck is initialized is up to the recipients, shuffling the deck perfectly randomly is preferable, although there are many other methods. For this example, the deck will simply start at 1 and count up by 3's, modulo 28. Thus the starting deck will look like this:
    • 1 4 7 10 13 16 19 22 25 28 3 6 9 12 15 18 21 24 27 2 5 8 11 14 17 20 23 26
  2. Locate the first joker (value 27) and move it down the deck by one place, basically just exchanging with the card below it. The deck now looks like this:
    • 1 4 7 10 13 16 19 22 25 28 3 6 9 12 15 18 21 24 2 27 5 8 11 14 17 20 23 26
  3. Locate the second joker (value 28) and move it down the deck by two places.
    • 1 4 7 10 13 16 19 22 25 3 6 28 9 12 15 18 21 24 2 27 5 8 11 14 17 20 23 26
  4. Perform a triple-cut on the deck. That is, split the deck into three sections. Everything above the top joker (which, after several repetitions, may not necessarily be the first joker) and everything below the bottom joker will be exchanged. The jokers themselves, and the cards between them, are left untouched.
    • 5 8 11 14 17 20 23 26 28 9 12 15 18 21 24 2 27 1 4 7 10 13 16 19 22 25 3 6
  5. Observe the value of the card at the bottom of the deck, if the card is either joker let the value just be 27. Take that number of cards from the top of the deck and insert them back to the bottom of the deck just above the last card.
    • 23 26 28 9 12 15 18 21 24 2 27 1 4 7 10 13 16 19 22 25 3 5 8 11 14 17 20 6
  6. Note the value of the top card. Count this many places below that card and take the value of the card there. This value is the next value in the keystream, in this example it would be 11. (Note that no cards are changing places in this step, this step simply determines the value).
  7. Repeat steps 2 through 6 for as many keystream values as required.

[edit] References

  1. ^ Schneier, Bruce (May 1999). Solitaire. Retrieved on 2 July, 2006.
  2. ^ Crowley, Paul (1999). Problems with Bruce Schneier's "Solitaire". Retrieved on 2007-05-30.

[edit] External links

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