Slight rewordings and restyling of the cards variant
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README.md
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README.md
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@ -198,12 +198,15 @@ This works because the cipher output is message-dependent: Having a wrong bit
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somewhere in the middle causes avalanche effect and erases any meaning from the
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text after several characters.
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### Alternative playing-card-compatible board
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### Alternative board with playing cards ♥♦♠♣
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The following board can be used so that characters and offsets can be easily
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mapped to playing cards, similar to the Solitaire cipher [2]. Using playing
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cards could be more innocuous and easily explainable to the secret police than
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a set of peculiar numbered tiles.
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If you find the above tiles complicated to obtain or create, you can very
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easily use playing cards to do the same, similarly as with the [Solitaire
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cipher by Schneier](https://www.schneier.com/academic/solitaire/). (Moreover,
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use of playing cards could be more innocuous and easily explainable to a
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suddenly appearing adversary,t p than a set of very peculiarly numbered tiles! :])
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To simplify things a bit, we will use the following layout:
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```
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a b c d e f g
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@ -215,52 +218,65 @@ v w x y z _ .
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4 5 6 7 8 9 0
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```
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**This board uses a 1-based index**, so `a=1`, `b=2`, and so on. With this layout,
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the following mapping to playing cards is used:
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This maps nicely to the playing card suits:
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| **Character** | Card | Index | **Character** | Card | Index | **Character** | Card | Index | **Character** | Card | Index |
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|-----------|------|-------|-----------|------|-------|-----------|------|-------|-----------|------|--------|
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| a | A♦ | 1 | n | A♣ | 14 | _ | A♥ | 27 | 1 | A♠ | 40 |
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| b | 2♦ | 2 | o | 2♣ | 15 | . | 2♥ | 28 | 2 | 2♠ | 41 |
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| c | 3♦ | 3 | p | 3♣ | 16 | , | 3♥ | 29 | 3 | 3♠ | 42 |
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| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
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| j | 10♦ | 10 | w | 10♣ | 23 | ! | 10♥ | 39 | 7 | 7♠ | 46 |
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| k | J♦ | 11 | x | J♣ | 24 | ' | J♥ | 39 | 8 | 8♠ | 47 |
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| l | Q♦ | 12 | y | Q♣ | 25 | ( | Q♥ | 39 | 9 | 9♠ | 48 |
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| m | K♦ | 13 | z | K♣ | 26 | ) | K♥ | 39 | 0 | 10♠ | 49 (0) |
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| Card value | ♦ | ♣ | ♥ | ♠ |
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|------------|---|---|---|---|
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| A | a | n | _ | 1 |
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| 2 | b | o | . | 2 |
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| 3 | c | p | , | 3 |
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| 4 | d | q | - | 4 |
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| 5 | e | r | + | 5 |
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| 6 | f | s | * | 6 |
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| 7 | g | t | / | 7 |
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| 8 | h | u | : | 8 |
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| 9 | i | v | ? | 9 |
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| 10 | j | w | ! | 0 |
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| J | k | x | ' | |
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| Q | l | y | ( | |
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| K | m | z | ) | |
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The (x, y) offset can be calculated by first determining the index: take the
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number of the suit (0-3), multiply by 13, and add the card number (using 1 for
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the Ace, 11-13 for face cards). Then, determine the offset from the index
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using the usual modular arithmetic: `x = index % 7` and `y = index / 7`.
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The last 3 cards are not used. (actually, you are free to use the suits in
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whatever order you like and discard the last 3 of the suit you like the least.)
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Alphanumeric characters can be easily mapped to cards, with letters mapping to
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Diamonds or Clubs and numbers mapping to Spades (note that Spades face cards
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are ommitted). All of the special characters are mapped to the Hearts, though
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coming up with a mnemonic for the mapping of each special character to each
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Heart is left as an exercise for the reader.
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Getting the X and Y offsets from the cards is a slightly more challenging than
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with the tiles that have the offsets marked, but still doable. Calculate
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`13*suit + card value - 1`, then compute the standard quotient and remainder
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for division by 7. I settled with having the second card set laid out next to
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the "active" board, serving as a reference.
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For an example, view [this image](card-tiles.jpg). In this example, the marker
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is on J♣ (at the top left), and we want to encrypt the plaintext character `e`.
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The image includes the character, index, and offsets for the relevant cards.
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The result may look like this:
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1. From the card mapping, `e` maps to 5♦ (letters `a` through `m` map to Diamonds), which is on the second row.
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1. The marker card, J♣, has:
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- an index of 24 (Clubs are suit 1, and the Jack is the 11th card in the suit): `i = 1 * 13 + 11 = 24`
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- an x-offset of 3: `x = i % 7 = 24 % 7 = 3`
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- a y-offset of 3: `y = i / 7 = 24 / 7 = 3`
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1. Using the marker offsets, the ciphertext card is three rows down and three columns to the right of 5♦, which is 6♠.
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1. From the card mapping, 6♠ maps to `6` (Spades map directly to digits), and has:
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- an index of 45 (Spades are suit 3, and 6 is the 6th card in the suit): `i = 3 * 13 + 6 = 45`
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- an x-offset of 3: `x = i % 7 = 45 % 7 = 3`
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- a y-offset of 6: `y = i / 7 = 45 / 7 = 6`
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1. We then complete the cipher as normal:
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- Output `6` as the ciphertext
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- Rotate the row containing the plaintext card, 5♦
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- Rotate the column containing the ciphertext card, 6♠
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- Move the marker according to the offsets of the ciphertext card, to the right 3 and down 6
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For LC4, the following board could be used:
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In this example, the marker is on J♣ (at the top left), and we want to encrypt
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the plaintext character `e`. The image includes the character, index, and
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offsets for the relevant cards.
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1. From the card mapping, `e` maps to 5♦ (letters `a` through `m` map to
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Tiles), which is on the second row.
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2. The marker card, J♣, has:
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- an index of 24 (Clubs are suit 1, and the Jack is the 11th card in the
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suit): `i = 1 * 13 + 11 = 24`
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- an x-offset of 3: `x = i % 7 = 24 % 7 = 3`
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- a y-offset of 3: `y = i / 7 = 24 / 7 = 3`
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3. Using the marker offsets, the ciphertext card is three rows down and three
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columns to the right of 5♦, which is 6♠.
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4. From the card mapping, 6♠ maps to `6` (Spades map directly to digits), and
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has:
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- an index of 45 (Spades are suit 3, and 6 is the 6th card in the suit): `i
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= 3 * 13 + 6 = 45`
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- an x-offset of 3: `x = i % 7 = 45 % 7 = 3`
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- a y-offset of 6: `y = i / 7 = 45 / 7 = 6`
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5. We then complete the cipher as normal:
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- Output `6` as the ciphertext
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- Rotate the row containing the plaintext card, 5♦
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- Rotate the column containing the ciphertext card, 6♠
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- Move the marker according to the offsets of the ciphertext card, to the
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right 3 and down 6
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For the original LC4, you need just 3 suits, modifying the board to "align" to
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the suits e.g. as follows:
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```
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a b c d e f
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@ -271,11 +287,6 @@ y z _ 2 3 4
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5 6 7 8 9 #
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```
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The "Hearts" suit would be ommitted from the card mapping table, and the index
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of each of the Spades would be decreased by 13 to compensate. `_` and `#`
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would map to A♠ and 10♠, respectively.
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## References
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[1] *Kaminsky, Alan. "ElsieFour: A Low-Tech Authenticated Encryption Algorithm For Human-to-Human Communication." IACR Cryptology ePrint Archive 2017 (2017): 339.*
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[2] *Schneier, Bruce. ["The Solitaire Encryption Algorithm"](https://www.schneier.com/academic/solitaire/).*
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