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Slight rewordings and restyling of the cards variant

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Mirek Kratochvil 2021-04-23 17:36:07 +02:00
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@ -198,12 +198,15 @@ This works because the cipher output is message-dependent: Having a wrong bit
somewhere in the middle causes avalanche effect and erases any meaning from the somewhere in the middle causes avalanche effect and erases any meaning from the
text after several characters. text after several characters.
### Alternative playing-card-compatible board ### Alternative board with playing cards ♥♦♠♣
The following board can be used so that characters and offsets can be easily If you find the above tiles complicated to obtain or create, you can very
mapped to playing cards, similar to the Solitaire cipher [2]. Using playing easily use playing cards to do the same, similarly as with the [Solitaire
cards could be more innocuous and easily explainable to the secret police than cipher by Schneier](https://www.schneier.com/academic/solitaire/). (Moreover,
a set of peculiar numbered tiles. use of playing cards could be more innocuous and easily explainable to a
suddenly appearing adversary,t p than a set of very peculiarly numbered tiles! :])
To simplify things a bit, we will use the following layout:
``` ```
a b c d e f g a b c d e f g
@ -215,52 +218,65 @@ v w x y z _ .
4 5 6 7 8 9 0 4 5 6 7 8 9 0
``` ```
**This board uses a 1-based index**, so `a=1`, `b=2`, and so on. With this layout, This maps nicely to the playing card suits:
the following mapping to playing cards is used:
| **Character** | Card | Index | **Character** | Card | Index | **Character** | Card | Index | **Character** | Card | Index | | Card value | ♦ | ♣ | ♥ | ♠ |
|-----------|------|-------|-----------|------|-------|-----------|------|-------|-----------|------|--------| |------------|---|---|---|---|
| a | A♦ | 1 | n | A♣ | 14 | _ | A♥ | 27 | 1 | A♠ | 40 | | A | a | n | _ | 1 |
| b | 2♦ | 2 | o | 2♣ | 15 | . | 2♥ | 28 | 2 | 2♠ | 41 | | 2 | b | o | . | 2 |
| c | 3♦ | 3 | p | 3♣ | 16 | , | 3♥ | 29 | 3 | 3♠ | 42 | | 3 | c | p | , | 3 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | | 4 | d | q | - | 4 |
| j | 10♦ | 10 | w | 10♣ | 23 | ! | 10♥ | 39 | 7 | 7♠ | 46 | | 5 | e | r | + | 5 |
| k | J♦ | 11 | x | J♣ | 24 | ' | J♥ | 39 | 8 | 8♠ | 47 | | 6 | f | s | * | 6 |
| l | Q♦ | 12 | y | Q♣ | 25 | ( | Q♥ | 39 | 9 | 9♠ | 48 | | 7 | g | t | / | 7 |
| m | K♦ | 13 | z | K♣ | 26 | ) | K♥ | 39 | 0 | 10♠ | 49 (0) | | 8 | h | u | : | 8 |
| 9 | i | v | ? | 9 |
| 10 | j | w | ! | 0 |
| J | k | x | ' | |
| Q | l | y | ( | |
| K | m | z | ) | |
The (x, y) offset can be calculated by first determining the index: take the The last 3 cards are not used. (actually, you are free to use the suits in
number of the suit (0-3), multiply by 13, and add the card number (using 1 for whatever order you like and discard the last 3 of the suit you like the least.)
the Ace, 11-13 for face cards). Then, determine the offset from the index
using the usual modular arithmetic: `x = index % 7` and `y = index / 7`.
Alphanumeric characters can be easily mapped to cards, with letters mapping to Getting the X and Y offsets from the cards is a slightly more challenging than
Diamonds or Clubs and numbers mapping to Spades (note that Spades face cards with the tiles that have the offsets marked, but still doable. Calculate
are ommitted). All of the special characters are mapped to the Hearts, though `13*suit + card value - 1`, then compute the standard quotient and remainder
coming up with a mnemonic for the mapping of each special character to each for division by 7. I settled with having the second card set laid out next to
Heart is left as an exercise for the reader. the "active" board, serving as a reference.
For an example, view [this image](card-tiles.jpg). In this example, the marker The result may look like this:
is on J♣ (at the top left), and we want to encrypt the plaintext character `e`.
The image includes the character, index, and offsets for the relevant cards.
1. From the card mapping, `e` maps to 5♦ (letters `a` through `m` map to Diamonds), which is on the second row. ![Using cards instead of tiles](card-tiles.jpg)
1. The marker card, J♣, has:
- an index of 24 (Clubs are suit 1, and the Jack is the 11th card in the suit): `i = 1 * 13 + 11 = 24`
- an x-offset of 3: `x = i % 7 = 24 % 7 = 3`
- a y-offset of 3: `y = i / 7 = 24 / 7 = 3`
1. Using the marker offsets, the ciphertext card is three rows down and three columns to the right of 5♦, which is 6♠.
1. From the card mapping, 6♠ maps to `6` (Spades map directly to digits), and has:
- an index of 45 (Spades are suit 3, and 6 is the 6th card in the suit): `i = 3 * 13 + 6 = 45`
- an x-offset of 3: `x = i % 7 = 45 % 7 = 3`
- a y-offset of 6: `y = i / 7 = 45 / 7 = 6`
1. We then complete the cipher as normal:
- Output `6` as the ciphertext
- Rotate the row containing the plaintext card, 5♦
- Rotate the column containing the ciphertext card, 6♠
- Move the marker according to the offsets of the ciphertext card, to the right 3 and down 6
For LC4, the following board could be used: In this example, the marker is on J♣ (at the top left), and we want to encrypt
the plaintext character `e`. The image includes the character, index, and
offsets for the relevant cards.
1. From the card mapping, `e` maps to 5♦ (letters `a` through `m` map to
Tiles), which is on the second row.
2. The marker card, J♣, has:
- an index of 24 (Clubs are suit 1, and the Jack is the 11th card in the
suit): `i = 1 * 13 + 11 = 24`
- an x-offset of 3: `x = i % 7 = 24 % 7 = 3`
- a y-offset of 3: `y = i / 7 = 24 / 7 = 3`
3. Using the marker offsets, the ciphertext card is three rows down and three
columns to the right of 5♦, which is 6♠.
4. From the card mapping, 6♠ maps to `6` (Spades map directly to digits), and
has:
- an index of 45 (Spades are suit 3, and 6 is the 6th card in the suit): `i
= 3 * 13 + 6 = 45`
- an x-offset of 3: `x = i % 7 = 45 % 7 = 3`
- a y-offset of 6: `y = i / 7 = 45 / 7 = 6`
5. We then complete the cipher as normal:
- Output `6` as the ciphertext
- Rotate the row containing the plaintext card, 5♦
- Rotate the column containing the ciphertext card, 6♠
- Move the marker according to the offsets of the ciphertext card, to the
right 3 and down 6
For the original LC4, you need just 3 suits, modifying the board to "align" to
the suits e.g. as follows:
``` ```
a b c d e f a b c d e f
@ -271,11 +287,6 @@ y z _ 2 3 4
5 6 7 8 9 # 5 6 7 8 9 #
``` ```
The "Hearts" suit would be ommitted from the card mapping table, and the index
of each of the Spades would be decreased by 13 to compensate. `_` and `#`
would map to A♠ and 10♠, respectively.
## References ## References
[1] *Kaminsky, Alan. "ElsieFour: A Low-Tech Authenticated Encryption Algorithm For Human-to-Human Communication." IACR Cryptology ePrint Archive 2017 (2017): 339.* [1] *Kaminsky, Alan. "ElsieFour: A Low-Tech Authenticated Encryption Algorithm For Human-to-Human Communication." IACR Cryptology ePrint Archive 2017 (2017): 339.*
[2] *Schneier, Bruce. ["The Solitaire Encryption Algorithm"](https://www.schneier.com/academic/solitaire/).*