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@@ -142,6 +142,8 @@ stays the same. Grab a bag full of tiles and randomly draw them one by one. Key is the 49-item permutation of them. +## Modifications + ### Key expansion from a password Remembering 49-position random permutation that includes weird characters is @@ -196,6 +198,84 @@ 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 text after several characters. +### Alternative playing-card-compatible board + +The following board can be used so that characters and offsets can be easily +mapped to playing cards, similar to the Solitaire cipher [2]. Using playing +cards could be more innocuous and easily explainable to the secret police than +a set of peculiar numbered tiles. + +``` +a b c d e f g +h i j k l m n +o p q r s t u +v w x y z _ . +, - + * / : ? +! ' ( ) 1 2 3 +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, +the following mapping to playing cards is used: + +| **Character** | Card | Index | **Character** | Card | Index | **Character** | Card | Index | **Character** | Card | Index | +|-----------|------|-------|-----------|------|-------|-----------|------|-------|-----------|------|--------| +| a | A♦ | 1 | n | A♣ | 14 | _ | A♥ | 27 | 1 | A♠ | 40 | +| b | 2♦ | 2 | o | 2♣ | 15 | . | 2♥ | 28 | 2 | 2♠ | 41 | +| c | 3♦ | 3 | p | 3♣ | 16 | , | 3♥ | 29 | 3 | 3♠ | 42 | +| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | +| j | 10♦ | 10 | w | 10♣ | 23 | ! | 10♥ | 39 | 7 | 7♠ | 46 | +| k | J♦ | 11 | x | J♣ | 24 | ' | J♥ | 39 | 8 | 8♠ | 47 | +| l | Q♦ | 12 | y | Q♣ | 25 | ( | Q♥ | 39 | 9 | 9♠ | 48 | +| m | K♦ | 13 | z | K♣ | 26 | ) | K♥ | 39 | 0 | 10♠ | 49 (0) | + +The (x, y) offset can be calculated by first determining the index: take the +number of the suit (0-3), multiply by 13, and add the card number (using 1 for +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 +Diamonds or Clubs and numbers mapping to Spades (note that Spades face cards +are ommitted). All of the special characters are mapped to the Hearts, though +coming up with a mnemonic for the mapping of each special character to each +Heart is left as an exercise for the reader. + +For an example, view [this image](card-tiles.jpg). 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 Diamonds), which is on the second row. +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: + +``` +a b c d e f +g h i j k l +m n o p q r +s t u v w x +y z _ 2 3 4 +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 -[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/).* |