initial state
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LS47.scad
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103
LS47.scad
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// text_on_cube.scad - Example for text() usage in OpenSCAD
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echo(version=version());
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//font = "URW Bookman L";
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font = "Monospace";
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font2 = "Droid Sans Mono";
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//TODO: kulaty rohy
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tilesize=25.4;
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off=tilesize*1.05;
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tileheight=tilesize/8;
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module tilec(letter, x, y, c) {
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translate([x*off,(6-y)*off,0]) {
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difference() {
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color(c)
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cube([tilesize,tilesize,tileheight]);
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color(c)
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translate([tilesize*.4,tilesize*.4,tileheight*.51])
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linear_extrude (height=tileheight/2)
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text(letter, font=font, size=tilesize*.5,
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halign="center", valign="baseline");
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color(c)
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translate([tilesize*.83, tilesize/2, tileheight*.76])
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linear_extrude(height=tileheight/4)
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text(str(x), font=font2, size=tilesize*.2,
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halign="center", valign="center");
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color(c)
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translate([tilesize/2, tilesize*.14, tileheight*.76])
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linear_extrude(height=tileheight/4)
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text(str(y), font=font2, size=tilesize*.2,
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halign="center", valign="center");
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}
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}
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}
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//tiles
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module tile(letter,x,y) {
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tilec(letter,x,y,"darkgray");
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}
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tile("_",0,0);
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tile("A",1,0);
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tile("B",2,0);
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tile("C",3,0);
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tile("D",4,0);
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tile("E",5,0);
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tile("F",6,0);
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tile("G",0,1);
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tile("H",1,1);
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tile("I",2,1);
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tile("J",3,1);
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tile("K",4,1);
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tile("L",5,1);
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tile("M",6,1);
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tile("N",0,2);
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tile("O",1,2);
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tile("P",2,2);
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tile("Q",3,2);
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tile("R",4,2);
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tile("S",5,2);
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tile("T",6,2);
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tile("U",0,3);
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tile("V",1,3);
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tile("W",2,3);
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tile("X",3,3);
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tile("Y",4,3);
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tile("Z",5,3);
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tile(".",6,3);
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tile("0",0,4);
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tile("1",1,4);
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tile("2",2,4);
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tile("3",3,4);
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tile("4",4,4);
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tile("5",5,4);
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tile("6",6,4);
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tile("7",0,5);
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tile("8",1,5);
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tile("9",2,5);
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tile(",",3,5);
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tile("-",4,5);
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tile("+",5,5);
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tile("*",6,5);
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tile("/",0,6);
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tile(":",1,6);
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tile("?",2,6);
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tile("!",3,6);
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tile("'",4,6);
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tile("(",5,6);
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tile(")",6,6);
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//the token
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translate([-off/2,off/2,0]) {
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color("red") difference() {
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cylinder(h=tileheight, d=tilesize*.7);
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translate([0,0,-.1])
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cylinder(h=tileheight*1.2, d=tilesize*.7-tileheight);
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}
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}
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126
README.md
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126
README.md
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@ -0,0 +1,126 @@
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# LS47 hand-computable cipher
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This is a slight improvement of the ElsieFour cipher as described by Alan Kaminsky [1]. We use 7x7 characters instead of previous (barely fitting) 6x6 to be able to encrypt some structured information and add a simple key-expansion algorithm. Similar security considerations hold.
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There's 3D-printable SCAD model of the whole thing.
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### Character board
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We have added some real punctuation, basic stuff for writing a bit of markdown,
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and quotes&parens for writing structured information. The letters of the board
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now look like this:
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```
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_ a b c d e f
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g h i j k l m
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n o p q r s t
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u v w x y z .
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0 1 2 3 4 5 6
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7 8 9 , - + *
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/ : ? ! ' ( )
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```
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Zoomed in, it's nice to have extra position information written on the tiles:
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```
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/-----\ /-----\ /-----\ /-----\ /-----\
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| | | | | | | | | |
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| _ 0| | a 1| | b 2| | c 3| | d 4| ...
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| 0 | | 0 | | 0 | | 0 | | 0 |
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\-----/ \-----/ \-----/ \-----/ \-----/
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/-----\ /-----\
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| | | |
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| g 0| | h 1| ...
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| 1 | | 1 |
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\-----/ \-----/
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. .
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. .
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. .
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```
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You also need some kind of a marker (e.g. a small shiny stone, bolt nut or similar kinds of well-shaped trash).
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## How-To
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You may as well see the paper [1], there are also pictures. This is somewhat more concentrated:
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### Encryption
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1. The symmetric key is the initial state of the board. Arrange your tiles to 7x7 square according to the key.
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2. Put the marker on (0,0).
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3. Find the next letter you want to encrypt on the board, its position is `P`.
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4. Look at the marker; numbers written on the marked tile are coordinates `M`.
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5. Compute position of the ciphertext as `C := P + M mod (7,7)`. Output the letter found on position `C` as ciphertext.
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6. Rotate the row that contains the plaintext letter one position to the right, carry the marker if present.
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7. Rotate the column that now (after the first rotation) contains the ciphertext letter one position down, carry the marker if present.
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8. Update the position of the marker: `M := M + C' mod (7,7)` where `C'` are the numbers written on the ciphertext tile.
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9. Repeat from 3 as many times as needed to encrypt the whole plaintext.
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### Decryption
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Decryption procedure is basically the same, except that in step 5 you know `C`
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and `M`, and need to produce `P` by subtraction: `P := C - M mod (7,7)`.
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Otherwise (except that you input ciphertext and output plaintext) everything
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stays the same.
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### Key generation
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Grab a bag full of tiles and randomly draw them one by one. Key is the 49-item permutation of them.
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### Key expansion from a password
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Remembering 49-position random permutation that includes weird characters is
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not very handy. You can instead derive the keys from an arbitrary string of
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sufficient length.
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"Sufficient" means "provides enough entropy". Full keys store around 208 bits
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of entropy. To reach that, your password should have:
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- at least around 61 decimal digits if made only from random decimal digits
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- at least around 44 letters if made only from completely random letters
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- at least around 40 alphanumeric characters if made randomly only from them
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To have the "standard" 128 bits of entropy, the numbers reduce to roughly 39,
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28 and 25, respectively.
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Note that you can save the expanded tile board for later if you don't want to
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expand the passwords before each encryption/decryption.
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The actual expansion can be as simple as this:
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1. initialize `I:=0`, put the tiles on the board sorted by their numbers (i.e. as on the picture above)
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2. Take the first letter of the password and see the numbers on its tile; mark them `Px, Py`.
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3. Rotate `I`-th row `Px` positions right
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4. Rotate `I`th column `Py` positions down
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5. `I := I + 1 mod 7`, repeat from 2 with next letter of the password.
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6. Resulting tile positions are the expanded key
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### Undistinguishable ciphertexts
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To get a different ciphertext even if the same plaintext is encrypted; prepend
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it with a nonce. A nonce is a completely random sequence of letters of a
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pre-negotiated length (at least 10 tiles drawn randomly from a bag is
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adviseable).
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You may also want to add a random number of spaces to the end of the ciphertext
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-- it prevents the enemy from seeing the difference between ciphertexts for
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'yes please' and 'no', which would otherwise encrypt to easily measurable
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gibberish like `qwc3w_cs'(` and `+v`.
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### Authenticated encryption
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Because ciphertext may be altered in the transfer or during the error-prone
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human processing, it is advised to append a simple "signature" to the end of
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the message; e.g. a simple string `__YourHonorableNameHere`. If the signature
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doesn't match expectations (which happens with overwhelming probability if
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there was any error in the process), you discard the message and ask the sender
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to re-transmit.
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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 breaks the signature.
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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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