share
TeX - LaTeXHow to create a Caesar's encryption disk using LaTeX
[+49] [6] Uwe Ziegenhagen
[2013-03-20 05:47:24]
[ tikz-pgf fun circles ]
[ https://tex.stackexchange.com/questions/103364/how-to-create-a-caesars-encryption-disk-using-latex ]

How can I create a Caesar's encryption disk with LaTeX?

Caesar's encryption disk

I guess, the ultimate solution would take a arbitrary list of letters and calculate the spaces and angles for each letter automatically. So if I pass 4 letters to it, each space should have 90 degrees.

(2) This looks like fun. Can we add that to the tag? - hpesoj626
Done, added 'fun' :-) - Uwe Ziegenhagen
(1) What have you tried so far? MWE? Do you want to give a list of letters? The number of letters? What should happen when the number is greater than 26? - Qrrbrbirlbel
I have no idea how to tackle this problem, so there is no MWE yet. I could imagine it as the following: \ceasar[circleouterwidth=5cm]{a,b,c,d,e,f,g}{a,b,c,d,e,f,g} with character for the inner and the outer circle. Giving two separate lists could allow to use math symbols as well or Greek characters. There should not be a problem if there are more than 26 chars. - Uwe Ziegenhagen
@Qrrbrbirlbel, well it could be done using an optional parameter for the shift, let's say [0] for no shift or [13] for Rot13, etc. - Uwe Ziegenhagen
(4) Next challenge - build an Enigma machine in TeX? en.wikipedia.org/wiki/Enigma_machine - Ethan Bolker
Go Lahead, at least with LuaTeX it could actually work! - Uwe Ziegenhagen
Related A circular table? (where the rows form concentric circles). - moewe
[+59] [2013-03-20 06:59:02] Qrrbrbirlbel [ACCEPTED]

Commands

  • \drawCaesarsDisk that works with a number of letters (only A to Z)
  • \drawCaesarsList that works with one list for both rings or two different lists

Keys

  • inner radius/middle radius/outer radius
    • Improvements: Specify inner radius and add inner height and outer height respectively to calculate the actual radii.
    • Improvements: With these heights, scale the letters so that they fit right into one ring segment.
  • number of letters (only \drawCaesarsDisk)
  • inner letters and outer letters (only \drawCaesarsList): If only inner letters is specified the letters in the outer ring will be the same as in the inner ring.
  • shift

Parameters (both commands)

  • First (optional): Key=Values for the disk.
  • Second (mandatory): where the Disk is placed.

Improvement:

  • Radii/font-size calculation (see above)
  • Starting with the first letter at the north position or right of it (possible style)
  • Adding styles for circles, separators, letters, etc.

  • Bug: The List command breaks with

    ! Dimension too large. <recently read> \pgfmath@x

    when 46 or more letters are specified.

  • I forgot something …

Code

\documentclass[tikz]{standalone}
\usetikzlibrary{backgrounds}
\makeatletter
\tikzset{
    /caesar/.cd,
    inner radius/.store in=\qrr@caesar@innerR,
    middle radius/.store in=\qrr@caesar@middleR,
    outer radius/.store in=\qrr@caesar@outerR,
    inner letters/.store in=\qrr@caesar@innerL,
    outer letters/.store in=\qrr@caesar@outerL,
    number of letters/.code=\pgfmathtruncatemacro\qrr@caesar@number{#1},
    shift/.store in=\qrr@caesar@shift,
    % defaults:
    outer letters=,
    shift=0
}
\newcommand*{\drawCaesarsDisk}[2][]{%
    \begingroup
    \pgfqkeys{/caesar}{#1}%
    \foreach \radius in {\qrr@caesar@innerR,\qrr@caesar@middleR,\qrr@caesar@outerR}
        \draw (#2) circle [radius=\radius];
    \foreach \step in {0,...,\numexpr\qrr@caesar@number-1}{
        \draw[shift={(#2)}] (\step*360/\qrr@caesar@number:\qrr@caesar@innerR) -- (\step*360/\qrr@caesar@number:\qrr@caesar@outerR);
        \node[shift={(#2)},rotate=(\step+.5)*360/\qrr@caesar@number-90] at ({(\step+.5)*360/\qrr@caesar@number}:{.5*(\qrr@caesar@innerR)+.5*(\qrr@caesar@middleR)} ) {\@Alph{\numexpr26-\step}};
        \pgfmathtruncatemacro\pgf@temp{mod(\step+\qrr@caesar@shift,\qrr@caesar@number)}%
        \node[shift={(#2)},rotate=(\step+.5)*360/\qrr@caesar@number-90] at ({(\step+.5)*360/\qrr@caesar@number}:{.5*(\qrr@caesar@outerR)+.5*(\qrr@caesar@middleR)} ) {\@Alph{\numexpr26-\pgf@temp}};
    }
    \endgroup
}
\newcount\qrr@caesar@c
\newcommand*{\drawCaesarsList}[2][]{%
    \begingroup
    \pgfqkeys{/caesar}{#1}%
    \foreach \radius in {\qrr@caesar@innerR,\qrr@caesar@middleR,\qrr@caesar@outerR}
        \draw (#2) circle [radius=\radius];
    \qrr@caesar@c=0\relax
    \foreach \element in \qrr@caesar@innerL {\global\advance\qrr@caesar@c1}
    \ifx\pgfutil@empty\qrr@caesar@outerL
        \let\qrr@caesar@outerL\qrr@caesar@innerL
    \fi
    \edef\qrr@caesar@number{\number\qrr@caesar@c}%
    \foreach \innerLetter[count=\step from 0] in \qrr@caesar@innerL {
        \draw[shift={(#2)}] (\step*360/\qrr@caesar@number:\qrr@caesar@innerR) -- (\step*360/\qrr@caesar@number:\qrr@caesar@outerR);
        \node[shift={(#2)},rotate=-(\step+.5)*360/\qrr@caesar@number-90] at ({-(\step+.5)*360/\qrr@caesar@number}:{.5*(\qrr@caesar@innerR)+.5*(\qrr@caesar@middleR)} ) {\innerLetter};
    }
    \foreach \outerLetter[count=\step@ from 0] in \qrr@caesar@outerL {
        \ifnum\step@=\qrr@caesar@number\breakforeach\fi
        \pgfmathtruncatemacro\step{mod(\step@+\qrr@caesar@shift,\qrr@caesar@number)}%
        \node[shift={(#2)},rotate=-(\step+.5)*360/\qrr@caesar@number-90] at ({-(\step+.5)*360/\qrr@caesar@number}:{.5*(\qrr@caesar@outerR)+.5*(\qrr@caesar@middleR)} ) {\outerLetter};
    }
    \endgroup
}
\makeatother
\begin{document}
\begin{tikzpicture}
\drawCaesarsDisk[
    inner radius=2cm,
    middle radius=2cm+1.3em,
    outer radius=2cm+3em,
    number of letters=26,
    shift=13,
    ]{0,0}
\end{tikzpicture}

\begin{tikzpicture}
\drawCaesarsList[
    inner radius=.5cm,
    middle radius=.5cm+1.3em,
    outer radius=.5cm+3em,
    inner letters={a,b,c,d,e,f,g},
    outer letters={A,B,C,D,E,F,G}
    ]{2,0}
\end{tikzpicture}

\begin{tikzpicture}
\drawCaesarsList[
    inner radius=2cm,
    middle radius=2cm+1.3em,
    outer radius=2cm+3em,
    inner letters={a,...,z,A,B,...,T},%,U,V,W,X,Y,Z},
    shift=26,
    ]{0,0}
\end{tikzpicture}
\end{document}

Output

enter image description here

enter image description here

enter image description here


Wow! However I get an error: "! Package tikz Error: A node must have a (possibly empty) label text. ... l.58 ]{0,0} - Uwe Ziegenhagen
@UweZiegenhagen I have added some explanation since you made your comment. I also updated the solution to work with the 2.10 version of TikZ. The problem was a parsing error that was already discussed in other questions. And to clarify: Yes, you can give two (possibly different) lists and you can specify a shift. - Qrrbrbirlbel
You are awesome! :-) - Uwe Ziegenhagen
An alternative way of getting the length of a \foreach list is: \foreach \x [count=\c from 1, remember=\c] in {A,...,Z}{}. Then \c holds the length of the list. - Mark Wibrow
1
[+23] [2013-03-20 06:40:13] m0nhawk

Here is what I've done so far:

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
  \begin{tikzpicture}
    \pgfmathsetmacro{\alphsize}{26}

    \pgfmathsetmacro{\ang}{360/\alphsize}
    \pgfmathsetmacro{\d}{10}
    \pgfmathsetmacro{\op}{98 + \ang/2 - 1.2}
    \pgfmathsetmacro{\e}{\ang + \ang*\d}
    \pgfmathsetmacro{\ep}{\op + \ang*\d}

    \foreach \x in {0,\ang,...,360} {
      \draw[gray] (\x:8em) -- (\x:12em);
    }

    \foreach \x [count=\xi] in {A,...,Z} {
      \node[rotate=\ang - \ang*\xi] at (\op - \ang*\xi:11em) {\Large\x};
      \node[rotate=\e - \ang*\xi] at (\ep - \ang*\xi:9em) {\Large\x};
    }

    \draw[thick] (0cm,0cm) circle(12em);
    \draw[gray] (0cm,0cm) circle(10em);
    \draw[thick] (0cm,0cm) circle(8em);
  \end{tikzpicture}
\end{document}

Caesar latin circle


2
[+19] [2013-03-20 06:27:50] Toscho

Here:

\documentclass{article}
\usepackage{tikz}
\usepackage{ifthen}

\newcounter{encrypted}
\newcounter{original}

\newcommand{\increase}[1]{%command to increase a counter by 1 modulo 26
\ifthenelse{\arabic{#1}<26}{\addtocounter{#1}{1}}{\setcounter{#1}{1}}
}

\begin{document}

\setcounter{encrypted}{7}
\setcounter{original}{1}
\begin{tikzpicture}[scale=0.5]
\draw(0,0)circle(5)circle(7)circle(9);
\foreach \x in {1,2,...,26}
{
\draw(\x*360/26:5)--(\x*360/26:9);
\node at (\x*360/26+360/26+180/26:6){\Alph{encrypted}};
\node at (\x*360/26+360/26+180/26:8){\Alph{original}};
\increase{encrypted}
\increase{original}
}
\end{tikzpicture}

\end{document}

enter image description here


(1) This looks really promising. Is there an easy way to take just a list of characters instead of hard-coding the 26 letters? - Uwe Ziegenhagen
(1) @Toscho I have added the picture for you. I hope you don't mind. :-) - hpesoj626
3
[+16] [2013-03-20 20:10:57] kiss my armpit

Just 4 fun with PSTricks.

enter image description here

\documentclass[pstricks,border=12pt]{standalone}
\SpecialCoor
\makeatletter
\def\N{26}

\begin{document}
% speficy the angular distance between the 2 sets of alphabets
\def\offset{13}
\begin{pspicture}(-5,-5)(5,5)
    \psforeach{\r} {2,3,4}{\pscircle{\r}}
    \degrees[\N]
    \psforeach{\t}{65,66,..,90}{%
        \psline(2;\the\psLoopIndex)(4;\the\psLoopIndex)
        \pstVerb{/angle {\the\psLoopIndex\space 0.5 add} bind def}%
        \rput{!angle 6.5 sub}(!3.5 angle \pst@angleunit PtoC){\char\t\relax}
        \rput{!angle \offset\space add 6.5 sub}(!2.5 angle \offset\space add \pst@angleunit PtoC){\char\t\relax}
    }
\end{pspicture}
\end{document}

Animated version

To be funner!

enter image description here

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{multido}
\SpecialCoor
\makeatletter
\def\N{26}

\begin{document}
\multido{\i=0+1}{\N}{%
% speficy the angular distance between the 2 sets of alphabets
\def\offset{\i}
\begin{pspicture}(-5,-5)(5,5)
    \psforeach{\r} {2,3,4}{\pscircle{\r}}
    \degrees[\N]
    \psforeach{\t}{65,66,..,90}{%
        \psline(2;\the\psLoopIndex)(4;\the\psLoopIndex)
        \pstVerb{/angle {\the\psLoopIndex\space 0.5 add} bind def}%
        \rput{!angle 6.5 sub}(!3.5 angle \pst@angleunit PtoC){\char\t\relax}
        \rput{!angle \offset\space add 6.5 sub}(!2.5 angle \offset\space add \pst@angleunit PtoC){\char\t\relax}
    }
\end{pspicture}}
\end{document}

Warning

If we invoke \degrees[<value other than 360>] previously, conversion with \pst@angleunit is needed for representing points in RPN notation but it is NOT need for representing rotation angle. See the following code snippet.

\rput{!angle 6.5 sub}(!3.5 angle \pst@angleunit PtoC){\t}

It is funny? Don't ask me! I just knew this feature several minutes ago!

One more feature, unlike \foreach \t in {A,...,Z}{} that produces a correct result, \psforeach{\t}{A,..,Z}{} produces a weird output!


4
[+7] [2025-01-02 23:34:18] matexmatics

The answer below uses the wheelchart [1] package, which I wrote.

The letters are placed in the diagram with the key wheel data. Their position is determined by the key wheel data pos. The letters are rotated using the key wheel data style.

\documentclass[border=6pt]{standalone}
\usepackage{wheelchart}
\begin{document}
\begin{tikzpicture}
\makeatletter
\pgfkeys{
  /wheelchart,
  slices style={draw,fill=none},
  total count=26,
  wheel data=\@Alph{\WCcount},
  wheel data pos=0.5,
  wheel data style={rotate=\WCmidangle-90}
}
\makeatother
\wheelchart[
  start angle=90+4*(360/26)
]{}
\wheelchart[
  radius={3}{4},
  start angle=90+1*(360/26)
]{}
\end{tikzpicture}
\end{document}

how-to-create-a-caesars-encryption-disk-using-latex

Below, a command \caesar is defined. The first argument is optional and can contain keys for the inner ring. The second argument is mandatory and contains the letters for the inner ring. The third and fourth argument are similar for the outer ring.

\documentclass[border=6pt]{standalone}
\usepackage{wheelchart}
\NewDocumentCommand\caesar{O{}mO{}m}
  {
    {%note the double braces {{...}} so that the contents is in a group and in particular, \pgfkeys is applied locally
      \pgfkeys{
        /wheelchart,
        data=,
        slices style={draw,fill=none},
        value=1,
        wheel data=\WCvarA,
        wheel data pos=0.5,
        wheel data style={rotate=\WCmidangle-90}
      }
      \wheelchart[#1]{#2}
      \wheelchart[#3]{#4}
    }
  }
\begin{document}
\begin{tikzpicture}
\caesar[radius={1}{2},slices style={draw=black,fill=gray!20},start angle=90+5*(360/7)]{e,n,c,r,y,p,t}[slices style={draw=black,fill=gray!50},start angle=90+2*(360/7)]{E,N,C,R,Y,P,T}
\end{tikzpicture}
\end{document}

how-to-create-a-caesars-encryption-disk-using-latex_2

[1] https://ctan.org/pkg/wheelchart

5
[+5] [2025-01-03 15:02:27] wipet

Just for fun, with OpTeX. Note, we needn't use TikZ.

\fontfam[lm]

\newdimen\radiusA \radiusA=50pt % radius od big circle
\newdimen\radiusB \radiusB=35pt % radius of medium circle
\newdimen\radiusC \radiusC=24pt % radius of inner circle
\newdimen\radiusD \radiusD=\dimexpr\radiusA-\radiusB
\def\letterlist{ABCDEFGHIJKLMNOP}  % list of used characters

\def\getletter{\ifx\letterlist\empty \def\useletter{}\else \ea\getletterA\letterlist\end \fi}
\def\getletterA#1#2\end{\def\useletter{#1}\def\letterlist{#2}}
\def\rul{\vrule height.75\radiusD depth.25\radiusD}
\def\circ#1#2#3{{% #1: first angle, #2: number of items, #3: object
   \pdfsave \pdfrotate{#1}%
   \fornum 0..#2-1 \do {\ifx\useletter#3\getletter\fi
      \pdfsave\pdfrotate{-##1*360/#2}%
      \raise\dimexpr\tmpdim+.25\radiusD \hbox to0pt{\hss#3\hss}\pdfrestore}%
   \pdfrestore
}}
\def\cdisk#1#2{% #1: number of items, #2: shift in second disc
   \hbox to2\radiusA{\hss
      \incircle[\vvkern=\radiusA \hhkern=0pt]{}%
      \incircle[\vvkern=\radiusB \hhkern=0pt]{}%
      \incircle[\vvkern=\radiusC \hhkern=0pt]{}%
      \sans\bf
      \tmpdim=\radiusB  \circ{0}{#1}\useletter            \circ{180/#1}{#1}\rul
      \typoscale[800/]\sans\bf \radiusD=\dimexpr \radiusB-\radiusC
      \tmpdim=\radiusC  \circ{-(#2*360)/#1}{#1}\useletter \circ{180/#1}{#1}\rul
\hss}}

\cdisk{15}{5}  % prints a disk with 2x15 letters, second disc shifted by 5

\bye

disk


6