contributions for Tikz for cryptographers
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| \begin{tikzpicture} | |
| \begin{scope}[scale=.28,local bounding box=scope1] | |
| \coordinate (Origin) at (0,0); | |
| \coordinate (XAxisMin) at (-1,0); | |
| \coordinate (XAxisMax) at (10,0); | |
| \coordinate (YAxisMin) at (0,-1); | |
| \coordinate (YAxisMax) at (0,10); | |
| \draw [thin, black!40, <->] (XAxisMin) -- (XAxisMax);% Draw x axis | |
| \draw [thin, black!40,<->] (YAxisMin) -- (YAxisMax);% Draw y axis | |
| %\draw[style=help lines,dashed,black!20] (-5,-5) grid[step=1cm] (5,5); | |
| % basis vectors | |
| \draw [->] (Origin) -- (4,1); | |
| \draw [->] (Origin) -- (1,3); | |
| % explanation | |
| \node[right] at (-7, 9) {\small{non-lattice vector}}; | |
| \draw[->, black!50] (-3, 8) -- (6,6.25); | |
| \node[right] at (-7, 4) {\small{basis vectors}}; | |
| \draw[->, black!50] (-5, 3) -- (-1, 2); | |
| % our little node | |
| \node[shape=circle,fill=purple,scale=0.4] at (6.7,6.25){}; | |
| \node[shape=circle,draw=purple,fill=none,scale=0.8] at (6.7,6.25){}; | |
| \end{scope} | |
| \begin{scope}[scale=.28,shift={(13,0)}] | |
| \coordinate (Origin) at (0,0); | |
| \coordinate (XAxisMin) at (-1,0); | |
| \coordinate (XAxisMax) at (10,0); | |
| \coordinate (YAxisMin) at (0,-1); | |
| \coordinate (YAxisMax) at (0,10); | |
| \draw [thin, black!40, <->] (XAxisMin) -- (XAxisMax);% Draw x axis | |
| \draw [thin, black!40,<->] (YAxisMin) -- (YAxisMax);% Draw y axis | |
| %\draw[style=help lines,dashed,black!20] (-5,-5) grid[step=1cm] (5,5); | |
| % basis vectors | |
| \draw [->] (Origin) -- (4,1); | |
| \draw [->] (Origin) -- (1,3); | |
| % extended basis vectors | |
| \draw [black!40] (4,1) -- (5,1.25); | |
| \draw [black!40] (1,3) -- (1.6,5); | |
| \draw [black!40] (5.1,1.25) -- (6.7,6.25); | |
| \draw [black!40] (1.6,5) -- (6.7,6.25); | |
| %\draw [black!40] (4,1) -- (5,4); | |
| %\draw [black!40] (1,3) -- (5,4); | |
| % our little node | |
| \node[shape=circle,fill=purple,scale=0.4] at (6.7,6.25){}; | |
| \end{scope} | |
| \begin{scope}[scale=.28,shift={(26,0)}] | |
| \coordinate (Origin) at (0,0); | |
| \coordinate (XAxisMin) at (-1,0); | |
| \coordinate (XAxisMax) at (10,0); | |
| \coordinate (YAxisMin) at (0,-1); | |
| \coordinate (YAxisMax) at (0,10); | |
| \draw [thin, black!40, <->] (XAxisMin) -- (XAxisMax);% Draw x axis | |
| \draw [thin, black!40,<->] (YAxisMin) -- (YAxisMax);% Draw y axis | |
| %\draw[style=help lines,dashed,black!20] (-5,-5) grid[step=1cm] (5,5); | |
| % basis vectors | |
| \draw (Origin) -- (4,1); | |
| \draw (Origin) -- (1,3); | |
| % extended basis vectors | |
| \draw [black!40] (4,1) -- (5,4); | |
| \draw [black!40] (1,3) -- (5,4); | |
| % our little node | |
| \node[shape=circle,fill=purple!60,scale=0.4] at (6.7,6.25){}; | |
| % our new little node :) | |
| \node[shape=circle,fill=purple,scale=0.4] at (5,4){}; | |
| \node[shape=circle,fill=none,draw=purple,scale=0.8] at (5,4){}; | |
| \end{scope} | |
| \end{tikzpicture} |
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| \begin{tikzpicture} | |
| \tikzstyle{every node}=[draw, shape=circle, ultra thick]; | |
| \node (D) at (2,2) {Alice}; | |
| \node (A) at (0,0) {David}; | |
| \node (B) at (2,0) {Bob}; | |
| \node (C) at (4,0) {Charles}; | |
| \tikzstyle{every node}=[draw,shape=rectangle,solid,fill=white]; | |
| \draw [->,dashed] (D) -- (A) node [above right=10mm] {$m^3 \pmod{N_1}$}; | |
| \draw [->,dashed] (D) -- (B) node [above=15mm] {$m^3 \pmod{N_2}$}; | |
| \draw [->,dashed] (D) -- (C) node [above left=10mm] {$m^3 \pmod{N_3}$}; | |
| \end{tikzpicture} |
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| \begin{tikzpicture} | |
| \begin{scope}[scale=.55,local bounding box=scope1] | |
| \coordinate (Origin) at (0,0); | |
| \coordinate (XAxisMin) at (-5,0); | |
| \coordinate (XAxisMax) at (5,0); | |
| \coordinate (YAxisMin) at (0,-5); | |
| \coordinate (YAxisMax) at (0,5); | |
| \draw [thin, black!40, <->] (XAxisMin) -- (XAxisMax);% Draw x axis | |
| \draw [thin, black!40,<->] (YAxisMin) -- (YAxisMax);% Draw y axis | |
| %\draw[style=help lines,dashed,black!20] (-5,-5) grid[step=1cm] (5,5); | |
| \begin{scope} | |
| \clip (-5,-5) rectangle (5,5); % Clips the picture... | |
| \pgftransformcm{1}{0.6}{0.7}{1}{\pgfpoint{0cm}{0cm}} | |
| % setup the nodes | |
| \foreach \x in {-15,...,15} | |
| \foreach \y in {-15,...,15} | |
| { | |
| \node[shape=circle,fill=black!45,scale=0.35] (\x-\y) at (2*\x,\y+3){}; | |
| } | |
| \end{scope} | |
| % our little node | |
| \node[shape=circle,fill=purple,scale=0.4] at (2.5,3.4){}; | |
| \node[shape=circle,draw=purple,fill=none,scale=0.8] at (2.5,3.4){}; | |
| \end{scope} | |
| \begin{scope}[scale=.55,shift={(12,0)}] | |
| \coordinate (Origin) at (0,0); | |
| \coordinate (XAxisMin) at (-5,0); | |
| \coordinate (XAxisMax) at (5,0); | |
| \coordinate (YAxisMin) at (0,-5); | |
| \coordinate (YAxisMax) at (0,5); | |
| \draw [thin, black!40, <->] (XAxisMin) -- (XAxisMax);% Draw x axis | |
| \draw [thin, black!40,<->] (YAxisMin) -- (YAxisMax);% Draw y axis | |
| %\draw[style=help lines,dashed,black!20] (-5,-5) grid[step=1cm] (5,5); | |
| \begin{scope} | |
| \clip (-5,-5) rectangle (5,5); % Clips the picture... | |
| \pgftransformcm{1}{0.6}{0.7}{1}{\pgfpoint{0cm}{0cm}} | |
| % setup the nodes | |
| \foreach \x in {-15,...,15} | |
| \foreach \y in {-15,...,15} | |
| { | |
| \node[shape=circle,fill=black!45,scale=0.35] (\x-\y) at (2*\x,\y+3){}; | |
| } | |
| \end{scope} | |
| % our little node | |
| \node[shape=circle,fill=purple!60,scale=0.4] at (2.5,3.4){}; | |
| \node[shape=circle,fill=purple,scale=0.4] at (2.1,3){}; | |
| \node[shape=circle,fill=none,draw=purple,scale=0.8] at (2.1,3){}; | |
| \end{scope} | |
| \end{tikzpicture} |
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| \begin{tikzpicture} | |
| \node [above] at (5,10) {\textbf{random basis}}; | |
| \node [above] at (18,10) {\textbf{reduced basis}}; | |
| \draw [lightgray] [<->] (0,5) -- (10,5); | |
| \draw [lightgray] [<->] (5,10) -- (5,0); | |
| \draw [fill,purple,opacity=.4] (9,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (7,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (8,2) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (9,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (5,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (6,2) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (7,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (8,4) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (9,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (3,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (4,2) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (5,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (6,4) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (7,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (8,6) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (9,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (1,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (2,2) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (3,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (4,4) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (5,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (6,6) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (7,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (8,8) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (9,9) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (1,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (2,4) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (3,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (4,6) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (5,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (6,8) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (7,9) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (1,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (2,6) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (3,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (4,8) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (5,9) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (1,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (2,8) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (3,9) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (1,9) circle [radius=0.1]; | |
| % | |
| \draw [thick,black] [->] (11,5) -- (12,5); | |
| \node [above] at (11.5,5) {$_{LLL}$}; | |
| % | |
| \draw [lightgray] [<->] (13,5) -- (23,5); | |
| \draw [lightgray] [<->] (18,10) -- (18,0); | |
| \draw [fill,purple,opacity=.4] (22,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (20,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (21,2) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (22,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (18,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (19,2) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (20,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (21,4) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (22,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (16,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (17,2) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (18,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (19,4) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (20,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (21,6) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (22,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (14,1) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (15,2) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (16,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (17,4) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (18,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (19,6) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (20,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (21,8) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (22,9) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (14,3) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (15,4) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (16,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (17,6) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (18,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (19,8) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (20,9) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (14,5) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (15,6) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (16,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (17,8) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (18,9) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (14,7) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (15,8) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (16,9) circle [radius=0.1]; | |
| \draw [fill,purple,opacity=.4] (14,9) circle [radius=0.1]; | |
| % vectors | |
| \draw [thick,purple] [->] (5,5) -- (7, 9); | |
| \draw [thick,purple] [->] (5,5) -- (6, 8); | |
| \draw [thick,purple] [->] (18,5) -- (19, 4); | |
| \draw [thick,purple] [->] (18,5) -- (19, 6); | |
| \end{tikzpicture} |
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| \begin{tikzpicture} | |
| % main formula | |
| \node[align=center] (main) {$y = g^x \pmod{p}$\\ | |
| $\varphi(p) = p-1 = p_1 \times \cdots \times p_k$}; | |
| % first line | |
| \node (xmodp1) [below left=.9cm and -1.2cm of main, align=left] {$x \pmod{p_1}$}; | |
| \node (dots) [below=1.1cm of main, align=left] {$\cdots$}; | |
| \node (xmodpk) [below right=.9cm and -1.2cm of main, align=left] {$x \pmod{p_k}$}; | |
| % Pohlig Hellman | |
| \node (PH) [above=.2cm of dots, align=left] {Pohlig-Hellman}; | |
| % arrows | |
| \draw (main) edge[out=200,in=90,->] (xmodp1); | |
| \draw (main) edge[out=340,in=90,->] (xmodpk); | |
| % second line | |
| \node (xmodpm1) [below=.9cm of dots, align=left] {$x \pmod{\varphi(p)}$}; | |
| % CRT | |
| \node (CRT) [above=.2cm of xmodpm1, align=left] {CRT}; | |
| % arrows | |
| \draw [->] (xmodp1) -- (xmodpm1); | |
| \draw [->] (xmodpk) -- (xmodpm1); | |
| \end{tikzpicture} |
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| \begin{tikzpicture} | |
| \begin{scope}[scale=.55,local bounding box=scope1] | |
| \coordinate (Origin) at (0,0); | |
| \coordinate (XAxisMin) at (-5,0); | |
| \coordinate (XAxisMax) at (5,0); | |
| \coordinate (YAxisMin) at (0,-5); | |
| \coordinate (YAxisMax) at (0,5); | |
| \draw [thin, black!40, <->] (XAxisMin) -- (XAxisMax);% Draw x axis | |
| \draw [thin, black!40,<->] (YAxisMin) -- (YAxisMax);% Draw y axis | |
| %\draw[style=help lines,dashed,black!20] (-5,-5) grid[step=1cm] (5,5); | |
| \begin{scope} | |
| \clip (-5,-5) rectangle (5,5); % Clips the picture... | |
| \pgftransformcm{1}{0.6}{0.7}{1}{\pgfpoint{0cm}{0cm}} | |
| % setup the nodes | |
| \foreach \x in {-15,...,15} | |
| \foreach \y in {-15,...,15} | |
| { | |
| \node[shape=circle,fill=black!45,scale=0.35] (\x-\y) at (2*\x,\y+3){}; | |
| } | |
| \end{scope} | |
| \end{scope} | |
| \begin{scope}[scale=.55,shift={(12,0)}] | |
| \coordinate (Origin) at (0,0); | |
| \coordinate (XAxisMin) at (-5,0); | |
| \coordinate (XAxisMax) at (5,0); | |
| \coordinate (YAxisMin) at (0,-5); | |
| \coordinate (YAxisMax) at (0,5); | |
| \draw [thin, black!40, <->] (XAxisMin) -- (XAxisMax);% Draw x axis | |
| \draw [thin, black!40,<->] (YAxisMin) -- (YAxisMax);% Draw y axis | |
| \draw [thin, purple,->] (0,0) -- (-.5,.7); | |
| %\draw[style=help lines,dashed,black!20] (-5,-5) grid[step=1cm] (5,5); | |
| \begin{scope} | |
| \clip (-5,-5) rectangle (5,5); % Clips the picture... | |
| \pgftransformcm{1}{0.6}{0.7}{1}{\pgfpoint{0cm}{0cm}} | |
| % setup the nodes | |
| \foreach \x in {-15,...,15} | |
| \foreach \y in {-15,...,15} | |
| { | |
| \node[shape=circle,fill=black!45,scale=0.35] (\x-\y) at (2*\x,\y+3){}; | |
| } | |
| \end{scope} | |
| % our little node | |
| \node[shape=circle,fill=purple,scale=0.35] at (-.6,.8){}; | |
| \end{scope} | |
| \end{tikzpicture} |
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