add b&w versions; cleanup

.gitignore

@@ -22,4 +22,5 @@ __pycache__
 # Other
 images/
 spring/ShamirSS-centered.ipynb
-spring/plot_examples.ipynb
+spring/plot_examples.ipynb
+*comments*

packet/README.md

@@ -1,6 +1,6 @@
 # Packet: Cryptographic Secret Sharing
 *[Girls Talk Math Camp 2021](http://gtm.math.umd.edu/virtualcamp2021.html) at UMD*
 
-- **Packet** [[source](main.tex) | [.pdf](main.pdf)]: General outline of the file stolen from [this other GTM packet](https://github.com/Girls-Talk-Math/curriculum/tree/master/RSA-Encryption-Cryptography). 
-- **Answers** [[source](answers.tex) | [.pdf](answers.pdf)]
-- **Jupyter Notebook** [[source](../spring/ShamirSS.ipynb) | [CoLab](https://colab.research.google.com/drive/18NxRFaAb3H65EaUUPwlHN7pQFXYvsy6n?usp=sharing)]: Jupyter notebook for interactive portion; currently links to the spring event version.
+- **[Packet](main.pdf)** ([source](main.tex)). Black-and-white version [here](main-bw.pdf).
+- **[Answers](answers.pdf)** ([source](answers.tex)). Black-and-white version [here](answers-bw.pdf).
+- **[Jupyter Notebook](https://colab.research.google.com/drive/18NxRFaAb3H65EaUUPwlHN7pQFXYvsy6n?usp=sharing)** ([source](../spring/ShamirSS.ipynb)): Jupyter notebook for interactive portion; currently links to the spring event version.

packet/ans/shamir.tex

@@ -44,35 +44,64 @@ \subsection{Polynomials}
         ymax=8.5,
         grid,
     ]
+        \ifbw
+        %%% BLACK-AND-WHITE VERSION %%%
         % part a
-        \node [magenta] (point-a1) at (axis cs: 3,2) {\textbullet};
+        \node (point-a1) at (axis cs: 3,2) {$\star$};
+        \addplot[domain=-1.5:5.5,samples=50,mark=none,dashed]{-2*x+8};
+        \addplot[domain=-1.5:5.5,samples=50,mark=none,dashed]{.33*x+1};
+        % part b
+        \node (point-b1) at (axis cs: 0,0) {$\diamond$};
+        \node (point-b2) at (axis cs: 2,2) {$\diamond$};
+        \addplot[domain=-1.5:5.5,samples=50,mark=none,densely dotted]{x};
+        % part c
+        \node (point-c1) at (axis cs: 1,3) {$\times$};
+        \node (point-c2) at (axis cs: 3,4) {$\times$};
+        \node (point-c3) at (axis cs: 4,5) {$\times$};
+        \addplot[domain=-1.5:5.5,samples=50,mark=none,dashdotted]{.5*x+2.5};
+        \addplot[domain=-1.5:5.5,samples=50,mark=none,dashdotted]{x+1};
+        % part d
+        \node (point-d1) at (axis cs: -1,1) {\textbullet};
+        \node (point-d2) at (axis cs: 0,3) {\textbullet};
+        \node (point-d3) at (axis cs: 2,7) {\textbullet};
+        \addplot[domain=-1.5:5.5,samples=50,mark=none,thick]{2*x+3};
+        \else
+        %%% COLOR VERSION %%%
+        % part a
+        \node (point-a1) [magenta] at (axis cs: 3,2) {\textbullet};
         \addplot[domain=-1.5:5.5,samples=50,mark=none,magenta,dashed]{-2*x+8};
         \addplot[domain=-1.5:5.5,samples=50,mark=none,magenta,dashed]{.33*x+1};
         % part b
         \node [cyan] (point-b1) at (axis cs: 0,0) {\textbullet};
         \node [cyan] (point-b2) at (axis cs: 2,2) {\textbullet};
         \addplot[domain=-1.5:5.5,samples=50,mark=none,cyan,thick]{x};
         % part c
-        \node [green] (point-c1) at (axis cs: 1,3) {\textbullet};
-        \node [green] (point-c2) at (axis cs: 3,4) {\textbullet};
-        \node [green] (point-c3) at (axis cs: 4,5) {\textbullet};
-        \addplot[domain=-1.5:5.5,samples=50,mark=none,green,dashed]{.5*x+2.5};
-        \addplot[domain=-1.5:5.5,samples=50,mark=none,green,dashed]{x+1};
+        \node [orange] (point-c1) at (axis cs: 1,3) {\textbullet};
+        \node [orange] (point-c2) at (axis cs: 3,4) {\textbullet};
+        \node [orange] (point-c3) at (axis cs: 4,5) {\textbullet};
+        \addplot[domain=-1.5:5.5,samples=50,mark=none,orange,dashed]{.5*x+2.5};
+        \addplot[domain=-1.5:5.5,samples=50,mark=none,orange,dashed]{x+1};
         % part d
         \node (point-d1) at (axis cs: -1,1) {\textbullet};
         \node (point-d2) at (axis cs: 0,3) {\textbullet};
         \node (point-d3) at (axis cs: 2,7) {\textbullet};
         \addplot[domain=-1.5:5.5,samples=50,mark=none,thick]{2*x+3};
+        \fi
     \end{axis}
+    % labels
+    \node [below,font=\small,\ifbw\else magenta\fi] at (point-a1) {(a)};
+    \node [font=\small,\ifbw\else cyan\fi] at (5.2,2.7) {(b)};
+    \node [above left,font=\small,\ifbw\else orange\fi] at (point-c2) {(c)};
+    \node [font=\small] at (4.2,6) {(d)};
     \end{tikzpicture}
     \end{center}
 
     \renewcommand{\labelenumi}{(\alph{enumi})} 
     \begin{enumerate}
-        \item No; there are not enough points to define a \emph{unique} degree-1 polynomial, and in fact there are infinitely many degree-1 polynomials passing through this point. (In \textcolor{magenta}{pink} above.)
-        \item Yes; these points uniquely define the polynomial $f(x) = x$. (In \textcolor{cyan}{light blue} above.)
-        \item No; there is no degree-1 polynomial passing through these points because they are not properly aligned. However, they do define a unique degree-2 polynomial. (In \textcolor{green}{green} above.)
-        \item Yes; these points uniquely define the polynomial $f(x) = 2x + 3$. (In black above.)
+        \item No; there are not enough points to define a \emph{unique} degree-1 polynomial, and in fact there are infinitely many degree-1 polynomials passing through this point. \ifbw($\star$ above.)\else(In \textcolor{magenta}{pink} above.)\fi
+        \item Yes; these points uniquely define the polynomial $f(x) = x$. \ifbw($\diamond$ above.)\else(In \textcolor{cyan}{light blue} above.)\fi
+        \item No; there is no degree-1 polynomial passing through these points because they are not properly aligned. However, they do define a unique degree-2 polynomial. \ifbw($\times$ above.)\else(In \textcolor{orange}{orange} above.)\fi
+        \item Yes; these points uniquely define the polynomial $f(x) = 2x + 3$. \ifbw(\textbullet\ above.)\else(In black above.)\fi
     \end{enumerate}
 \end{answer}
 

packet/answers.tex

@@ -1,5 +1,9 @@
 \documentclass[12 pt]{article}
+\newif\ifbw
+\bwfalse
+
 \hbadness=10
+
 \input{src/header.tex}
 
 \def\share{\ensuremath{\mathsf{Share}}}

packet/main.tex

@@ -1,5 +1,9 @@
 \documentclass[12 pt]{article}
-\hbadness=10
+\newif\ifbw
+\bwfalse
+
+\hbadness=200
+
 \input{src/header.tex}
 
 %%% Title and Abstract

packet/src/header.tex

@@ -33,13 +33,14 @@
 %%%% added by NG
 \usetikzlibrary{shapes,backgrounds,decorations,patterns}
 \usepackage{pgfplots}
+\pgfplotsset{compat=1.17}
 \usepackage{xurl}
 \usepackage{pifont}% http://ctan.org/pkg/pifont
 \usepackage{colortbl}
 \newcommand{\cmark}{\ding{51}}%
 \newcommand{\xmark}{\ding{55}}%
 % externalize the figures
-% \usepgfplotslibrary{external
+% \usepgfplotslibrary{external}
 % \tikzexternalize
 
 % Crypto commands
@@ -62,7 +63,7 @@
 %%% Exercises & Examples
 \newcounter{exercise}[section]
 \newenvironment{exercise}{\refstepcounter{exercise}\par\bigskip \begin{quotation}{}{\leftmargin .25in\rightmargin .25in}
-    \noindent \textbf{Exercise~\thesection.\theexercise }  \rmfamily}{\end{quotation}\par\bigskip}
+    \noindent \textbf{Exercise~\thesection.\theexercise }  \rmfamily}{\end{quotation}\hfill\par\bigskip}
 \newcommand{\exref}[1]{\hyperref[#1]{\thesection.\ref*{#1}}}
 
 \newenvironment{bonus}{\refstepcounter{exercise}\par\bigskip \begin{quotation}{}{\leftmargin .25in\rightmargin .25in}

packet/src/probability.tex

@@ -27,7 +27,7 @@ \section{Probability and Randomness}\label{sec:prob}
         \footnotetext[2]{
             \url{https://www.statista.com/statistics/236550/percentage-of-us-population-that-own-a-iphone-smartphone/}
         }
-        \item The distribution over the outcomes of a dice roll $\{1,2,3,4,5,6\}$
+        \item The distribution over the outcomes $\{1,2,3,4,5,6\}$ of a dice roll
         is $\{\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6}\}$.
     \end{enumerate}
 \end{example}
@@ -38,8 +38,7 @@ \section{Probability and Randomness}\label{sec:prob}
     \renewcommand{\labelenumi}{(\alph{enumi})} 
     \begin{enumerate}
         \item Card drawn from a shuffled deck.
-        \item Whether or not a student is registered for classes at a 2000-person high school 
-        where all but 100 students register for classes every year.
+        \item Whether or not a student is registered for classes at a 2000-person high school where all but 100 students register for classes every year.
     \end{enumerate}
 \end{exercise}
 
@@ -117,19 +116,17 @@ \section{Probability and Randomness}\label{sec:prob}
 would mean that there's some other event that could happen instead, so the sample space
 is incomplete.
 
-The pie charts below illustrate this idea. On the left is the probability 
-distribution of a coin toss; on the right, the probability distribution 
-of a dice roll. Notice that in both cases, the probabilities sum to 1.
-
-\begin{figure}[h]
-    \includegraphics[width=.5\linewidth]{imgs/coin-pie.png}
-    \includegraphics[width=.5\linewidth]{imgs/die-pie.png}
-    % \caption{Left: probability distribution of a coin toss. Right: 
-    % probability distribution of a dice roll. Probabilities always 
-    % sum to 1.}
+\begin{figure}[hb]
+    \centering
+    \includegraphics[width=.45\linewidth]{imgs/coin-pie.png}
+    \includegraphics[width=.45\linewidth]{imgs/die-pie.png}
     \label{fig:pies}
   \end{figure}
 
+The pie charts above illustrate this idea. On the left is the probability 
+distribution of a coin toss; on the right, the probability distribution 
+of a dice roll. Notice that in both cases, the probabilities sum to 1.
+
 When two events are not mutually exclusive, however, we can't add 
 their probabilities. For example, what's the probability of rolling a 
 multiple of 2 or a multiple of 3? These are not mutually exclusive
@@ -150,7 +147,7 @@ \section{Probability and Randomness}\label{sec:prob}
 
 where $d$ is the random variable representing the outcome of the die roll.
 
-\hfill\\
+\bigskip
 
 Conditional probability is the probability that something occurs 
 \emph{assuming that another event has already happened}. This is written with the symbol 
@@ -350,7 +347,7 @@ \section{Probability and Randomness}\label{sec:prob}
             \end{tikzpicture}
             \end{center}
 
-            Now exactly one number, 11, is in both $A$ and $B$, so $\Pr[A \text{ and } 
+            Now exactly one number, 11, is in both $A$ and $B$, so $\Pr[A \text{ and }\allowbreak 
             B] = \frac{1}{16}$. Thus $\Pr[A \mid B] = \frac{1}{16} \div \frac{1}{2}
             = \frac{1}{8}$. Visually, we notice that $A$ in fact occupies one-eighth
             of $B$'s space.

packet/src/shamir.tex

@@ -169,20 +169,23 @@ \subsubsection{Uniqueness}\label{sec:unique}
 \addplot[domain=-1:5,samples=50,mark=none,thick]{x^2-4*x+3};
 % other degree-2 polys through these points
 %%% BW VERSION %%%%%%
-% \addplot[domain=-1:5,samples=50,mark=none,dotted]{-(x^2-4*x+3)+6};
-% \addplot[domain=-1:5,samples=50,mark=none,dotted]{x^2/4-x+3};
+\ifbw
+\addplot[domain=-1:5,samples=50,mark=none,dashed]{-(x^2-4*x+3)+6};
+\addplot[domain=-1:5,samples=50,mark=none,dashed]{x^2/4-x+3};
+\else
 %%% COLOR VERSION %%%%%
 \addplot[domain=-1:5,samples=50,mark=none,magenta]{-(x^2-4*x+3)+6};
 \addplot[domain=-1:5,samples=50,mark=none,cyan]{x^2/4-x+3};
+\fi
 % points (on top)
 \node (point1) at (axis cs: 0,3) {\textbullet};
 \node [above right,font=\small] at (point1) {$(0,3)$};
 \node (point2) at (axis cs: 4,3) {\textbullet};
 \node [above left,font=\small] at (point2) {$(4,3)$};
 \end{axis}
 \node [font=\small] at (8,5) {$f(x)=x^2-4x+3$};
-\node [font=\small,magenta] at (-1,1.3) {$f(x)=-x^2+4x+3$};
-\node [font=\small,cyan] at (8,3.3) {$f(x)=\frac{1}{4}x^2-x+3$};
+\node [font=\small,\ifbw\else magenta\fi] at (-1,1.3) {$f(x)=-x^2+4x+3$};
+\node [font=\small,\ifbw\else cyan\fi] at (8,3.3) {$f(x)=\frac{1}{4}x^2-x+3$};
 \end{tikzpicture}
 \end{center}
 
@@ -313,7 +316,7 @@ \subsubsection{Uniqueness}\label{sec:unique}
         \item $\sum_{i=1}^5 2i$
         \item $\sum_{i=1}^5 1$
         \item $\sum_{i=0}^4 x_i$ where $x_i$ means the $i$th 
-        elements of the set $\{1, 5, -3, 0, 8\}$ and the numbering
+        elements of the set $\{1, 5, -3,\allowbreak 0, 8\}$ and the numbering
         starts at 0 (that is, $x_0=1$).
         \item $\sum_{i=0}^2 x_i$ for the same set.
     \end{enumerate}
@@ -323,8 +326,8 @@ \subsubsection{Uniqueness}\label{sec:unique}
     Repeat the previous exercise, substituting $\prod$ for $\sum$.
 \end{bonus}
 
-Now, back to Lagrange interpolation. We start with a set of points $(x_0, y_0), 
-\ldots,\allowbreak (x_m, y_m)$. For each point $(x_i, y_i)$, we compute the 
+Now, back to Lagrange interpolation. We start with a set of points $(x_0, y_0),\allowbreak
+\ldots, (x_m, y_m)$. For each point $(x_i, y_i)$, we compute the 
 expression $\ell_i(x)$. For instance, for $i=2$, it will be of the form
 
 \newcommand{\cyan}[1]{\textcolor{cyan}{#1}}
@@ -414,7 +417,8 @@ \subsubsection{Uniqueness}\label{sec:unique}
 \end{align*}
 
 Just as we deduced above! 
-\hfill\\
+
+\bigskip
 
 To return to our main task of computing $P(x)$, let's plug the expressions 
 for $\ell_0$ and $\ell_1$ back into the summation:
@@ -493,7 +497,7 @@ \subsubsection{Uniqueness}\label{sec:unique}
 
 \begin{bonus}
     Use Lagrange interpolation to find the unique degree-2 
-    polynomial through the points $\{(-1,-16),(1,-2),(2,14)\}$.
+    polynomial through the points $\{(-1,-16),(1,-2),\allowbreak (2,14)\}$.
 \end{bonus}
 
 \subsection{Sharing Secrets Using Polynomials}
@@ -519,14 +523,14 @@ \subsection{Sharing Secrets Using Polynomials}
 \end{definition}
 
 Now we're ready to put everything we've learned together and define 
-Shamir's secret sharing scheme\footnotemark.
+\allowbreak Shamir's secret sharing scheme\footnotemark.
 \footnotetext{Adi Shamir introduced this scheme in a short 1979 
 paper entitled ``How to share a secret''\cite{shamir1979share}.
 The paper is only two pages long, so if you're feeling adventurous 
 you could have a go at it! You can find it online at 
 \url{http://web.mit.edu/6.857/OldStuff/Fall03/ref/Shamir-HowToShareASecret.pdf}.}
 
-\begin{figure}[h!]
+\begin{figure}[ht]
 \begin{pchstack}[center]
 \fbox{%
 \procedure{$\share(s)$}{%
@@ -593,8 +597,13 @@ \subsection{Sharing Secrets Using Polynomials}
 \node (share1) at (axis cs: 1,17) {\textbullet};
 \node (share2) at (axis cs: 2,22) {\textbullet};
 \node (share3) at (axis cs: 3,27) {\textbullet};
-\node [magenta] (s) at (axis cs: 0,12) {\textbullet};
+\node [\ifbw\else magenta\fi] (s) at (axis cs: 0,12) {\textbullet};
+\ifbw
+\setlength{\fboxsep}{.1\fboxsep}
+\node [right,font=\small] at (s) {$\boxed{s=12}$};
+\else
 \node [right,magenta,font=\small] at (s) {$s=12$};
+\fi
 \end{axis}
 \node [right,font=\small] at (share1) {$s_1=(1,17)$};
 \node [right,font=\small] at (share2) {$s_2=(2,22)$};