\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}


\newtheorem{problem}{Problem}
\newtheorem{experiment}[problem]{Experiment}

\numberwithin{problem}{section}



\title{Anton's Crypto Textbook}
\author{Anton }
\date{September 2016}

\begin{document}

\maketitle

\section{Chapter 1}

Some introductory stuff goes here.

\begin{problem}
asdf
\end{problem}
Let's start solving the problem and write it out very carefully and so on and very long text run on sentence.


\begin{experiment}
asdf

\end{experiment}

\section{New section!}

\begin{problem}
new stuff
\end{problem}

\end{document}
