\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}

\usepackage[utf8]{inputenc} % this is needed for umlauts
\usepackage[ngerman]{babel} % this is needed for umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
\usepackage{braket} % needed for \Set
\usepackage{algorithm,algpseudocode}

\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing,calc}
\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}
\newcommand*{\AddNote}[4]{%
    \begin{tikzpicture}[overlay, remember picture]
        \draw [decoration={brace,amplitude=0.5em},decorate,very thick]
            ($(#3)!(#1.north)!($(#3)-(0,1)$)$) --  
            ($(#3)!(#2.south)!($(#3)-(0,1)$)$)
                node [align=center, text width=2.5cm, pos=0.5, anchor=west] {#4};
    \end{tikzpicture}
}%

\begin{document}
\begin{preview}
    \begin{algorithm}[H]
        \begin{algorithmic}
            \Require $p \in \mathbb{P}, a \in \mathbb{Z}, p \geq 3$
            \If{$a \geq p$ or $a < 0$}\Comment{Regel (III)}
				\State \Return $\Call{CalculateLegendre}{a \mod p, p}$ \Comment{nun: $a \in [0, \dots, p-1]$}
			\ElsIf{$a \equiv 0 \mod p$} \Comment{Null-Fall}
				\State \Return 0
			\ElsIf{$a \equiv 1 \mod p$} \Comment{Eins-Fall}
				\State \Return 1
			\ElsIf{$a \equiv -1 \mod p$} \Comment{Regel (VI)}
				\If{$p \equiv 1 \mod 4$}
					\State \Return 1
				\Else
					\State \Return -1
				\EndIf
			\ElsIf{!$\Call{isPrime}{|a|}$} \Comment{Regel (II)}
				\State $p_1, p_2, \dots, p_n \gets \Call{Faktorisiere}{a}$
				\State \Return $\prod_{i=1}^n \Call{CalculateLegendre}{p_i, a}$
			\ElsIf{$p == 3$} \Comment{Regel (IV)}
				\State $t \gets p \mod 3$
				\If{$t == 2$}
					\State $t \gets -1$
				\EndIf
				\State \Return $t$
			\Else
				\State \Return $a^\frac{p-1}{2} \mod p$
			\EndIf
        \end{algorithmic}
    \caption{Calculate Legendre-Symbol}
    %\AddNote{top}{bottom}{right}{calclulate $p$ such that: $b^p \leq Z < b^{p+1}$}  %\tikzmark{top},\tikzmark{right},\tikzmark{bottom}
    \label{alg:euclidBaseTransformation}
    \end{algorithm}
\end{preview}
\end{document}