zkproofs2020.tex

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 \newcommand{\prot}{\mathbf{P}}
\newcommand{\adv}{\ensuremath{\mathcal A}}
\newcommand{\aggdeg}[1]{\mathfrak{d}(#1)}
\renewcommand{\deg}{\mathrm{deg}}
\newcommand{\xor}{\ensuremath{\oplus}}
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 \newcommand{\polysofdeg}[1]{\F_{< #1}[X]}
 \newcommand{\polys}{\F[X]}
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\newcommand{\ideal}{\mathbf{I}}
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\title{\large{Ranged Polynomial Protocols}}    % Enter your title between curly braces
\author{\small{Ariel Gabizon}\\                 % Enter your name between curly braces
\tt{\footnotesize{\textbf{Aztec}\\ (Based on work with Zachary J. Williamson)                                        } }      }% Enter your institute name between curly braces
\date{}                    % Enter the date or \today between curly braces
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\begin{document}
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\begin{frame}
\frametitle{Divisors on $k(X)$}   % insert frame title between curly braces

% \textbf{Preprocessing/inputs:} Predefined polynomials $g_1,\ldots,g_t\in \polysofdeg{d}$\\
% \textbf{Range:} $H\subset\F$.\\ \pause
% \vspace{0.4in}
% \textbf{Protocol:}
$P\defeq = k\cup\infty$. \\ \pause
A divisor is
\[D=\sum_{a\in P}{d_a \cdot [P]\]
where $d_a\in\mathbb{Z}$ is non-zero for finitely many $a$.

%  \begin{itemize}
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% \item  
% \item At end, $\ver$ asks $\ideal$ if some identity holds between $\set{f_1,\ldots,f_\ell,g_1,\ldots,g_t}$   \textbf{\textit{on $H$}}. 
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