1149 lines
37 KiB
TeX
1149 lines
37 KiB
TeX
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\newcommand{\Section}[2]{\section[#1\newline\scriptsize{#2}]{#1}}
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\input{definitions}
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\title{Are you old enough to buy this?}
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\subtitle{Zero-Knowledge Age Restriction for GNU Taler}
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\author{Özgür Kesim}
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\institute{FU Berlin}
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\date{December 29, 2022}
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\titlegraphic{\centering\includegraphics[width=0.5\textwidth]{images/hip2022.jpg}}
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\begin{document}
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%\justifying
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\begin{frame}
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\titlepage
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\end{frame}
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\section*{Prolog}%{Who am I, what do I want and who pays for all this?}
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\begin{frame}{Who am I}
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Özgür Kesim,
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\begin{itemize}
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\item security consultant for 20+ years,
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\item PhD candidate at FU Berlin,
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\item member of GNU Taler dev-team.
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\end{itemize}
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\vfill
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\url{oec-taler@kesim.org} \hfill \url{@oec@mathstodon.xyz} \hfill
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\end{frame}
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\begin{frame}{What to expect}
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\small
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\begin{description}
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\item<1->[Deliverable]~\\
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Present a solution to age restriction and its integration in GNU Taler.
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\vfill
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\item<2->[Side-Channel]~\\
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Show concepts from cryptography by example:
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Zero-Knowledge protocol, Security Game and Security Proof
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This will be technical.
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\vfill
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\item<3->[Non-goals]~\\
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\begin{itemize}
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\item[] \underline{Rigorous} introduction into GNU Taler
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\item[] Demos
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\end{itemize}
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\end{description}
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\end{frame}
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\begin{frame}{Sponsors}
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\centering\begin{columns}[T]
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\column{0.5\textwidth}
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\centering NGI Pointer program of the European Commission\\[2em]
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\centering\includegraphics[width=0.7\textwidth]{images/ngi-ap3.png}
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\column{0.5\textwidth}
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\centering Project \textit{Concrete Contracts} in the
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\textit{KMU-innovativ} programm\\[2em]
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\centering\includegraphics[width=0.9\textwidth]{images/bmbf-english.jpg}
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\end{columns}
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\end{frame}
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\begin{frame}{Chapters}
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\tableofcontents[pausesections,hideallsubsections]
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\end{frame}
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\section[Introduction\newline\scriptsize Age Restriction in E-commerce]{Introduction}
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\begin{frame}{Youth protection}
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Broad consensus in society about the necessity to protect minors from
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harmful content.
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\vfill
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Also wanted from policy makers:\\[1em]
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\begin{quote}
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11. Member states should encourage the \textbf{use of
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conditional access tools} by content and service providers in
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relation to content harmful to minors, \textbf{such as
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age-verification systems}, ...
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\end{quote}
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\tiny
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From the
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\href{https://rm.coe.int/CoERMPublicCommonSearchServices/DisplayDCTMContent?documentId=0900001680645b44}
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{\textit{Recommendation Rec (2001) 8 of the Committee of
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Ministers to member states on self-regulation concerning cyber
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content}} of the Council of Europe.
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\end{frame}
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\begin{frame}{Age restriction in E-commerce}
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\begin{description}[<+->]
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\item[Problem:]~\\[1em]
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Verification of minimum age requirements in e-commerce.\\[2em]
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\item[Common solutions:]
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\begin{tabular}{l<{\onslide<3->}c<{\onslide<4->}cr<{\onslide}}
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& \blue{Privacy} & \tikzmark{topau} \blue{Ext. authority}& \\[\medskipamount]
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1. ID Verification & bad & required & \\[\medskipamount]
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2. Restricted Accounts & bad & required & \\[\medskipamount]
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3. Attribute-based & good & required &\tikzmark{bottomau} \\[\medskipamount]
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\end{tabular}
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\end{description}
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\uncover<5->{
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\begin{tikzpicture}[overlay,remember picture]
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\draw[orange,thick,rounded corners]
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($(pic cs:topau) +(0,0.5)$) rectangle ($(pic cs:bottomau) -(0.3, 0.2)$);
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\end{tikzpicture}
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\begin{center}
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\bf Principle of subsidiarity is ignored
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\end{center}
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}
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\end{frame}
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\begin{frame}{Principle of Subsidiarity}
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\begin{center}\large
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Functions of government\\
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---such as granting and restricting rights---\\
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should be performed\\
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{\it at the lowest level of authority possible},\\
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as long as they can be performed {\it adequately}.
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\end{center}
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\vfill
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\uncover<2->{
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For age-restriction, the lowest level of authority is:\\
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\begin{center}\Large
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Parents, guardians and caretakers
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\end{center}
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}
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\end{frame}
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\begin{frame}{Our goal}
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A design and implementation of an age restriction scheme\\
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with the following properties:
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\pause
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\begin{enumerate}[<+->]
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\item It ties age restriction to the \textbf{ability to pay} (not to ID's),
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\item maintains the \textbf{anonymity of buyers},
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\item maintains \textbf{unlinkability of transactions},
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\item aligns with the \textbf{principle of subsidiarity},
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\item is \textbf{practical and efficient}.
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\end{enumerate}
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\end{frame}
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\begin{frame}{Teaser}
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\centering \includegraphics[height=0.9\textheight]{images/wallet-age.png}
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\end{frame}
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\Section{The quest for a solution to age restriction}{A journey through cryptic territory}
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\begin{frame}{Basic assumption and ideas}
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\small
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Assumption: Bank accounts are under control of adults/guardians.
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\vfill
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Sketch of scheme, independent of payment service protocol:
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\begin{columns}
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\column{7cm}
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\begin{enumerate}
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\item<2-> \textit{Guardians} \textbf{commit} to a maximum age
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\item<4-> \tikzmark{sstart}\textit{Minors} \textbf{attest} their adequate age
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\item<6-> \textit{Merchants} \textbf{verify} the attestations
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\item<7-> \textit{Minors} \textbf{derive} age commitments from existing ones
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\item<9-> \textit{Exchanges} \textbf{compare} the derived age commitments
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\item<10-> \tikzmark{send}{\large \texttt{GOTO}} 2.
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\begin{tikzpicture}[overlay, remember picture]
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\draw[line width=1pt,->]
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([shift=({-6mm, 1mm})]pic cs:send) to
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([shift=({-1cm, 1mm})]pic cs:send) to
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([shift=({-1cm, 1mm})]pic cs:sstart) to
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([shift=({-6mm, 1mm})]pic cs:sstart);
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\end{tikzpicture}
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\end{enumerate}
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\column{4.5cm}
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\begin{center}
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\fontsize{7pt}{7pt}\selectfont
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\begin{tikzpicture}[scale=.5]
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\uncover<2->{
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\node[circle,minimum size=15pt,fill=blue!15] at (140:3) (Guardian) {$\Guardian$};
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\draw[->] (Guardian) to [out=50,in=130, loop] node[above]
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{$\Commit$} (Guardian);
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}
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\uncover<3->{
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\node[circle,minimum size=15pt,fill=black!15] at ( 0:0) (Client) {$\Child$};
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\draw[,|->] (Guardian) to node[above,sloped,align=left]
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{{\scriptsize }} (Client);
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}
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\uncover<4->{
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\draw[->,blue] (Client) to [out=-125,in=-190, loop] node[below,left]
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{\blue{$\Attest$}} (Client);
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}
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\uncover<5->{
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\node[circle,minimum size=15pt,fill=black!15] at ( 0:4) (Merchant) {$\Merchant$};
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\draw[blue,|->] (Client) to node[sloped, above]
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{\blue{\scriptsize }} (Merchant);
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}
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\uncover<6->{
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\draw[->,blue] (Merchant) to [out=50,in=130, loop] node[above]
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{\blue{$\Verify$}} (Merchant);
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}
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\uncover<7->{
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\draw[->,orange] (Client) to [out=-35,in=-100, loop] node[below]
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{\orange{$\Derive$}} (Client);
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}
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\uncover<8->{
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\node[circle,minimum size=15pt,fill=black!15] at ( 60:4) (Exchange) {$\Exchange$};
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\draw[orange,|->] (Client) to node[sloped,above,align=left]
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{\orange{\scriptsize }} (Exchange);
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}
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\uncover<9->{
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\draw[->,orange] (Exchange) to [out=50,in=130, loop] node[above]
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{\orange{$\Compare$}} (Exchange);
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}
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\end{tikzpicture}
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\end{center}
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\end{columns}
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\end{frame}
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\begin{frame}{Specification of the Function Signatures}
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\small
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Searching for functions \uncover<2->{with the following signatures}
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\begin{align*}
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&\bf \Commit\uncover<2->{:
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&(\age, \omega) &\mapsto (\commitment, \pruf)
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&\scriptstyle \N_\Age \times \Omega &\scriptstyle \to \Commitments\times\Proofs,
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}
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\\
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%FIXME: This is how Attest was defined in the orignal paper (_with_) commitment!
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%&\bf \Attest\uncover<3->{:
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% &(\minage, \commitment, \pruf) &\mapsto \attest
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% &\scriptstyle \N_\Age\times\Commitments\times\Proofs &\scriptstyle \to \Attests \cup \{\Nil\},
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% }
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%\\
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&\bf \Attest\uncover<3->{:
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&(\minage, \pruf) &\mapsto \attest
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&\scriptstyle \N_\Age\times\Proofs &\scriptstyle \to \Attests \cup \{\Nil\},
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}
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\\
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&\bf \Verify\uncover<4->{:
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&(\minage, \commitment, \attest) &\mapsto b
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&\scriptstyle \N_\Age\times\Commitments\times\Attests &\scriptstyle \to \Z_2,
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}
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\\
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&\bf \Derive\uncover<5->{:
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&(\commitment, \pruf, \omega) &\mapsto (\commitment', \pruf', \blinding)
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&\scriptstyle \Commitments\times\Proofs\times\Omega &\scriptstyle \to \Commitments\times\Proofs\times\Blindings,
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}
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\\
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&\bf \Compare\uncover<6->{:
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&(\commitment, \commitment', \blinding) &\mapsto b
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&\scriptstyle \Commitments\times\Commitments\times\Blindings &\scriptstyle \to \Z_2,
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}
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\end{align*}
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\uncover<7->{
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with $\Omega, \Proofs, \Commitments, \Attests, \Blindings$
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sufficiently large sets.\\[1em]
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}
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%\uncover<8->{
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% The blindings $\beta$ ensure that only the Exchange can compare commitments.\\[1em]
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%}
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\uncover<8->{
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We will define basic and security requirements later.\\[1em]
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}
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\scriptsize
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\uncover<2->{
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Mnemonics:\\
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$\Commitments=$ \textit{c$\Commitments$mmitments},
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$\commitment=$ \textit{Q-mitment} (commitment),
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$\Proofs=$ \textit{$\Proofs$roofs},
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}
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\uncover<3->{
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$\pruf=$ \textit{$\pruf$roof},\\
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$\Attests=$ \textit{a$\Attests$testations},
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$\attest=$ \textit{a$\attest$testation},
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}
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\uncover<5->{
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$\Blindings=$ \textit{$\Blindings$lindings},
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$\blinding=$ \textit{$\blinding$linding}.
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}
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\end{frame}
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\begin{frame}{Naïve scheme}
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\begin{center}
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\begin{tikzpicture}[scale=.8]
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\node[circle,minimum size=20pt,fill=blue!15] at (140:3) (Guardian) {$\Guardian$};
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\node[circle,minimum size=20pt,fill=black!15] at ( 0:0) (Client) {$\Child$};
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\node[circle,minimum size=20pt,fill=black!15] at ( 60:4) (Exchange) {$\Exchange$};
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\node[circle,minimum size=20pt,fill=black!15] at ( 0:4) (Merchant) {$\Merchant$};
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\draw[->] (Guardian) to [out=50,in=130, loop] node[above]
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{$\Commit$} (Guardian);
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\draw[->,blue] (Client) to [out=-125,in=-190, loop] node[below,left]
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{\blue{$\Attest$}} (Client);
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\draw[->,blue] (Merchant) to [out=50,in=130, loop] node[above]
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{\blue{$\Verify$}} (Merchant);
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\draw[->,orange] (Client) to [out=-35,in=-100, loop] node[below]
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{\orange{$\Derive$}} (Client);
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\draw[->,orange] (Exchange) to [out=50,in=130, loop] node[above]
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{\orange{$\Compare$}} (Exchange);
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\draw[,|->] (Guardian) to node[above,sloped,align=left]
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{\scriptsize ($\commitment$, $\pruf_\age$)} (Client);
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\draw[blue,|->] (Client) to node[sloped, above]
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{\blue{\scriptsize($\minage$, $\commitment$, $\attest$) }} (Merchant);
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\draw[orange,|->] (Client) to node[sloped,above,align=left]
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{\orange{\scriptsize($\commitment$, $\commitment'$, $\beta$) }} (Exchange);
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\end{tikzpicture}
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\end{center}
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% \pause{Why should $\Merchant$ trust those $\commitment$? Will solve later.
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% \tiny (Hint: blind signature from $\Exchange$)}
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\end{frame}
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\begin{frame}{Problem of unlinkability}
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\begin{columns}
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\column{3cm}
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\begin{center}
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\fontsize{8pt}{9pt}\selectfont
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\begin{tikzpicture}[scale=.65]
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\node[circle,minimum size=20pt,fill=black!15] at ( 60:4) (Exchange) {$\Exchange$};
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\node[circle,minimum size=20pt,fill=black!15] at ( 0:0) (Client) {$\Child$};
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\draw[->,orange] (Client) to [out=-35,in=-100, loop] node[below]
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{\orange{$\footnotesize \Derive()$}} (Client);
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\draw[->,orange] (Exchange) to [out=50,in=130, loop] node[above]
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{\orange{$\footnotesize \Compare()$}} (Exchange);
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\draw[orange,|->] (Client) to node[sloped,above,align=left]
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{\orange{\tiny \uncover<2->{$(\commitment_i,\commitment_{i+1})$}}} (Exchange);
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\end{tikzpicture}
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\end{center}
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\column{9cm}
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Simple use of $\Derive()$ and $\Compare()$ is problematic.
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\pause
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\begin{itemize}[<+->]
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\item Calling $\Derive()$ iteratively generates sequence
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$(\commitment_0, \commitment_1, \dots)$ of commitments.
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\item Exchange calls $\Compare(\commitment_i, \commitment_{i+1},~.~)$
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\item[$\implies$]Exchange identifies sequence
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\item[$\implies$]{\bf Unlinkability broken}
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\end{itemize}
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\end{columns}
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\end{frame}
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\begin{frame}{Achieving Unlinkability}
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Given $\Derive()$ and $\Compare()$, define the Zero-Knowledge-protocol
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\orange{$\DeriveCompare$} as follows (sketch):
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\uncover<2->{
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\small
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Let $\kappa \in \N$ (say: $\kappa = 3$)
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\begin{itemize}[<+->]
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\item[$\Child$:]
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\begin{enumerate}
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\item generates $(\commitment_1,\dots,\commitment_\kappa)$
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and $(\beta_1,\dots,\beta_\kappa)$ from $\commitment_0$\\
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by calling $\kappa$ times $\Derive(\commitment_0, \pruf_0, \omega_i)$
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\item calculates $h_0:=H\left(H(\commitment_1, \beta_1)\parallel \dots\parallel H(\commitment_\kappa, \beta_\kappa)\right)$
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\item sends $\commitment_0$ and $h_0$ to $\Exchange$
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\end{enumerate}
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\item[$\Exchange$:]
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\begin{enumerate}
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\item[4.] saves $\commitment_0$ and $h_0$ and sends $\Child$ random $\gamma \in \{1,\dots,\kappa\}$
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\end{enumerate}
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\item[$\Child$:]
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\begin{enumerate}
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\item[5.] reveals $h_\gamma:=H(\commitment_\gamma, \beta_\gamma)$ and all $(\commitment_i, \beta_i)$, except $(\commitment_\gamma, \beta_\gamma)$
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\end{enumerate}
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\item[$\Exchange$:]
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\begin{enumerate}
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\item[6.] compares $h_0$ and
|
|
$H\left(H(\commitment_1, \beta_1)\parallel ...\parallel h_\gamma\parallel ...\parallel H(\commitment_\kappa, \beta_\kappa)\right)$
|
|
\item[7.] evaluates $\Compare(\commitment_0, \commitment_i, \beta_i)$ for all $i \neq \gamma$.
|
|
\end{enumerate}
|
|
\end{itemize}
|
|
\pause
|
|
If all steps succeed, $\commitment_\gamma$ is the new commitment.
|
|
}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Achieving Unlinkability}%{Certainty trade-off}
|
|
|
|
With \orange{$\DeriveCompare$}
|
|
\begin{itemize}
|
|
\item $\Exchange$ learns nothing about $\commitment_\gamma$ or $H(\commitment_\gamma)$,
|
|
\item trusts outcome with $\frac{\kappa-1}{\kappa}$ certainty,
|
|
\item i.e. $\Child$ has $\frac{1}{\kappa}$ chance to cheat.
|
|
\item<2->[$\implies$] \textbf{Gives us unlinkability at the price of (adjustable) uncertainty!}
|
|
\end{itemize}
|
|
|
|
\vfill
|
|
\uncover<3->{Notes:
|
|
\begin{itemize}
|
|
\item similar to the cut\&choose {\it refresh} protocol in GNU Taler
|
|
\item still need to define $\Derive()$ and $\Compare()$.
|
|
\end{itemize}
|
|
}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Refined scheme}
|
|
\begin{center}
|
|
\begin{tikzpicture}[scale=.8]
|
|
\node[circle,minimum size=25pt,fill=blue!15] at (130:3) (Guardian) {$\Guardian$};
|
|
\node[circle,minimum size=25pt,fill=black!15] at ( 0:0) (Client) {$\Child$};
|
|
\node[circle,minimum size=25pt,fill=black!15] at ( 0:5) (Merchant) {$\Merchant$};
|
|
\node[circle,minimum size=25pt,fill=black!15] at ( 60:5) (Exchange) {$\Exchange$};
|
|
|
|
\uncover<2-3,8->{
|
|
\draw[->] (Guardian) to [out=150,in=70, loop] node[above]
|
|
{$\Commit(\age)$} (Guardian);
|
|
}
|
|
\uncover<3,8->{
|
|
\draw[->] (Guardian) to node[below,sloped]
|
|
{($\commitment$, $\pruf_\age$)} (Client);
|
|
}
|
|
|
|
\uncover<4-6,8->{
|
|
\draw[->,blue] (Client) to [out=-50,in=-130, loop] node[below]
|
|
% FIXME: This is in the original paper:
|
|
% {\blue{$\Attest(\minage, \commitment, \pruf_{\age})$}} (Client);
|
|
{\blue{$\Attest(\minage, \pruf_{\age})$}} (Client);
|
|
}
|
|
\uncover<5-6,8->{
|
|
\draw[blue,->] (Client) to node[sloped, below]
|
|
{\blue{$(\attest_\minage, \commitment)$}} (Merchant);
|
|
}
|
|
\uncover<6,8->{
|
|
\draw[->,blue] (Merchant) to [out=-50,in=-130, loop] node[below]
|
|
{\blue{$\Verify(\minage, \commitment, \attest_{\minage})$}} (Merchant);
|
|
}
|
|
\uncover<7,8->{
|
|
\draw[orange,<->] (Client) to
|
|
node[sloped,below,align=center] {\orange{$\commitment \mapsto \commitment_\gamma$}}
|
|
node[sloped,above,align=center] {\orange{$\DeriveCompare$}} (Exchange);
|
|
}
|
|
|
|
\end{tikzpicture}
|
|
\end{center}
|
|
\end{frame}
|
|
|
|
|
|
\begin{frame}{Sensible solutions}
|
|
Quest for functions should lead to \textit{sensible} solutions.
|
|
|
|
\pause
|
|
F. e. $\Verify()$ should not simply always return \texttt{true}.
|
|
|
|
\pause
|
|
We need more requirements.
|
|
\end{frame}
|
|
|
|
% \begin{frame}{Achieving Unlinkability}
|
|
% \scriptsize
|
|
% $\DeriveCompare : \Commitments\times\Proofs\times\Omega \to \{0,1\}$\\
|
|
% \vfill
|
|
% $\DeriveCompare(\commitment, \pruf, \omega) =$
|
|
% \begin{itemize}
|
|
% \it
|
|
% \itemsep0.5em
|
|
% \item[$\Child$:]
|
|
% \begin{enumerate}
|
|
% \scriptsize
|
|
% \itemsep0.3em
|
|
% \item for all $i \in \{1,\dots,\kappa\}:
|
|
% (\commitment_i,\pruf_i,\beta_i) \leftarrow \Derive(\commitment, \pruf, \omega + i)$
|
|
% \item $h \leftarrow \Hash\big(\Hash(\commitment_1,\beta_1)\parallel\dots\parallel\Hash(\commitment_\kappa,\beta_\kappa) \big)$
|
|
% \item send $(\commitment, h)$ to $\Exchange$
|
|
% \end{enumerate}
|
|
% \item[$\Exchange$:]
|
|
% \begin{enumerate}
|
|
% \setcounter{enumi}{4}
|
|
% \scriptsize
|
|
% \itemsep0.3em
|
|
% \item save $(\commitment, h)$ \label{st:hash}
|
|
% \item $\gamma \drawfrom \{1,\dots ,\kappa\}$
|
|
% \item send $\gamma$ to $\Child$
|
|
% \end{enumerate}
|
|
% \item[$\Child$:]
|
|
% \begin{enumerate}
|
|
% \setcounter{enumi}{7}
|
|
%
|
|
% \scriptsize
|
|
% \itemsep0.3em
|
|
% \item $h'_\gamma \leftarrow \Hash(\commitment_\gamma, \beta_\gamma)$
|
|
% \item $\mathbf{E}_\gamma \leftarrow \big[(\commitment_1,\beta_1),\dots,
|
|
% (\commitment_{\gamma-1}, \beta_{\gamma-1}),
|
|
% \Nil,
|
|
% (\commitment_{\gamma+1}, \beta_{\gamma+1}),
|
|
% \dots,(\commitment_\kappa, \beta_\kappa)\big]$
|
|
% \item send $(\mathbf{E}_\gamma, h'_\gamma)$ to $\Exchange$
|
|
% \end{enumerate}
|
|
% \item[$\Exchange$:]
|
|
% \begin{enumerate}
|
|
% \setcounter{enumi}{10}
|
|
% \scriptsize
|
|
% \itemsep0.3em
|
|
% \item for all $i \in \{1,\dots,\kappa\}\setminus\{\gamma\}: h_i \leftarrow \Hash(\mathbf{E}_\gamma[i])$
|
|
% \item if $h \stackrel{?}{\neq} \HashF(h_1\|\dots\|h_{\gamma-1}\|h'_\gamma\|h_{\gamma+1}\|\dots\|h_{\kappa-1})$ return 0
|
|
% \item for all $i \in \{1,\dots,\kappa\}\setminus\{\gamma\}$:
|
|
% if $0 \stackrel{?}{=} \Compare(\commitment,\commitment_i, \beta_i)$ return $0$
|
|
% \item return 1
|
|
% \end{enumerate}
|
|
% \end{itemize}
|
|
% \end{frame}
|
|
|
|
\section*{Requirements}
|
|
|
|
\begin{frame}{Basic Requirements}
|
|
\label{fr:basicRequirements}
|
|
Candidate functions
|
|
\[ (\Commit, \Attest, \Verify, \Derive, \Compare) \]
|
|
must meet \textit{basic requirements}:
|
|
|
|
\begin{itemize}
|
|
\item Existence of attestations
|
|
\item Efficacy of attestations
|
|
\item Derivability of commitments and attestations
|
|
\end{itemize}
|
|
\pause
|
|
More details in the published paper and \hyperlink{fr:detailedBasicRequirements}{Appendix}.
|
|
\end{frame}
|
|
|
|
\begin{frame}{Security Requirements}
|
|
Candidate functions must also meet \textit{security requirements},
|
|
defined via security games:
|
|
\vfill
|
|
{
|
|
\small
|
|
\pause
|
|
\hspace*{-1em}\begin{tabular}{rp{9cm}}
|
|
\bf Requirement:& Unforgeability of minimum age\pause\\
|
|
\bf $\leftrightarrow$\hfill Game:& Forging an attestation\pause\\[0.5em]
|
|
\bf Requirement: & Non-disclosure of age \pause\\
|
|
\bf$\leftrightarrow$\hfill Game: & Age disclosure by commitment or attestation \pause\\[0.5em]
|
|
\bf Requirement:& Unlinkability of commitments and attestations\pause\\
|
|
\bf $\leftrightarrow$\hfill Game:& Distinguishing derived commitments and attestations
|
|
\end{tabular}
|
|
}
|
|
\vfill
|
|
|
|
\pause
|
|
Meeting the security requirements means that adversaries can win
|
|
those games only with negligible advantage.
|
|
\vfill
|
|
\pause
|
|
Adversaries are arbitrary polynomial-time algorithms, acting on all
|
|
relevant input.
|
|
\end{frame}
|
|
|
|
\begin{frame}{Security Requirements}{Simplified Example}
|
|
|
|
\begin{description}[<+->]
|
|
\item[Game $\Game{FA}$: Forging an attest]~\\
|
|
{\small
|
|
\begin{enumerate}
|
|
\item $ (\age, \omega) \drawfrom \N_{\Age-1}\times\Omega $
|
|
\item $ (\commitment, \pruf) \leftarrow \Commit(\age, \omega) $
|
|
\item $ (\minage, \attest) \leftarrow \Adv(\age, \commitment, \pruf)$
|
|
\item Return 0 if $\minage \leq \age$
|
|
\item Return $\Verify(\minage,\commitment,\attest)$
|
|
\item[]~\\[0.5em] Adversary $\Adv$ wins the game, if $\Game{FA}$ returns 1.
|
|
\end{enumerate}
|
|
}
|
|
\vfill
|
|
\item[Requirement: Unforgeability of minimum age]
|
|
{\small
|
|
\begin{equation*}
|
|
\Forall_{\Adv\in\PPT(\N_\Age\times\Commitments\times\Proofs\to \N_\Age\times\Attests)}:
|
|
\Probability\Big[\Game{FA} = 1\Big] \le \negl
|
|
\end{equation*}
|
|
}
|
|
\end{description}
|
|
|
|
% \pause
|
|
% Note: This example does not take $\Derive()$ into account.
|
|
\end{frame}
|
|
|
|
\begin{frame}{Our task}
|
|
\large
|
|
Finding functions
|
|
\[ (\Commit, \Attest, \Verify, \Derive, \Compare) \]
|
|
that meet the basic and security requirements.
|
|
\end{frame}
|
|
|
|
\section*{A solution}
|
|
|
|
|
|
\begin{frame}{Instantiation with ECDSA}
|
|
We propose a solution based on ECDSA.
|
|
|
|
Think: One key-pair per age group.
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}{Definition of Commit with ECDSA}%{Definition of Commit}
|
|
|
|
\begin{description}
|
|
\item[To \blue{Commit} to age group $\age \in \{1,\dots,\Age\}$]~\\
|
|
\begin{enumerate}[<+->]
|
|
\item Guardian generates ECDSA-keypairs, one per age group:
|
|
\[\langle(q_1, p_1),\dots,(q_\Age,p_\Age)\rangle\]
|
|
\item Guardian then \textbf{drops} all private keys
|
|
$p_i$ for $i > \age$:
|
|
\[\Big \langle(q_1, p_1),\dots,
|
|
(q_\age, p_\age),
|
|
(q_{\age +1}, \red{\Nil}),\dots,
|
|
(q_\Age, \red{\Nil})\Big\rangle\]
|
|
\item[] then set \begin{itemize}
|
|
\setlength{\itemindent}{5em}
|
|
\item[\bf Commitment:] $\Vcommitment := (q_1,~\dots~\dots~\dots~,q_\Age)$
|
|
\item[\bf Proof:] $\Vpruf_\age := (p_1, \dots, p_\age, \Nil,\dots,\Nil)$
|
|
\end{itemize}
|
|
\vfill
|
|
\item Guardian gives child $\langle \Vcommitment, \Vpruf_\age \rangle$
|
|
\vfill
|
|
\end{enumerate}
|
|
\end{description}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Attest and Verify with ECDSA}
|
|
Child has
|
|
\begin{itemize}
|
|
\item ordered public-keys $\Vcommitment = (q_1, \dots~\dots~\dots, q_\Age) $,
|
|
\item (some) private-keys $\Vpruf = (p_1, \dots, p_\age, \Nil, \dots, \Nil)$.
|
|
\end{itemize}
|
|
\begin{description}
|
|
\item<2->[To \blue{Attest} a minimum age (group) $\blue{\minage} \leq \age$:]~\\
|
|
Sign a message with ECDSA using private key
|
|
$p_\blue{\minage}$. The signature $\sigma_\blue{\minage}$ is the
|
|
attestation.
|
|
\end{description}
|
|
|
|
\vfill
|
|
|
|
\uncover<3->{
|
|
Merchant gets
|
|
\begin{itemize}
|
|
\item ordered public-keys $\Vcommitment = (q_1, \dots, q_\Age) $
|
|
\item Signature $\sigma_\blue{\minage}$
|
|
\end{itemize}
|
|
\begin{description}
|
|
\item<4->[To \blue{Verify} a minimum age (group) \blue{$\minage$}:]~\\
|
|
Verify the ECDSA-Signature $\sigma_\blue{\minage}$ with public key $q_\blue{\minage}$.
|
|
\end{description}
|
|
}
|
|
\vfill
|
|
\end{frame}
|
|
|
|
\begin{frame}{Derive and Compare with ECDSA}
|
|
Child has
|
|
$\Vcommitment = (q_1, \dots, q_\Age) $ and
|
|
$\Vpruf = (p_1, \dots, p_\age, \Nil, \dots, \Nil)$.
|
|
\begin{description}
|
|
\item<2->[To \blue{Derive} new $\Vcommitment'$ and $\Vpruf'$:]
|
|
Choose random $\beta\in\Z_g$ and calculate
|
|
\small
|
|
\begin{align*}
|
|
\Vcommitment' &= \big(q'_1,~\ldots~\ldots~\ldots~,q'_\Age\big) &&:= \big(\beta * q_1,\ldots~\ldots,\beta * q_\Age\big) ,\\
|
|
\Vpruf' &= \big(p'_1,\ldots,p'_\age, \Nil, \ldots, \Nil\big) &&:= \big(\beta p_1,\ldots,\beta p_\age,\Nil,\ldots,\Nil\big)
|
|
\end{align*}
|
|
\uncover<3->{
|
|
\small
|
|
Note:
|
|
\begin{itemize}
|
|
\item $\beta*q_i$ is scalar multiplication on the elliptic curve.
|
|
\item $p'_i*G$ = $(\beta p_i)*G = \beta*(p_i*G) = \beta*q_i = q'_i$
|
|
\item[$\implies$] {\bf $p'_i$ actually \textit{is} private key to $q'_i$}
|
|
\end{itemize}
|
|
}
|
|
\end{description}
|
|
|
|
\vfill
|
|
\uncover<4->{
|
|
Exchange gets $\Vcommitment = (q_1,\dots,q_\Age)$, $\Vcommitment' = (q_1', \dots, q_\Age')$ and $\beta$
|
|
\begin{description}
|
|
\item[To \blue{Compare}, calculate:]
|
|
\small
|
|
$(\beta * q_1, \ldots , \beta * q_\Age) \stackrel{?}{=} (q'_1,\ldots, q'_\Age)$
|
|
\end{description}
|
|
\vfill
|
|
}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Instantiation with ECDSA}
|
|
|
|
Functions
|
|
(Commit, Attest, Verify, Derive, Compare)\\
|
|
as defined in the instantiation with ECDSA\\[0.5em]
|
|
\begin{itemize}
|
|
\item meet the basic requirements,\\[0.5em]
|
|
\item also meet all security requirements.\\
|
|
\end{itemize}
|
|
|
|
Security proofs by reduction, details are in the paper.
|
|
\end{frame}
|
|
|
|
|
|
\begin{frame}{Example: Proof of Unforgeability}
|
|
\begin{columns}
|
|
\column{0.4\textwidth}
|
|
\begin{minipage}{\textwidth}
|
|
\tiny
|
|
\begin{description}
|
|
\item[Game $\Game{FA}$: Forging an attest]~\\
|
|
1. $(\age, \omega) \drawfrom \N_{\Age-1}\times\Omega $\\
|
|
2. $(\commitment, \pruf) \leftarrow \Commit(\age, \omega) $\\
|
|
3. $(\minage, \attest) \leftarrow \Adv(\age, \commitment, \pruf)$\\
|
|
4. Return 0 if $\minage \leq \age$\\
|
|
5. Return $\Verify(\minage,\commitment,\attest)$\\
|
|
\vfill
|
|
\item[Requirement:]~\\
|
|
$\Forall_{\Adv}: \Probability\Big[\Game{FA} = 1\Big] \le \negl$
|
|
\end{description}
|
|
\end{minipage}
|
|
\column{0.7\textwidth}
|
|
Proof by reduction:
|
|
\pause
|
|
\small
|
|
\begin{enumerate}[<+->]
|
|
\item Adversary wins if $1 = \Verify(\minage,\commitment,\attest)$.
|
|
\item That means: $\sigma$ was a valid ECDSA-signature, validated with $q_m$.
|
|
\item But adversary does not have the private key $p_m$ to $q_m$.
|
|
\item[$\implies$] So winning this game would require to existentially forge
|
|
the signature, which is negligible.
|
|
\end{enumerate}
|
|
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Instantiation with Edx25519}
|
|
But... isn't ECDSA considered to be difficult to implement correctly?
|
|
|
|
\pause
|
|
We also formally define another signature scheme, Edx25519:\\[1em]
|
|
|
|
\begin{itemize}
|
|
\item based on EdDSA (Bernstein et al.),
|
|
\item generates compatible signatures,
|
|
\item allows for key derivation from both, private and public keys, independently and
|
|
\item is already in use in GNUnet.
|
|
\end{itemize}~\\[1em]
|
|
|
|
Current implementation of age restriction in GNU Taler uses Edx25519.
|
|
\end{frame}
|
|
|
|
|
|
% \begin{frame}{Instantiation with ECDSA}
|
|
% \framesubtitle{Full definitions}
|
|
% \scriptsize
|
|
%
|
|
% \begin{align*}
|
|
% \Commit_{E,\FDHg{\cdot}}(\age, \omega) &:= \Big\langle
|
|
% \overbrace{(q_1,\ldots,q_\Age)}^{= \Vcommitment},\;
|
|
% \overbrace{(p_1,\ldots,p_\age, \Nil,\ldots,\Nil)}^{= \Vpruf \text{, length }\Age}
|
|
% \Big\rangle\\
|
|
% \Attest_{E,\HashF}(\bage, \Vcommitment, \Vpruf) &:=
|
|
% \begin{cases}
|
|
% \attest_\bage := \Sign_{E,\HashF}\big(\bage,\Vpruf[\bage]\big) & \text{if } \Vpruf[\bage] \stackrel{?}{\neq} \Nil\\
|
|
% \Nil & \text{otherwise}
|
|
% \end{cases}\\
|
|
% %
|
|
% \Verify_{E,\HashF}(\bage, \Vcommitment, \attest) &:= \Ver_{E,\HashF}(\bage, \Vcommitment[\bage], \attest)\\
|
|
% %
|
|
% \Derive_{E, \FDHg{\cdot}}(\Vcommitment, \Vpruf, \omega) &:=
|
|
% \Big\langle(\beta * q_1,\ldots,\beta * q_\Age),
|
|
% (\beta p_1,\ldots,\beta p_\age,\Nil,\ldots,\Nil), \beta \Big\rangle \\
|
|
% & \text{ with } \beta := \FDHg{\omega} \text{ and multiplication } \beta p_i \text{ modulo } g \nonumber\\
|
|
% %
|
|
% \Compare_E(\Vcommitment, \Vcommitment', \beta) &:=
|
|
% \begin{cases}
|
|
% 1 & \text{if } (\beta * q_1, \ldots , \beta * q_\Age) \stackrel{?}{=} (q'_1,\ldots, q'_\Age)\\
|
|
% 0 & \text{otherwise}
|
|
% \end{cases}
|
|
% \end{align*}
|
|
% \end{frame}
|
|
|
|
\section{Integration with GNU Taler}
|
|
|
|
\begin{frame}{GNU Taler}{https://www.taler.net}
|
|
\label{fr:GnuTaler}
|
|
\begin{columns}
|
|
\column{4cm}
|
|
\fontsize{8pt}{9pt}\selectfont
|
|
\begin{tikzpicture}[scale=.55]
|
|
\node[circle,fill=black!10] at (3, 4) (Exchange) {$\Exchange$};
|
|
\node[circle,fill=black!10] at (0, 0) (Customer) {$\Customer$};
|
|
\node[circle,fill=black!10] at (6, 0) (Merchant) {$\Merchant$};
|
|
|
|
\draw[<->] (Customer) to [out=65,in=220] node[sloped,above] {\sf withdraw} (Exchange);
|
|
\draw[<->] (Customer) to [out=45,in=240] node[sloped,below] {\sf refresh} (Exchange);
|
|
\draw[<->] (Customer) to node[sloped, below] {\sf purchase} (Merchant);
|
|
\draw[<->] (Merchant) to node[sloped, above] {\sf deposit} (Exchange);
|
|
\end{tikzpicture}
|
|
\column{8cm}
|
|
\begin{itemize}
|
|
\item Protocol suite for online payment services
|
|
\item Based on Chaum's \hyperlink{fr:reminderBlindSignature}{blind signatures}
|
|
\item Taxable, efficient, free software
|
|
\item Allows for change and refund
|
|
\item Privacy preserving: anonymous and unlinkable payments
|
|
\end{itemize}
|
|
\end{columns}
|
|
|
|
\vfill
|
|
\uncover<2->{
|
|
\begin{itemize}
|
|
\item Coins are public-/private key-pairs $(C_p, c_s)$.
|
|
\item Exchange \hyperlink{fr:reminderBlindSignature}{blindly signs} $H(C_p)$ with denomination key $d_p$
|
|
\item Verification:
|
|
\begin{eqnarray*}
|
|
1 &\stackrel{?}{=}&
|
|
\mathsf{SigCheck}\big(H(C_p), D_p, \sigma_p\big)
|
|
\end{eqnarray*}
|
|
\scriptsize($D_p$ = public key of denomination and $\sigma_p$ = signature)
|
|
|
|
\end{itemize}
|
|
}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Integration with GNU Taler}{Binding age restriction to coins}
|
|
\label{fr:bindingToCoins}
|
|
|
|
To bind an age commitment $\commitment$ to a coin $C_p$, instead of
|
|
blindly signing \[ H(C_p), \]
|
|
$\Exchange$ now \hyperlink{fr:reminderBlindSignature}{blindly signs}
|
|
\[ H\left(C_p\parallel\orange{H(\commitment)}\right) \]
|
|
|
|
\vfill
|
|
Therefore, verfication of a coin now requires $H(\commitment)$, too:
|
|
\[
|
|
1 \stackrel{?}{=}
|
|
\mathsf{SigCheck}\big(H\left(C_p\parallel\orange{H(\commitment)}\right), D_p, \sigma_p\big)
|
|
\]
|
|
\vfill
|
|
\end{frame}
|
|
|
|
\begin{frame}{Integration with GNU Taler}
|
|
\framesubtitle{Integrated schemes}
|
|
\fontsize{8pt}{9pt}\selectfont
|
|
\begin{tikzpicture}[scale=.9]
|
|
\node[circle,minimum size=25pt,fill=black!15] at ( 0:0) (Client) {$\Child$};
|
|
\node[circle,minimum size=25pt,fill=black!15] at ( 60:5) (Exchange) {$\Exchange$};
|
|
\node[circle,minimum size=25pt,fill=black!15] at ( 0:5) (Merchant) {$\Merchant$};
|
|
\node[circle,minimum size=25pt,fill=blue!15] at (130:3) (Guardian) {$\Guardian$};
|
|
|
|
\draw[<->] (Guardian) to node[sloped,above,align=center]
|
|
{{\sf withdraw}\orange{, using}\\ $H(C_p\orange{\parallel H(\commitment)})$} (Exchange);
|
|
\draw[<->] (Client) to node[sloped,below,align=center]
|
|
{{\sf refresh} \orange{ + }\\ \orange{$\DeriveCompare$}} (Exchange);
|
|
\draw[<->] (Client) to node[sloped, below]
|
|
{{\sf purchase} \blue{+ $(\attest_\minage, \commitment)$}} (Merchant);
|
|
\draw[<->] (Merchant) to node[sloped, above]
|
|
{{\sf deposit} \orange{+ $H(\commitment)$}} (Exchange);
|
|
|
|
\draw[->] (Guardian) to [out=70,in=150, loop] node[above]
|
|
{$\Commit(\age)$} (Guardian);
|
|
\draw[->] (Guardian) to node[below,sloped]
|
|
{($\commitment$, $\pruf_\age$)} (Client);
|
|
\draw[->,blue] (Client) to [out=-50,in=-130, loop] node[below]
|
|
{\blue{$\Attest(\minage, \commitment, \pruf_{\age})$}} (Client);
|
|
\draw[->,blue] (Merchant) to [out=-50,in=-130, loop] node[below]
|
|
{\blue{$\Verify(\minage, \commitment, \attest_{\minage})$}} (Merchant);
|
|
\end{tikzpicture}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Age restriction in the wallet}
|
|
\centering \includegraphics[height=0.9\textheight]{images/wallet-age.png}
|
|
\end{frame}
|
|
|
|
\include{gnu}
|
|
|
|
\begin{frame}{Interested in GNU Taler?}
|
|
We are looking for developers, testers, users!
|
|
|
|
\begin{description}
|
|
\item[Intro:] \url{https://taler.net}
|
|
\item[Learn:] \url{https://docs.taler.net}
|
|
\item[Develop:] \url{https://git.taler.net}, \url{https://bugs.taler.net}
|
|
\end{description}
|
|
\end{frame}
|
|
|
|
\section{Discussion \& Conclusion}
|
|
|
|
\begin{frame}{Discussion}
|
|
\begin{itemize}[<+->]
|
|
\item Our solution can in principle be used with any token-based payment scheme
|
|
\item[] However, GNU Taler best aligned with our design goals
|
|
(security, privacy and efficiency).
|
|
|
|
\item Subsidiarity requires bank accounts being owned by adults.
|
|
\item[] However, scheme can be adapted to cases of
|
|
\begin{itemize}
|
|
\item minors have bank accounts
|
|
\item peer-to-peer payments
|
|
\item[] Hint: Know-Your-Customer (KYC) and adapted
|
|
withdraw protocol.
|
|
\end{itemize}
|
|
\item Our scheme offers an alternative to identity management systems (IMS)
|
|
\end{itemize}
|
|
\end{frame}
|
|
|
|
% \begin{frame}{Related Work}
|
|
% \begin{itemize}
|
|
% \item Current privacy-perserving systems all based on
|
|
% attribute-based credentials (Koning et al.,
|
|
% Schanzenbach et al., Camenisch et al., Au et al.)
|
|
%
|
|
% \item Attribute-based approach lacks support:
|
|
% \begin{itemize}
|
|
% \item Complex for consumers and retailers
|
|
% \item Requires trusted third authority
|
|
% \end{itemize}
|
|
% \vfill
|
|
% \item Other approaches tie age-restriction to ability to pay ("debit cards for kids")
|
|
% \begin{itemize}
|
|
% \item Advantage: mandatory to payment process
|
|
% \item Not privacy friendly
|
|
% \end{itemize}
|
|
% \end{itemize}
|
|
% \end{frame}
|
|
|
|
\begin{frame}{Conclusion}
|
|
Age restriction is a technical, ethical and legal challenge.
|
|
|
|
\pause
|
|
Existing solutions are
|
|
\begin{itemize}
|
|
\item without strong protection of privacy or
|
|
\item based on identity management systems (IMS)
|
|
\end{itemize}
|
|
\vfill
|
|
|
|
\pause
|
|
Our scheme offers a solution that
|
|
\begin{itemize}
|
|
\item aligns with subsidiarity
|
|
\item preserves privacy
|
|
\item is efficient
|
|
\item and an alternative to IMS
|
|
\end{itemize}
|
|
\end{frame}
|
|
|
|
|
|
\begin{frame}{}
|
|
\large
|
|
\begin{center}
|
|
{\Huge \textbf{Thank you!}}\\
|
|
Questions?
|
|
\end{center}
|
|
|
|
\begin{center}
|
|
\texttt{oec-taler@kesim.org}\\
|
|
\texttt{@oec@mathstodon.xyz}
|
|
\vfill
|
|
{Interested in GNU Taler?}
|
|
\begin{description}
|
|
\item[Intro:] \url{https://taler.net}
|
|
\item[Learn:] \url{https://docs.taler.net}
|
|
\item[Develop:] \url{https://git.taler.net}, \url{https://bugs.taler.net}
|
|
\end{description}
|
|
\end{center}
|
|
\end{frame}
|
|
|
|
\appendix
|
|
|
|
\begin{frame}{Taler Overview}
|
|
\hspace*{-3em}\includegraphics[width=\paperwidth]{images/taler-overview-blue.png}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Basic Requirements - Details}
|
|
\label{fr:detailedBasicRequirements}
|
|
{\scriptsize \it back to \hyperlink{fr:basicRequirements}{Basic Requirements}}
|
|
\begin{description}[<+->]
|
|
\item[Existence of attestations]
|
|
{\scriptsize
|
|
\begin{align*}
|
|
\Forall_{\age\in\N_\Age \atop \omega \in \Omega}:
|
|
\Commit(\age, \omega) =: (\commitment, \pruf)
|
|
\implies
|
|
\Attest(\minage, \commitment, \pruf) =
|
|
\begin{cases}
|
|
\attest \in \Attests, \text{ if } \minage \leq \age\\
|
|
\Nil \text{ otherwise}
|
|
\end{cases}
|
|
\end{align*}}
|
|
\item[Efficacy of attestations]
|
|
{\scriptsize
|
|
\begin{align*}
|
|
\Verify(\minage, \commitment, \attest) = \
|
|
\begin{cases}
|
|
1, \text{if } \Exists_{\pruf \in \Proofs}: \Attest(\minage, \commitment, \pruf) = \attest\\
|
|
0 \text{ otherwise}
|
|
\end{cases}
|
|
\end{align*}}
|
|
|
|
{\scriptsize
|
|
\begin{align*}
|
|
\forall_{n \leq \age}: \Verify\big(n, \commitment, \Attest(n, \commitment, \pruf)\big) = 1.
|
|
\end{align*}}
|
|
|
|
...
|
|
\item[Derivability of commitments and attestations]...
|
|
\end{description}
|
|
|
|
\pause
|
|
More details in the published paper.
|
|
\end{frame}
|
|
|
|
\begin{frame}{Reminder: RSA blind signature}
|
|
\label{fr:reminderBlindSignature}
|
|
\small
|
|
In RSA, a public key $(e, N)$ and private key $(d, N)$ have the property
|
|
\[ x^{ed} = x \mod N \]
|
|
|
|
\pause
|
|
Bob (B) creates a blind signature of a message $m$ for Alice (A):
|
|
\begin{itemize}[<+->]
|
|
\item[A:]
|
|
\begin{itemize}
|
|
\item chooses random integer $b$
|
|
\item calculates $m' := m*b^e$ {\hfill \scriptsize \textit{(blinding)}}
|
|
\item sends $m'$ to B.
|
|
\end{itemize}
|
|
\item[B:]
|
|
\begin{itemize}
|
|
\item signs $m'$, by calculating
|
|
$\sigma' := (m')^d \mod N$ {\hfill \scriptsize \textit{(B doesn't learn $m$)}}
|
|
\item sends $\sigma'$ to A.
|
|
\item[] \scriptsize Note: $(m')^d = (m*b^e)^d = m^d*b^{ed} = m^d*b \mod N$
|
|
\end{itemize}
|
|
\item[A:]\begin{itemize}
|
|
\item unblinds $\sigma'$ by calculating
|
|
\[ \sigma := \sigma'*b^{-1} (= m^d) \]
|
|
\item[$\implies$]$\sigma$ is a valid RSA signature to message $m$.
|
|
\end{itemize}
|
|
\end{itemize}
|
|
\hfill \tiny back to \hyperlink{fr:GnuTaler}{\textit{taler}} or \hyperlink{fr:bindingToCoins}{\textit{binding}}
|
|
\end{frame}
|
|
|
|
%\begin{frame}{Requirements}
|
|
% \framesubtitle{Details}
|
|
%
|
|
% \begin{description}
|
|
% \item[Derivability of commitments and proofs:]~\\[0.1em]
|
|
% {\scriptsize
|
|
% Let \begin{align*}
|
|
% \age & \in\N_\Age,\,\, \omega_0, \omega_1 \in\Omega\\
|
|
% (\commitment_0, \pruf_0) & \leftarrow \Commit(\age, \omega_0),\\
|
|
% (\commitment_1, \pruf_1, \blinding) & \leftarrow \Derive(\commitment_0, \pruf_0, \omega_1).
|
|
% \end{align*}
|
|
% We require
|
|
% \begin{align*}
|
|
% \Compare(\commitment_0, \commitment_1, \blinding) = 1 \label{req:comparity}
|
|
% \end{align*}
|
|
% and for all $n\leq\age$:
|
|
% \begin{align*}
|
|
% \Verify(n, \commitment_1, \Attest(n, \commitment_1, \pruf_1)) &%
|
|
% =
|
|
% \Verify(n, \commitment_0, \Attest(n, \commitment_0, \pruf_0))
|
|
% \end{align*}}
|
|
% \end{description}
|
|
%\end{frame}
|
|
|
|
\end{document}
|