From 5379ebf5c9fd1e4397ec71d6f5337e8fde661e26 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=C3=96zg=C3=BCr=20Kesim?= Date: Tue, 27 Dec 2022 10:26:04 +0100 Subject: [PATCH] init --- hip2022/definitions.tex | 90 +++ hip2022/hip2022.pdf | Bin 0 -> 175790 bytes hip2022/hip2022.tex | 845 ++++++++++++++++++++++ hip2022/images/bfh.png | Bin 0 -> 16103 bytes hip2022/images/esorics2022.png | Bin 0 -> 31009 bytes hip2022/images/fraunhofer.png | Bin 0 -> 2204 bytes hip2022/images/fub.pdf | Bin 0 -> 63865 bytes hip2022/images/hip2022-color-inverted.jpg | Bin 0 -> 24061 bytes hip2022/images/hip2022-color.jpg | Bin 0 -> 25305 bytes hip2022/images/hip2022-mono-inverted.jpg | Bin 0 -> 19201 bytes hip2022/images/hip2022-mono.jpg | Bin 0 -> 23089 bytes hip2022/images/hip2022.jpg | Bin 0 -> 25284 bytes hip2022/images/taler-logo-2020.jpg | Bin 0 -> 39336 bytes hip2022/loop.sh | 20 + 14 files changed, 955 insertions(+) create mode 100644 hip2022/definitions.tex create mode 100644 hip2022/hip2022.pdf create mode 100644 hip2022/hip2022.tex create mode 100644 hip2022/images/bfh.png create mode 100644 hip2022/images/esorics2022.png create mode 100644 hip2022/images/fraunhofer.png create mode 100644 hip2022/images/fub.pdf create mode 100644 hip2022/images/hip2022-color-inverted.jpg create mode 100644 hip2022/images/hip2022-color.jpg create mode 100644 hip2022/images/hip2022-mono-inverted.jpg create mode 100644 hip2022/images/hip2022-mono.jpg create mode 100644 hip2022/images/hip2022.jpg create mode 100644 hip2022/images/taler-logo-2020.jpg create mode 100755 hip2022/loop.sh diff --git a/hip2022/definitions.tex b/hip2022/definitions.tex new file mode 100644 index 0000000..c2bdf3e --- /dev/null +++ b/hip2022/definitions.tex @@ -0,0 +1,90 @@ +\newcommand{\blue}[1]{{\color{blue}#1}} +\newcommand{\red}[1]{{\color{red}#1}} +\newcommand{\Guardian}{\mathcal{G}} +\newcommand{\Child}{\mathcal{C}} +\newcommand{\Customer}{\mathcal{C}} +\newcommand{\Merchant}{\mathcal{M}} +\newcommand{\Exchange}{\mathcal{E}} + +\newcommand{\Commit}{\mathsf{Commit}} +\newcommand{\Attest}{\mathsf{Attest}} +\newcommand{\Verify}{\mathsf{Verify}} +\newcommand{\Derive}{\mathsf{Derive}} +\newcommand{\DeriveCompare}{\mathsf{DeriveCompare_\kappa}} +\newcommand{\Compare}{\mathsf{Compare}} +\newcommand{\AgeVer}{\mathsf{AgeVer}} + +\newcommand{\HashF}{\mathsf{H}} +\newcommand{\Hash}{\mathsf{H}} +\newcommand{\Block}{\mathbb{B}} +\newcommand{\Pub}{\mathsf{Pub}} +\newcommand{\Sign}{\mathsf{Sig}} +\newcommand{\Ver}{\mathsf{Ver}} +\newcommand{\Encoding}{\mathsf{Encoding}} +\newcommand{\ECDSA}{\mathsf{ECDSA}} +\newcommand{\Null}{\mathcal{O}} +\newcommand{\EC}{\mathrm{ec}} +\newcommand{\Curve}{\mathsf{Curve25519}} +\newcommand{\SHA}{\mathsf{SHA256}} +\newcommand{\SHAF}{\mathsf{SHA252}} +\newcommand{\FDH}{\mathsf{FDH}} + +\newcommand{\negl}{\epsilon} + +\newcommand{\rand}{\mathsf{rand}} +\newcommand{\age}{\mathsf{a}} +\newcommand{\Age}{\mathsf{M}} +\newcommand{\bage}{\mathsf{b}} +\newcommand{\minage}{\mathsf{m}} +\newcommand{\attest}{\mathsf{T}} +\newcommand{\commitment}{\mathsf{Q}} +\newcommand{\pruf}{\mathsf{P}} +\newcommand{\Vcommitment}{\vec{\mathsf{Q}}} +\newcommand{\Vpruf}{\vec{\mathsf{P}}} +\newcommand{\blinding}{\beta} + +\newcommand{\ZN}{\mathbb{Z}_N} +\newcommand{\Z}{\mathbb{Z}} +\newcommand{\N}{\mathbb{N}} +\newcommand{\A}{\mathbb{A}} +\newcommand{\E}{\mathbb{E}} +\newcommand{\F}{\mathbb{F}} +\newcommand{\seck}{\mathsf{s}} +\newcommand{\pubk}{\mathsf{P}} +\renewcommand{\H}{\mathbb{H}} +\newcommand{\K}{\mathbb{K}} +\newcommand{\Proofs}{\mathbb{P}} +\newcommand{\Commitments}{\mathbb{O}} +\newcommand{\Attests}{\mathbb{T}} +\newcommand{\Blindings}{\mathbb{B}} +\newcommand{\Nil}{\perp} + +\newcommand{\p}{\mathsf{p}} +\newcommand{\com}{\mathsf{com}} +\newcommand{\prf}{\mathsf{prf}} + +\newcommand{\Adv}{\mathcal{A}} +\newcommand{\PPT}{\mathfrak{A}} +\newcommand{\Probability}{\mathrm{Pr}} +\newcommand{\Algorithm}{f} +\renewcommand{\Game}[1]{G_\Adv^\mathsf{#1}} + +\DeclareMathOperator{\Image}{Im} +\DeclareMathOperator{\Mod}{mod} + +\newcommand{\Encode}[1]{\overbracket[0.5pt][2pt]{\,#1\,}} +\newcommand{\Decode}[1]{\underbracket[0.5pt][3pt]{\,#1\,}} +\newcommand{\FDHg}[1]{[#1]_g\,} +\newcommand{\logg}{{\breve{g}}} + + +\newcommand{\drawfrom}{\xleftarrow{\$}} +\newcommand\Exists{% + \mathop{\lower0.75ex\hbox{\ensuremath{% + \mathlarger{\mathlarger{\mathlarger{\mathlarger{\exists}}}}}}}% + \limits} + +\newcommand\Forall{% + \mathop{\lower0.75ex\hbox{\ensuremath{% + \mathlarger{\mathlarger{\mathlarger{\mathlarger{\forall}}}}}}}% + \limits} diff --git a/hip2022/hip2022.pdf b/hip2022/hip2022.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5a8aea384e49c0359317a95e8272823342ed2e35 GIT binary patch literal 175790 zcmeFZb#zxvuQ0mn?(XjH?(XhTcQ-23-Cd}=Q1?=Wy1TcOQWvOGZ-M(O@I2pZ=X`gq zv+h54ohjWi$xJetB$LVPLZvDx&BVsc1y8kmesTxTMaoL*WNHg9D99phWAAR^$|5PD 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z0=E?(3%BU4=>oge{^{3WGByq!!CjQPpr8FPg6nAYlC(uQOzXP&oi3;o2IIeG7cZVV z_>#GDGJdKAnGxm*`n|-e3~{IA2|_M8C`0-`j%eY`UXBL*q0Ova04Bi#1e{JouWi`e zWa)D@4i^_-Uq2fkzd#=c UM_hooh>(~tE*qPY_8Z*)0urcgs{jB1 literal 0 HcmV?d00001 diff --git a/hip2022/hip2022.tex b/hip2022/hip2022.tex new file mode 100644 index 0000000..21098a6 --- /dev/null +++ b/hip2022/hip2022.tex @@ -0,0 +1,845 @@ +%\pdfminorversion=3 +\documentclass[fleqn,xcolor={usenames,dvipsnames}]{beamer} +\usepackage{appendixnumberbeamer} +\usepackage{amsmath} +\usepackage{multimedia} +\usepackage[utf8]{inputenc} +\usepackage{framed,color,ragged2e} +\usepackage[absolute,overlay]{textpos} +%\definecolor{shadecolor}{rgb}{0.8,0.8,0.8} +\setbeamertemplate{navigation symbols}{} +\usepackage{xcolor} +\usepackage[normalem]{ulem} +\usepackage{listings} +\usepackage{adjustbox} +\usepackage{array} +\usepackage{bbding} +\usepackage{relsize} +\usepackage{graphicx} +\usepackage{tikz,eurosym,calc} +\usetikzlibrary{tikzmark} +\usetikzlibrary{shapes,arrows,arrows.meta} +\usetikzlibrary{positioning,patterns} +\usetikzlibrary{calc} + +\usetheme[progressbar=frametitle]{metropolis} +\setbeamersize{description width=1em} +\usepackage{fontspec} +\setsansfont{IBM Plex Sans} + +%\setbeamertemplate{footline}{ +% \hbox{% +% \begin{beamercolorbox}[wd=\paperwidth,ht=3ex,dp=1.5ex,leftskip=2ex,rightskip=2ex]{page footer}% +% \usebeamerfont{title in head/foot}% +% \insertshorttitle \hfill +% \insertsection \hfill +% \insertframenumber{} / \inserttotalframenumber +% \end{beamercolorbox}}% +%} + +\definecolor{blue}{rgb}{0,0.4,1} +\newcommand{\orange}[1]{{\color{orange}#1}} +\newcommand{\TODO}[1]{\orange{TODO: #1}} + + +\input{definitions} + +\title{Are you old enough to buy this?} +\subtitle{Zero-Knowledge Age Restriction for GNU Taler} + +\author{Özgür Kesim} +\institute{FU Berlin} +\date{December 29, 2022} + +\titlegraphic{\centering\includegraphics[width=0.5\textwidth]{images/hip2022.jpg}} + + +\begin{document} + +\justifying + +\begin{frame} + \titlepage +\end{frame} + +\begin{frame}{Chapters} + \begin{enumerate} + \item \TODO{something something} + \end{enumerate} +\end{frame} + +\section{Introduction} + +\begin{frame}{Who am I} + \TODO{who am i} +\end{frame} + +\begin{frame}{Age restriction in E-commerce} + + \begin{description} + \item[Problem:]~\\[1em] + Verification of minimum age requirements in e-commerce.\\[2em] + + \item[Common solutions:] + +\begin{tabular}{l<{\onslide<2->}c<{\onslide<3->}cr<{\onslide}} + & \blue{Privacy} & \tikzmark{topau} \blue{Ext. authority}& \\[\medskipamount] + 1. ID Verification & bad & required & \\[\medskipamount] + 2. Restricted Accounts & bad & required & \\[\medskipamount] + 3. Attribute-based & good & required &\tikzmark{bottomau} \\[\medskipamount] +\end{tabular} + \end{description} + +\uncover<4->{ + \begin{tikzpicture}[overlay,remember picture] + \draw[orange,thick,rounded corners] + ($(pic cs:topau) +(0,0.5)$) rectangle ($(pic cs:bottomau) -(0.3, 0.2)$); + \end{tikzpicture} + \begin{center} + \bf Principle of Subsidiarity is violated + \end{center} +} +\end{frame} + + +\begin{frame}{Principle of Subsidiarity} +\begin{center} \Large + Functions of government---such as granting and restricting + rights---should be performed\\ + {\it at the lowest level of authority possible},\\ + as long as they can be performed {\it adequately}. +\end{center} +\vfill +\uncover<2->{ + For age-restriction, the lowest level of authority is:\\ + \begin{center}\Large + Parents, guardians and caretakers + \end{center} +} +\end{frame} + +\begin{frame}{Our contribution} +Design and implementation of an age restriction scheme\\ +with the following goals: + +\begin{enumerate} +\item It ties age restriction to the \textbf{ability to pay} (not to ID's) +\item maintains \textbf{anonymity of buyers} +\item maintains \textbf{unlinkability of transactions} +\item aligns with \textbf{principle of subsidiartiy} +\item is \textbf{practical and efficient} +\end{enumerate} + +\end{frame} + + +\section{Age Restriction} + +\begin{frame}{Age restriction} + \framesubtitle{Assumptions and scenario} + + \begin{columns} + \column{7.5cm} + \begin{itemize} + \item<1-> Assumption: Checking accounts are under control of eligible adults/guardians. + \item<2-> \textit{Guardians} \textbf{commit} to an maximum age + \item<3-> \textit{Minors} \textbf{attest} their adequate age + \item<4-> \textit{Merchants} \textbf{verify} the attestations + \item<5-> Minors \textbf{derive} age commitments from existing ones + \item<6-> \textit{Exchanges} \textbf{compare} the derived age commitments + \end{itemize} + \column{5cm} + \uncover<7-> + { + \begin{center} + \fontsize{7pt}{7pt}\selectfont + \begin{tikzpicture}[scale=.5] + \node[circle,minimum size=15pt,fill=black!15] at ( 60:4) (Exchange) {$\Exchange$}; + \node[circle,minimum size=15pt,fill=black!15] at ( 0:0) (Client) {$\Child$}; + \node[circle,minimum size=15pt,fill=black!15] at ( 0:4) (Merchant) {$\Merchant$}; + \node[circle,minimum size=15pt,fill=blue!15] at (140:3) (Guardian) {$\Guardian$}; + + \draw[->] (Guardian) to [out=50,in=130, loop] node[above] + {$\Commit$} (Guardian); + \draw[->,blue] (Client) to [out=-125,in=-190, loop] node[below,left] + {\blue{$\Attest$}} (Client); + \draw[->,blue] (Merchant) to [out=50,in=130, loop] node[above] + {\blue{$\Verify$}} (Merchant); + \draw[->,orange] (Client) to [out=-35,in=-100, loop] node[below] + {\orange{$\Derive$}} (Client); + \draw[->,orange] (Exchange) to [out=50,in=130, loop] node[above] + {\orange{$\Compare$}} (Exchange); + + \draw[orange,|->] (Client) to node[sloped,above,align=left] + {\orange{\scriptsize }} (Exchange); + \draw[blue,|->] (Client) to node[sloped, above] + {\blue{\scriptsize }} (Merchant); + \draw[,|->] (Guardian) to node[above,sloped,align=left] + {{\scriptsize }} (Client); + \end{tikzpicture} + \end{center} + } + \end{columns} + \vfill + \uncover<7->{Note: Scheme is independent of payment service protocol.} +\end{frame} + + +\begin{frame}{Formal Function Signatures} +\small +Searching for functions \uncover<2->{with the following signatures} +\begin{align*} + &\bf \Commit\uncover<2->{: + &(\age, \omega) &\mapsto (\commitment, \pruf) + &\scriptstyle \N_\Age \times \Omega &\scriptstyle \to \Commitments\times\Proofs, + } + \\ + &\bf \Attest\uncover<3->{: + &(\minage, \commitment, \pruf) &\mapsto \attest + &\scriptstyle \N_\Age\times\Commitments\times\Proofs &\scriptstyle \to \Attests \cup \{\Nil\}, + } + \\ + &\bf \Verify\uncover<4->{: + &(\minage, \commitment, \attest) &\mapsto b + &\scriptstyle \N_\Age\times\Commitments\times\Attests &\scriptstyle \to \Z_2, + } + \\ + &\bf \Derive\uncover<5->{: + &(\commitment, \pruf, \omega) &\mapsto (\commitment', \pruf', \blinding) + &\scriptstyle \Commitments\times\Proofs\times\Omega &\scriptstyle \to \Commitments\times\Proofs\times\Blindings, + } + \\ + &\bf \Compare\uncover<6->{: + &(\commitment, \commitment', \blinding) &\mapsto b + &\scriptstyle \Commitments\times\Commitments\times\Blindings &\scriptstyle \to \Z_2, + } +\end{align*} + \uncover<7->{ + with $\Omega, \Proofs, \Commitments, \Attests, \Blindings$ + sufficiently large sets.\\[1em] + Basic and security requirements are defined later.\\[2em] + } + + \scriptsize + \uncover<2->{ + Mnemonics:\\ + $\Commitments=$ \textit{c$\Commitments$mmitments}, + $\commitment=$ \textit{Q-mitment} (commitment), + $\Proofs=$ \textit{$\Proofs$roofs}, + } + \uncover<3->{ + $\pruf=$ \textit{$\pruf$roof},\\ + $\Attests=$ \textit{a$\Attests$testations}, + $\attest=$ \textit{a$\attest$testation}, + } + \uncover<5->{ + $\Blindings=$ \textit{$\Blindings$lindings}, + $\blinding=$ \textit{$\blinding$linding}. + } +\end{frame} + +\begin{frame}{Age restriction} + \framesubtitle{Naïve scheme} + \begin{center} + \begin{tikzpicture}[scale=.85] + \node[circle,minimum size=20pt,fill=black!15] at ( 60:4) (Exchange) {$\Exchange$}; + \node[circle,minimum size=20pt,fill=black!15] at ( 0:0) (Client) {$\Child$}; + \node[circle,minimum size=20pt,fill=black!15] at ( 0:4) (Merchant) {$\Merchant$}; + \node[circle,minimum size=20pt,fill=blue!15] at (140:3) (Guardian) {$\Guardian$}; + + \draw[->] (Guardian) to [out=50,in=130, loop] node[above] + {$\Commit$} (Guardian); + \draw[->,blue] (Client) to [out=-125,in=-190, loop] node[below,left] + {\blue{$\Attest$}} (Client); + \draw[->,blue] (Merchant) to [out=50,in=130, loop] node[above] + {\blue{$\Verify$}} (Merchant); + \draw[->,orange] (Client) to [out=-35,in=-100, loop] node[below] + {\orange{$\Derive$}} (Client); + \draw[->,orange] (Exchange) to [out=50,in=130, loop] node[above] + {\orange{$\Compare$}} (Exchange); + + \draw[orange,|->] (Client) to node[sloped,above,align=left] + {\orange{\scriptsize }} (Exchange); + \draw[blue,|->] (Client) to node[sloped, above] + {\blue{\scriptsize }} (Merchant); + \draw[,|->] (Guardian) to node[above,sloped,align=left] + {{\scriptsize }} (Client); + \end{tikzpicture} + \end{center} +\end{frame} + +\begin{frame}{Achieving Unlinkability} + \begin{columns} + \column{3cm} + \begin{center} + \fontsize{8pt}{9pt}\selectfont + \begin{tikzpicture}[scale=.65] + \node[circle,minimum size=20pt,fill=black!15] at ( 60:4) (Exchange) {$\Exchange$}; + \node[circle,minimum size=20pt,fill=black!15] at ( 0:0) (Client) {$\Child$}; + + \draw[->,orange] (Client) to [out=-35,in=-100, loop] node[below] + {\orange{$\footnotesize \Derive()$}} (Client); + \draw[->,orange] (Exchange) to [out=50,in=130, loop] node[above] + {\orange{$\footnotesize \Compare()$}} (Exchange); + + \draw[orange,|->] (Client) to node[sloped,above,align=left] + {\orange{\tiny \uncover<2->{$(\commitment_i,\commitment_{i+1})$}}} (Exchange); + \end{tikzpicture} + \end{center} + + \column{9cm} + Simple use of $\Derive()$ and $\Compare()$ is problematic. + + \begin{itemize} + \item<2-> Calling $\Derive()$ iteratively generates sequence + $(\commitment_0, \commitment_1, \dots)$ of commitments. + \item<2-> Exchange calls $\Compare(\commitment_i, \commitment_{i+1}, .)$ + \item[$\implies$]\uncover<3->{\bf Exchange identifies sequence} + \item[$\implies$]\uncover<3->{\bf Unlinkability broken} + \end{itemize} + \end{columns} +\end{frame} + +\begin{frame}{Achieving Unlinkability} + Define cut\&choose protocol \orange{$\DeriveCompare$}, + using $\Derive()$ and $\Compare()$.\\[0.5em] + \uncover<2->{ + Sketch: + \small + \begin{enumerate} + \item $\Child$ derives commitments $(\commitment_1,\dots,\commitment_\kappa)$ + from $\commitment_0$ \\ + by calling $\Derive()$ with blindings $(\beta_1,\dots,\beta_\kappa)$ + \item $\Child$ calculates $h_0:=H\left(H(\commitment_1, \beta_1)||\dots||H(\commitment_\kappa, \beta_\kappa)\right)$ + \item $\Child$ sends $\commitment_0$ and $h_0$ to $\Exchange$ + \item $\Exchange$ chooses $\gamma \in \{1,\dots,\kappa\}$ randomly + \item $\Child$ reveals $h_\gamma:=H(\commitment_\gamma, \beta_\gamma)$ and all $(\commitment_i, \beta_i)$, except $(\commitment_\gamma, \beta_\gamma)$ + \item $\Exchange$ compares $h_0$ and + $H\left(H(\commitment_1, \beta_1)||...||h_\gamma||...||H(\commitment_\kappa, \beta_\kappa)\right)$\\ + and evaluates $\Compare(\commitment_0, \commitment_i, \beta_i)$. + \end{enumerate} + \vfill + Note: Scheme is similar to the {\it refresh} protocol in GNU Taler. + } +\end{frame} + +\begin{frame}{Achieving Unlinkability} + With \orange{$\DeriveCompare$} + \begin{itemize} + \item $\Exchange$ learns nothing about $\commitment_\gamma$, + \item trusts outcome with $\frac{\kappa-1}{\kappa}$ certainty, + \item i.e. $\Child$ has $\frac{1}{\kappa}$ chance to cheat. + \end{itemize} + \vfill + Note: Still need Derive and Compare to be defined. +\end{frame} + +\begin{frame}{Refined scheme} + + \begin{tikzpicture}[scale=.8] + \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[orange,<->] (Client) to node[sloped,below,align=center] + {\orange{$\DeriveCompare$}} (Exchange); + \draw[blue,->] (Client) to node[sloped, below] + {\blue{$(\attest_\minage, \commitment)$}} (Merchant); + + \draw[->] (Guardian) to [out=150,in=70, 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}{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} + +\begin{frame}{Basic Requirements} + + Candidate functions + \[ (\Commit, \Attest, \Verify, \Derive, \Compare) \] + must first meet \textit{basic} requirements: + + \begin{itemize} + \item Existence of attestations + \item Efficacy of attestations + \item Derivability of commitments and attestations + \end{itemize} +\end{frame} + +\begin{frame}{Basic Requirements} + \framesubtitle{Formal Details} + + \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[etc.] + \end{description} +\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} + +\begin{frame}{Security Requirements} + Candidate functions must also meet \textit{security} requirements. + Those are defined via security games: + \begin{itemize} + \item Game: Age disclosure by commitment or attestation + \item[$\leftrightarrow$] Requirement: Non-disclosure of age + \vfill + + \item Game: Forging attestation + \item[$\leftrightarrow$] Requirement: Unforgeability of + minimum age + \vfill + + \item Game: Distinguishing derived commitments and attestations + \item[$\leftrightarrow$] Requirement: Unlinkability of + commitments and attestations + + \end{itemize} + \vfill + + Meeting the security requirements means that adversaries can win + those games only with negligible advantage. + \vfill + Adversaries are arbitrary polynomial-time algorithms, acting on all + relevant input. +\end{frame} + +\begin{frame}{Security Requirements} + \framesubtitle{Simplified Example} + + \begin{description} + \item[Game $\Game{FA}(\lambda)$---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 $\Verify(\minage,\commitment,\attest)$ + \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}(\lambda) = 1\Big] \le \negl(\lambda) + \end{equation*} + } + \end{description} +\end{frame} + +\section{Solution/Instantiation} + +\begin{frame}{Solution: Instantiation with ECDSA} +% \framesubtitle{Definition of Commit} + + \begin{description} + \item[To \blue{Commit} to age (group) $\age \in \{1,\dots,\Age\}$]~\\ + \begin{enumerate} + \item<2-> Guardian generates ECDSA-keypairs, one per age (group): + \[\langle(q_1, p_1),\dots,(q_\Age,p_\Age)\rangle\] + \item<3-> Guardian then \textbf{drops} all private keys + $p_i$ for $i > \age$: + \[\Big \langle(q_1, p_1),\dots, + (q_\age, p_\age), + (q_{\age +1}, \red{\Nil}),\dots, + (q_\Age, \red{\Nil})\Big\rangle\] + + \begin{itemize} + \item $\Vcommitment := (q_1, \dots, q_\Age)$ is the \textit{Commitment}, + \item $\Vpruf_\age := (p_1, \dots, p_\age, \Nil,\dots,\Nil)$ is the \textit{Proof} + \end{itemize} + \vfill + \item<4-> Guardian gives child $\langle \Vcommitment, \Vpruf_\age \rangle$ + \vfill + \end{enumerate} + \end{description} +\end{frame} + +\begin{frame}{Instantiation with ECDSA} + \framesubtitle{Definitions of Attest and Verify} + + Child has + \begin{itemize} + \item ordered public-keys $\Vcommitment = (q_1, \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 $\blue{\minage} \leq \age$:]~\\ + Sign a message with ECDSA using private key $p_\blue{\minage}$ + \end{description} + + \vfill + + \uncover<3->{ + Merchant gets + \begin{itemize} + \item ordered public-keys $\Vcommitment = (q_1, \dots, q_\Age) $ + \item Signature $\sigma$ + \end{itemize} + \begin{description} + \item<4->[To \blue{Verify} a minimum age $\minage$:]~\\ + Verify the ECDSA-Signature $\sigma$ with public key $q_\minage$. + \end{description} + } + \vfill +\end{frame} + +\begin{frame}{Instantiation with ECDSA} + \framesubtitle{Definitions of Derive and Compare} + 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(\beta * q_1,\ldots,\beta * q_\Age\big),\\ + \Vpruf' &:= \big(\beta p_1,\ldots,\beta p_\age,\Nil,\ldots,\Nil\big) + \end{align*} + Note: $ (\beta p_i)*G = \beta*(p_i*G) = \beta*q_i$\\ + \scriptsize $\beta*q_i$ is scalar multiplication on the elliptic curve. + \end{description} + + \vfill + \uncover<3->{ + 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.\\ + Proofs by security reduction, details are in the paper. + \end{itemize} + +\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} + \framesubtitle{https://www.taler.net} + \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 blind signatures + % \item Taxable, efficient, free software + \item Allows for change and refund (F. Dold) + \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 blindly signs $\FDH(C_p)$ with denomination key $d_p$ + \item Verification: + \begin{eqnarray*} + 1 &\stackrel{?}{=}& + \mathsf{SigCheck}\big(\FDH(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} + \framesubtitle{Binding age restriction to coins} + + To bind an age commitment $\commitment$ to a coin $C_p$, instead of + signing $\FDH(C_p)$, $\Exchange$ now blindly signs + \begin{center} + $\FDH(C_p, \orange{H(\commitment)})$ + \end{center} + + \vfill + Verfication of a coin now requires $H(\commitment)$, too: + \begin{center} + $1 \stackrel{?}{=} + \mathsf{SigCheck}\big(\FDH(C_p, \orange{H(\commitment)}), D_p, \sigma_p\big)$ + \end{center} + \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}\\ $\FDH(C_p\orange{, H(\commitment)})$} (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}{Instantiation with Edx25519} + Paper also formally defines another signature scheme: Edx25519.\\[1em] + + \begin{itemize} + \item Scheme already in use in GNUnet, + \item based on EdDSA (Bernstein et al.), + \item generates compatible signatures and + \item allows for key derivation from both, private and public keys, independently. + \end{itemize}~\\[1em] + + Current implementation of age restriction in GNU Taler uses Edx25519. +\end{frame} + +\section{Discussion, Related Work, Conclusion} + +\begin{frame}{Discussion} + \begin{itemize} + \item Our solution can in principle be used with any token-based payment scheme + \item GNU Taler best aligned with our design goals (security, privacy and efficiency) + \item Subsidiarity requires bank accounts being owned by adults + \begin{itemize} + \item Scheme can be adapted to case where minors have bank accounts + \begin{itemize} + \item Assumption: banks provide minimum age + information during bank + transactions. + \item Child and Exchange execute a variant of + the cut\&choose protocol. + \end{itemize} + \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. + + Existing solutions are + \begin{itemize} + \item without strong protection of privacy or + \item based on identity management systems (IMS) + \end{itemize} + \vfill + + Our scheme offers a solution that is + \begin{itemize} + \item based on subsidiarity + \item privacy preserving + \item efficient + \item an alternative to IMS + \end{itemize} +\end{frame} + + +\begin{frame}{} + \begin{center} + \Huge \textbf{Thank you!} + Questions? + \end{center} + + \begin{center} + \texttt{oec-taler@kesim.org}\\ + \texttt{@oec@mathstodon.xyz} + \end{center} +\end{frame} + +\appendix + +\begin{frame}{Nothing to see here} +\end{frame} + +\end{document} diff --git a/hip2022/images/bfh.png b/hip2022/images/bfh.png new file mode 100644 index 0000000000000000000000000000000000000000..4c9f8d1e53cc52d84262b1bc5de1177dd7d99514 GIT binary patch literal 16103 zcmeHtWmJ{x*7hO<6iGo5krWA~yF|LXn*}VoyOHi#NJ)p3N|&INq;yDkNF&_{-@V-X zocEmZy?@Ra-}mqAG2E>6Ja^9fo^xK;HCMQzyad)g;(HJX1WQU%R2c$6@&}(^V4#8j zXBM*)f#=(vs+!KqP&aaWM>|ssYZ$q+hdqoO=5ApMfw)iSztf7>>BSPg-J|~+l=?=P z0i8q49bLZ(hmr0=YJ9M2YWP`4lL#Rz{9ShDQJLTTIvKwuhfk{WXilno^{}|ZyyhkU zwa-9tXuwec6dufUo{h>|is^wR`^n-$ie*wa+cH-|sf_h3y%; zN0;+Ooe}r!PS1o_ymGW(`E@T~o}1}Ng`PCqLNf=q&#o07pZhFZ+?=a6q2HeFjTg^9 z{G}qp!!gnBRI+gA$2o(7%l!RJ85@!mE5C)_E8V6SIplsHMhCkL#ki8DZ`_BNimtuS zo@ig_q^`SFYhREm`@N{V@&3KCu8<^{cbIg;^ z8QJf*N&%P1dOV8mzmE-nU3no%x0eKWtlmS;PWoulUz|MRR1k;udSE2a>^X)Byi&`= zqK1A_GhD|>dT=jC>>in*cT9?ZkZS(m%S-HX?FZ+hX{{8=^m3xA4Jr2>N~Tp+YplX@ z&!%Ta^R4#gE;nq)Qp1Z~*q*HAMMaqR3=M}yv&_~PI>FYh*CA(GrWrOpY%Zr3PO=6= 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