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Özgür Kesim 2024-05-30 12:03:40 +02:00
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commit 18789d4ead
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GPG Key ID: F136A7F922D018D7
4 changed files with 33 additions and 33 deletions

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@ -65,10 +65,10 @@
\subtitle{Zero-Knowledge Age Restriction for GNU Taler}
\author{Özgür Kesim}
\institute{FU Berlin}
\date{December 29, 2022}
\institute{Code Blau GmbH, FU Berlin, TU Dresden}
\date{31 May 2024}
%TODO: \titlegraphic{\centering\includegraphics[width=0.5\textwidth]{images/hip2022.jpg}}
\titlegraphic{\centering\vspace*{-0.5cm}\includegraphics[width=0.4\textwidth]{images/surveilance-logo.png}}
\begin{document}
@ -88,7 +88,7 @@
\item PhD candidate at FU Berlin,
\item member of GNU Taler dev-team.
\end{itemize}
\note{fnord}
\vfill
\url{oec-taler@kesim.org} \hfill \url{@oec@mathstodon.xyz} \hfill
@ -153,7 +153,7 @@
relation to content harmful to minors, \textbf{such as
age-verification systems}, ...
\end{quote}
\tiny
From the
\href{https://rm.coe.int/CoERMPublicCommonSearchServices/DisplayDCTMContent?documentId=0900001680645b44}
@ -245,7 +245,7 @@ with the following properties:
\item<9-> \textit{Exchanges} \textbf{compare} the derived age commitments
\item<10-> \tikzmark{send}{\large \texttt{GOTO}} 2.
\begin{tikzpicture}[overlay, remember picture]
\draw[line width=1pt,->]
\draw[line width=1pt,->]
([shift=({-6mm, 1mm})]pic cs:send) to
([shift=({-1cm, 1mm})]pic cs:send) to
([shift=({-1cm, 1mm})]pic cs:sstart) to
@ -299,7 +299,7 @@ with the following properties:
\begin{frame}{Specification of the Function Signatures}
\small
\small
Searching for functions \uncover<2->{with the following signatures}
\begin{align*}
&\bf \Commit\uncover<2->{:
@ -417,9 +417,9 @@ Searching for functions \uncover<2->{with the following signatures}
\pause
\begin{itemize}[<+->]
\item Calling $\Derive()$ iteratively generates sequence
\item Calling $\Derive()$ iteratively generates sequence
$(\commitment_0, \commitment_1, \dots)$ of commitments.
\item Exchange calls $\Compare(\commitment_i, \commitment_{i+1},~.~)$
\item Exchange calls $\Compare(\commitment_i, \commitment_{i+1},~.~)$
\item[$\implies$]Exchange identifies sequence
\item[$\implies$]{\bf Unlinkability broken}
\end{itemize}
@ -436,23 +436,23 @@ Searching for functions \uncover<2->{with the following signatures}
\begin{itemize}[<+->]
\item[$\Child$:]
\begin{enumerate}
\item generates $(\commitment_1,\dots,\commitment_\kappa)$
\item generates $(\commitment_1,\dots,\commitment_\kappa)$
and $(\beta_1,\dots,\beta_\kappa)$ from $\commitment_0$\\
by calling $\kappa$ times $\Derive(\commitment_0, \pruf_0, \omega_i)$
\item calculates $h_0:=H\left(H(\commitment_1, \beta_1)\parallel \dots\parallel H(\commitment_\kappa, \beta_\kappa)\right)$
\item sends $\commitment_0$ and $h_0$ to $\Exchange$
\end{enumerate}
\item[$\Exchange$:]
\item[$\Exchange$:]
\begin{enumerate}
\item[4.] saves $\commitment_0$ and $h_0$ and sends $\Child$ random $\gamma \in \{1,\dots,\kappa\}$
\end{enumerate}
\item[$\Child$:]
\item[$\Child$:]
\begin{enumerate}
\item[5.] reveals $h_\gamma:=H(\commitment_\gamma, \beta_\gamma)$ and all $(\commitment_i, \beta_i)$, except $(\commitment_\gamma, \beta_\gamma)$
\end{enumerate}
\item[$\Exchange$:]
\item[$\Exchange$:]
\begin{enumerate}
\item[6.] compares $h_0$ and
\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}
@ -463,7 +463,7 @@ Searching for functions \uncover<2->{with the following signatures}
\end{frame}
\begin{frame}{Achieving Unlinkability}%{Certainty trade-off}
With \orange{$\DeriveCompare$}
\begin{itemize}
\item $\Exchange$ learns nothing about $\commitment_\gamma$ or $H(\commitment_\gamma)$,
@ -513,7 +513,7 @@ Searching for functions \uncover<2->{with the following signatures}
{\blue{$\Verify(\minage, \commitment, \attest_{\minage})$}} (Merchant);
}
\uncover<7,8->{
\draw[orange,<->] (Client) to
\draw[orange,<->] (Client) to
node[sloped,below,align=center] {\orange{$\commitment \mapsto \commitment_\gamma$}}
node[sloped,above,align=center] {\orange{$\DeriveCompare$}} (Exchange);
}
@ -562,7 +562,7 @@ Searching for functions \uncover<2->{with the following signatures}
% \item[$\Child$:]
% \begin{enumerate}
% \setcounter{enumi}{7}
%
%
% \scriptsize
% \itemsep0.3em
% \item $h'_\gamma \leftarrow \Hash(\commitment_\gamma, \beta_\gamma)$
@ -591,7 +591,7 @@ Searching for functions \uncover<2->{with the following signatures}
\begin{frame}{Basic Requirements}
\label{fr:basicRequirements}
Candidate functions
Candidate functions
\[ (\Commit, \Attest, \Verify, \Derive, \Compare) \]
must meet \textit{basic requirements}:
@ -602,7 +602,7 @@ Searching for functions \uncover<2->{with the following signatures}
\end{itemize}
\pause
More details in the published paper and \hyperlink{fr:detailedBasicRequirements}{Appendix}.
\end{frame}
\end{frame}
\begin{frame}{Security Requirements}
Candidate functions must also meet \textit{security requirements},
@ -685,9 +685,9 @@ Searching for functions \uncover<2->{with the following signatures}
\[\langle(q_1, p_1),\dots,(q_\Age,p_\Age)\rangle\]
\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,
\[\Big \langle(q_1, p_1),\dots,
(q_\age, p_\age),
(q_{\age +1}, \red{\Nil}),\dots,
(q_\Age, \red{\Nil})\Big\rangle\]
\item[] then set \begin{itemize}
\setlength{\itemindent}{5em}
@ -702,7 +702,7 @@ Searching for functions \uncover<2->{with the following signatures}
\end{frame}
\begin{frame}{Attest and Verify with ECDSA}
Child has
Child has
\begin{itemize}
\item ordered public-keys $\Vcommitment = (q_1, \dots~\dots~\dots, q_\Age) $,
\item (some) private-keys $\Vpruf = (p_1, \dots, p_\age, \Nil, \dots, \Nil)$.
@ -717,7 +717,7 @@ Searching for functions \uncover<2->{with the following signatures}
\vfill
\uncover<3->{
Merchant gets
Merchant gets
\begin{itemize}
\item ordered public-keys $\Vcommitment = (q_1, \dots, q_\Age) $
\item Signature $\sigma_\blue{\minage}$
@ -731,8 +731,8 @@ Searching for functions \uncover<2->{with the following signatures}
\end{frame}
\begin{frame}{Derive and Compare with ECDSA}
Child has
$\Vcommitment = (q_1, \dots, q_\Age) $ and
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 $\Vpruf'$:]
@ -820,7 +820,7 @@ Searching for functions \uncover<2->{with the following signatures}
\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 allows for key derivation from both, private and public keys, independently and
\item is already in use in GNUnet.
\end{itemize}~\\[1em]
@ -831,7 +831,7 @@ Searching for functions \uncover<2->{with the following signatures}
% \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},\;
@ -988,8 +988,8 @@ Searching for functions \uncover<2->{with the following signatures}
% \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:
%
% \item Attribute-based approach lacks support:
% \begin{itemize}
% \item Complex for consumers and retailers
% \item Requires trusted third authority
@ -1060,7 +1060,7 @@ Searching for functions \uncover<2->{with the following signatures}
\begin{align*}
\Forall_{\age\in\N_\Age \atop \omega \in \Omega}:
\Commit(\age, \omega) =: (\commitment, \pruf)
\implies
\implies
\Attest(\minage, \commitment, \pruf) =
\begin{cases}
\attest \in \Attests, \text{ if } \minage \leq \age\\
@ -1107,13 +1107,13 @@ Searching for functions \uncover<2->{with the following signatures}
\end{itemize}
\item[B:]
\begin{itemize}
\item signs $m'$, by calculating
\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
\item unblinds $\sigma'$ by calculating
\[ \sigma := \sigma'*b^{-1} (= m^d) \]
\item[$\implies$]$\sigma$ is a valid RSA signature to message $m$.
\end{itemize}

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