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long presentation: added simplified daa description

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Michael Preisach 6 years ago
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6 changed files with 202 additions and 28 deletions
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  1. BIN
      presentation/191119_long/long.pdf
  2. 133
      presentation/191119_long/long.tex
  3. 41
      resources/daajoin.fig
  4. BIN
      resources/daajoin.pdf
  5. 56
      resources/tpmcert.fig
  6. BIN
      resources/tpmcert.pdf

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presentation/191119_long/long.pdf
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presentation/191119_long/long.tex
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@ -22,25 +22,44 @@
\end{frame} \end{frame}
\begin{frame} \begin{frame}
\frametitle{Recap: Trust inside Biometric Sensor} \frametitle{Chain of Trust}
\begin{itemize} \begin{itemize}
\item manufacturer of TPM holds certificate \item Manufacturer of TPM creates certificate
\item TPM holds measurements of boot chain in PCR \item Core Root of Trust: key seed
\begin{itemize} \item \texttt{tpm2\_CreatePrimary} to generate new EK
\item CRTM measures BIOS
\item BIOS measures MBR/EFI Bootloader
\item bootloader measures Kernel (Grub 2.04 supports TPM2)
\item Kernel measures libs, executables, \ldots
\end{itemize}
\item TPM Quote: summarize the PCR state and sign it with TPM Endorsement Key (EK)
\end{itemize} \end{itemize}
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{../../resources/tpmcert}
\end{figure}
\end{frame} \end{frame}
\begin{frame} \begin{frame}
\frametitle{Problem: Create trust beween BS and PA} \frametitle{Chain of Trust - Platform Configuration Register (PCR)}
\begin{itemize} \begin{itemize}
\item network discovery \item Booting with TPM2 (PCR0-7)
\item \textbf{no Knowledge about BS} \begin{description}
\item[\texttt{PCR0}] EFI Boot Services, EFI Runtime Services, Platform Firmware
\item[\texttt{PCR1}] ACPI, SMBIOS, \ldots
\item[\texttt{PCR2}] Option ROMs, Drivers from disks, \ldots (not relevant)
\item[\texttt{PCR4}] EFI/Legacy os Loader
\item[\texttt{PCR5}] EFI Partition, GPT, OS Partition Table
\end{description}
\item Grub2.04 supports TPM2 (PCR8,9) \footnote{\url{www.gnu.org/software/grub/manual/grub/grub.html\#Measured-Boot}}
\begin{description}
\item[\texttt{PCR8}] Kernel-, Module- and all other commands
\item[\texttt{PCR9}] All files read by GRUB
\end{description}
\item Linux uses PCR10-15
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Problem: Create Trust between BS and PA}
\begin{itemize}
\item Network discovery
\item \textbf{No Knowledge about BS}
\begin{itemize} \begin{itemize}
\item \textbf{Hardware} \item \textbf{Hardware}
\item \textbf{Software} \item \textbf{Software}
@ -48,7 +67,7 @@
\item Correct client to certify identity for given biometric data \item Correct client to certify identity for given biometric data
\end{itemize} \end{itemize}
\item \textbf{BS faces same problem with PA} \item \textbf{BS faces same problem with PA}
\item establish a secure channel to submit sensitive data \item Establish a secure channel to submit sensitive data
\end{itemize} \end{itemize}
\end{frame} \end{frame}
@ -70,11 +89,44 @@
\end{itemize} \end{itemize}
\end{frame} \end{frame}
\begin{frame}
\frametitle{ECDAA Setup}
\begin{itemize}
\item Choose TPM-supported pairing-firendly Elliptic Curve: FP256BN
\item Generate Issuer keypair
\item $isk = (x,y)$
\item $ipk = (q,\mathbb{G}_1, \mathbb{G}_2, \mathbb{G}_T, g_1, g_2, e, X, Y)$
\item Publish ipk
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{ECDAA Member Join}
\begin{center}
\includegraphics[width=0.9\textwidth]{../../resources/daajoin}
\end{center}
\end{frame}
\begin{frame}
\frametitle{ECDAA Member Sign}
\begin{center}
\includegraphics[width=0.9\textwidth]{../../resources/daajoin}
\end{center}
\end{frame}
\begin{frame}
\frametitle{ECDAA Member Verify}
\begin{center}
\includegraphics[width=0.9\textwidth]{../../resources/daajoin}
\end{center}
\end{frame}
\begin{frame} \begin{frame}
\frametitle{DAA Setup: Issuer creates Bilinear Group and Keys} \frametitle{DAA Setup: Issuer creates Bilinear Group and Keys}
\begin{eqnarray*} \[
q,\mathbb{G}_1, \mathbb{G}_2, \mathbb{G}_T, g_1, g_2, e q,\mathbb{G}_1, \mathbb{G}_2, \mathbb{G}_T, g_1, g_2, e
\end{eqnarray*} \]
\begin{itemize} \begin{itemize}
\item $\mathbb{G}_1, \mathbb{G}_2, \mathbb{G}_T$: groups of prime order $q$ \item $\mathbb{G}_1, \mathbb{G}_2, \mathbb{G}_T$: groups of prime order $q$
\item $g_1 \in \mathbb{G}_1$, $g_2 \in \mathbb{G}_2$: generator points \item $g_1 \in \mathbb{G}_1$, $g_2 \in \mathbb{G}_2$: generator points
@ -86,24 +138,49 @@
\end{itemize} \end{itemize}
\item Choose secret key $x\leftarrow\mathbb{Z}_q$, $y\leftarrow\mathbb{Z}_q$ \item Choose secret key $x\leftarrow\mathbb{Z}_q$, $y\leftarrow\mathbb{Z}_q$
\item generate public key $X=g_2^x$, $Y=g_2^y$ \item generate public key $X=g_2^x$, $Y=g_2^y$
\item $ipk = (q,\mathbb{G}_1, \mathbb{G}_2, \mathbb{G}_T, g_1, g_2, e, X, Y)$
\item $isk = (x,y)$
\end{itemize} \end{itemize}
\end{frame} \end{frame}
\begin{frame} \begin{frame}
\frametitle{Bilinear Maps} \frametitle{Bilinear Maps - Sign Messages}
Definition Bilinear Maps:
\begin{itemize} \begin{itemize}
\item \emph{Bilinear}: For all $P,Q \in G$, for all $a,b \in \mathbb{Z}$, $e(P^a,Q^b) = e(P,Q)^{ab}$ \item Simplified Example: $\mathbb{G}_1 = \mathbb{G}_2$
\item \emph{Non-degenerate}: There exists some $P,Q \in G$ such that $e(P,Q) \not 1$ where 1 is the identity of $\mathrm{G}$ \item $pk = (q,\mathbb{G}_1, \mathbb{G}_T, g_1, g_T, e, X, Y)$
\end{itemize} \item Given message $m$
\end{frame}
\begin{frame}
\frametitle{Bilinear Maps: Signatures}
\begin{itemize}
\item given message $m$ and random number $r leftarrow \mathbb{Z}_q$
\end{itemize} \end{itemize}
\begin{columns}[t]
\begin{column}{4cm}
\emph{Signer:}
\begin{itemize}
\item Compute Signature $\sigma(a,b,c)$
\begin{itemize}
\item $a \in \mathbb{G}_1$
\item $b = a^y$
\item $c = a^{x+mxy}$
\end{itemize}
\item Send(m, $\sigma$)
\end{itemize}
\end{column}
\begin{column}{6cm}
\emph{Verifier:}
\begin{itemize}
\item Check, that
\begin{small}
\begin{displaymath}
\underline{e(a,Y)} = e(a,g^y) = e(a^y,g) = \underline{e(b,g)}
\end{displaymath}
\begin{displaymath}
\underline{e(X,a)\cdot e(X,b)^m} = e(g,a)^x \cdot e(g,a)^{xym}
\end{displaymath}
\begin{displaymath}
= e(g,a)^{x+xym} = \underline{e(g,c)}
\end{displaymath}
\end{small}
\end{itemize}
\end{column}
\end{columns}
\end{frame} \end{frame}
\begin{frame} \begin{frame}

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#FIG 3.2 Produced by xfig version 3.2.7
Landscape
Center
Inches
Letter
100.00
Single
-2
1200 2
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
2 0 1.00 120.00 180.00
4875 4425 6600 4425
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 1 2
2 0 1.00 120.00 180.00
2475 4800 6600 4800
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
2 0 1.00 120.00 180.00
2475 5475 6600 5475
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 1 2
2 0 1.00 120.00 180.00
2550 6450 6600 6450
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
2 0 1.00 120.00 180.00
2550 7425 4275 7425
4 1 0 50 -1 4 14 0.0000 0 180 510 1275 3900 TPM\001
4 0 0 50 -1 4 14 0.0000 0 180 1455 6825 4650 create Nonce\001
4 1 0 50 -1 4 14 0.0000 0 180 645 7500 3900 Issuer\001
4 1 0 50 -1 4 10 0.0000 0 120 1290 4500 4725 JOINSTART nonce\001
4 1 0 50 -1 4 14 0.0000 0 180 510 4500 3900 Host\001
4 0 0 50 -1 4 14 0.0000 0 240 1680 6825 5700 verify Signature\001
4 0 0 50 -1 4 14 0.0000 0 180 1965 6825 6000 create Credentials\001
4 0 0 50 -1 4 14 0.0000 0 240 960 6825 6300 SPK(isk)\001
4 1 0 50 -1 4 10 0.0000 0 150 1380 4500 5400 APPEND pEK, sign\001
4 1 0 50 -1 4 10 0.0000 0 120 360 5700 4350 JOIN\001
4 1 0 50 -1 4 10 0.0000 0 150 1545 4500 6375 PROCEED Cred, sign\001
4 0 0 50 -1 4 14 0.0000 0 240 1680 375 6675 verify Signature\001
4 0 0 50 -1 4 14 0.0000 0 225 1860 375 6975 verify Credentials\001
4 0 0 50 -1 4 14 0.0000 0 180 1830 375 7275 store Credentials\001
4 1 0 50 -1 4 10 0.0000 0 120 750 3300 7350 store Cred\001
4 0 0 50 -1 4 14 0.0000 0 240 1125 375 5025 create gsk\001
4 0 0 50 -1 4 14 0.0000 0 240 1050 375 5325 SPK(gsk)\001

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@ -0,0 +1,56 @@
#FIG 3.2 Produced by xfig version 3.2.7
Landscape
Center
Inches
Letter
100.00
Single
-2
1200 2
6 6000 6150 7500 6900
2 4 0 1 0 7 50 -1 -1 0.000 0 0 7 0 0 5
7500 6900 7500 6150 6000 6150 6000 6900 7500 6900
4 1 0 50 -1 4 14 0.0000 0 180 1455 6750 6450 Endorsement\001
4 1 0 50 -1 4 14 0.0000 0 225 420 6750 6750 Key\001
-6
6 450 6150 1950 6900
6 450 6225 1950 6750
4 1 0 50 -1 4 14 0.0000 0 180 1425 1200 6450 Manufacturer\001
4 1 0 50 -1 4 14 0.0000 0 180 345 1200 6750 CA\001
-6
2 4 0 1 0 7 50 -1 -1 0.000 0 0 7 0 0 5
1950 6900 1950 6150 450 6150 450 6900 1950 6900
-6
6 2625 6075 3225 6900
1 4 0 1 0 7 50 -1 -1 0.000 1 0.0000 3075 6225 106 106 3150 6150 3000 6300
1 3 0 1 0 7 50 -1 -1 0.000 1 0.0000 3075 6225 75 75 3075 6225 3075 6150
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 6
3225 6075 3225 6900 2625 6900 2625 6225 2775 6075 3225 6075
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 3
2625 6225 2775 6225 2775 6075
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
3150 6300 3150 6450 3075 6375 3000 6450 3000 6300
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
2775 6525 3075 6525
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
2775 6600 3075 6600
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
2775 6675 3075 6675
-6
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
2 0 1.00 120.00 180.00
3225 6525 4200 6525
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
2 0 1.00 120.00 180.00
1950 6525 2625 6525
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
2 0 1.00 120.00 180.00
5400 6525 6000 6525
2 2 1 1 0 7 50 -1 -1 4.000 0 0 -1 0 0 5
4200 6375 5400 6375 5400 6675 4200 6675 4200 6375
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
3900 6000 7800 6000 7800 7050 3900 7050 3900 6000
4 1 0 50 -1 4 14 0.0000 0 225 975 4800 6600 key seed\001
4 1 0 50 -1 4 10 0.0000 0 120 315 5700 6375 KDF\001
4 1 0 50 -1 4 10 0.0000 0 120 315 2925 7125 Cert\001
4 0 0 50 -1 4 14 0.0000 0 180 510 3975 6975 TPM\001

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