From 5c8d7579e8ff752b05508a683b6f951ca71f9468 Mon Sep 17 00:00:00 2001 From: Michael Preisach Date: Wed, 28 Apr 2021 11:13:35 +0200 Subject: [PATCH] updated DAA description and background chapter --- thesis/02_concept.tex | 223 ++++++++++++++++++++++++++++++++++++++++-- thesis/MAIN.pdf | Bin 1870750 -> 1894084 bytes thesis/literature.bib | 17 +++- 3 files changed, 229 insertions(+), 11 deletions(-) diff --git a/thesis/02_concept.tex b/thesis/02_concept.tex index f6c2bee..80b157d 100644 --- a/thesis/02_concept.tex +++ b/thesis/02_concept.tex @@ -132,7 +132,7 @@ IMA comes with three property variables which set the behaviour of the architect \end{itemize} These settings will be discussed in more detail in the following. -\subsubsection{Integrity Log}% +\subsection{Integrity Log}% \label{ssub:integrity_log} IMA uses the emph{integrity log} do keep track of any changes of local filesystem resources. @@ -162,7 +162,7 @@ The only difference between these formats lie in the used and logged metadata: The older template \texttt{ima} uses only SHA1 and is fully replaceyble with the \texttt{ima-ng} template. Therefore, it should not be used for newer applications. \ToDo{boot aggregate beschreiben} -\subsubsection{IMA Appraisal}% +\subsection{IMA Appraisal}% \label{ssub:ima_appraisal} IMA comes with four different runtime modes. @@ -172,21 +172,224 @@ These modes set the behaviour especially when there exists no additional informa \item \texttt{log}: Integrity measurements are done for all relevant resources and the integrity log is filled accordingly. \item \texttt{fix}: In addition to writing the log file, the filedata hashes are also written as extended file attribute into the file system. This is required for the last mode to work. - \item \texttt{enforce}: Only files that have a valid hash value are allowed to be read. - Accessing a resource without a hash or an invalid hash will be blocked by the kernel. + \item \texttt{enforce}: Only files with a valid hash value are allowed to be read. + Accessing a static resource without a hash or an invalid hash will be blocked by the kernel. \end{itemize} -\subsubsection{IMA Policies}% +\subsection{IMA Policies}% \label{ssub:ima_policies} +The IMA policies define which resources are targeted with IMA. +There exist three template policies which can be used concurrently: +\begin{itemize} + \item \texttt{tcb}: All files owned by root will be measured. + \item \texttt{appraise\_tcb}: All executables which are run, all files mapped in memory for execution, all loaded Kernel modules and all files opened for read by root will be measured by IMA. + \item \texttt{secure\_boot}: All loaded modules, firmwares, executed Kernels and IMA policies are checked. Therefore these resources need to have a provable signature to pass the check. The corresponding public key must be provided by the system manufacturere within the provided firmware or as Machine Owner Key in shim. +\end{itemize} +In addition to these templates, the system owner can define custom policies. +Some example policies can be found at the Gentoo Wiki\footnote{\url{https://wiki.gentoo.org/wiki/Integrity_Measurement_Architecture/Recipes}}. +It is, for example, useful to exclude constantly changing log files from being measured to reduce useless in the measurement log. - -\subsubsection{IMA extensions}% +\subsection{IMA extensions}% \label{ssub:ima_extensions} +\section{Direct Anonymous Attestation}% +\label{sec:direct_anonymous_attestation} +\emph{Direct Anonymous Attestation} (DAA) is a cryptographic scheme which makes use of the functions provided by the TPM. +DAA implements the concept of group signatures, where multiple secret keys can create a corresponding signature. +These signatures can be verified with a single public key, when these private keys are member of the same group. + +The scientific community is researching on TPM-backed DAA since the first standard of TPM went public in 2004. +Since then many different approaches of DAA were discussed. +According to the discussion in \cite{camenisch16} and \cite{camenisch17} almost all schemes were proven insecure, since many of them had bugs in the protocol or allowed trivial public\,/\,secret key pairs. +This includes also the impementation of DAA im the TPM1.2 standard. + +This section describes the concept of Camenisch et. al.\cite{camenisch16} including the cryptographic elements used for DAA. +Unlike the description in the original paper, we describe the practical approach, which will be used in the following concept. + +\subsection{Mathematical Foundations} + The following definitions form the mathematical building blocks for DAA. + It is noteworthy that these definitions work with RSA encryption as well as with \emph{Elliptic Curve Cryptography} (ECC). + + \subsubsection{Discrete Logarithm Problem} + Given a cyclic group $G = \langle g\rangle$ of order $n$, the discrete logarithm of $y\in G$ to the base $g$ is the smallest positive integer $\alpha$ satisfying + \begin{math} + g^\alpha = y + \end{math} + if this $x$ exists. + For sufficiently large $n$ and properly chosen $G$ and $g$, it is infeasible to compute the reverse + \begin{math} + \alpha = \log_g{y} + \end{math}. + This problem is known as \emph{Discrete Logarithm Problem} and is the basis for the following cryptographic algorithms. + + \subsubsection{Signature Proof of Knowledge (SPK)} + A SPK is a signature of a message which proof that the creator of this signature is in possession of a certain secret. + The secret itself is never revealed to any other party + Thus, this algorithm is a \emph{Zero Knowledge Proof of Knowledge} (ZPK). + + Camenisch and Stadler\cite{camenisch97} introduced the algorithm based on the Schnorr Signature Scheme. + It only assumes a collision resistant hash function $\mathcal{H}:\{0,1\}^*\rightarrow\{0,1\}^k$ for signature creation. + For instance, + \begin{equation*} + SPK\{(\alpha):y=g^\alpha\}(m) + \end{equation*} + denotes a proof of knowledge of the secret $\alpha$, which is embedded in the signature of message $m$. + The one-way protocol consists of three procedures: + \begin{enumerate} + \item \emph{Setup.} Let $m$ be a message to be signed, $\alpha$ be a secret and $y:=g^\alpha$ be the corresponding public representation. + \item \emph{Sign.} Choose a random number $r$ and create the signature tuple $(c,s)$ as + \begin{equation*} + c:=\mathcal{H}(m\,||\,y\,||\,g\,||\,g^r) \quad\text{and}\quad s:=r-c\alpha \quad\text{(mod n) .} + \end{equation*} -\ToDo{file signature, ima-appraise, enforcing ima} -\ToDo{Überleitung zu IMA und IMA beschreiben. Danach DAA theoretisch beschreiben, kopie aus dem Seminarpaper} - + \item \emph{Verify.} The verifier knows the values of $y$ and $g$, as they are usually public. The message $m$ comes with the signature values $c$ and $s$. She computes the value + \begin{equation*} + c':=\mathcal{H}(m\,||\,y\,||\,g\,||\,g^sy^c)\quad\text{and verifies, that}\quad c' = c\, . + \end{equation*} + The verification holds since + \begin{equation*} + g^sy^c = g^rg^{-c\alpha}g^{c\alpha} = g^r\, . + \end{equation*} + \end{enumerate} + This scheme is extensible to proof knowledge of arbitrary number of secrets as well as more complex relations between secret and public values. + + \subsubsection{Bilinear Maps} + \label{ssec:bilinear-maps} + Bilinear Mapr define a special property for mathematical groups which form the basis for verifying the signatures in DAA. + Consider three mathematical groups $\mathbb{G}_1$, $\mathbb{G}_2$, with their corresponding base points $g_1$, $g_2$, and $\mathbb{G}_T$. + Let $e:\mathbb{G}_1 \times \mathbb{G}_2 \rightarrow \mathbb{G}_T$ that satisfies three properties\cite{camenisch04,camenisch16}: + \begin{itemize} + \item \emph{Bilinearity.} For all $P\in\mathbb{G}_1, Q\in\mathbb{G}_2$, for all $a,b \in\mathbb{Z}: e(P^a,Q^b) = e(P,Q)^{ab}$. + \item \emph{Non-degeneracy.} For all generators $g1\in\mathbb{G}_1, g2\in\mathbb{G}_2: e(g_1,g_2)$ generates $\mathbb{G}_T$. + \item \emph{Efficiency.} There exists an efficient algorithm that outputs the bilinear group\\ + $(q, \mathbb{G}_1,\mathbb{G}_2,\mathbb{G}_T, e, g_1, g_2)$ and an efficient algorithm for computing $e$. + \end{itemize} + + \subsubsection{Camenisch-Lysyanskaya Signature Scheme} + The Camenisch-Lysyanskaya (CL) Signature Scheme\cite{camenisch04} is based on the LRSW-assumption and allows efficient proofs for signature posession and is the basis for the DAA scheme discussed below. + It is based on a bilinear group $(q, \mathbb{G}_1,\mathbb{G}_2,\mathbb{G}_T, e, g_1, g_2)$ that is available to all steps in the protocol. + \begin{itemize} + \item \emph{Setup.} Choose $x\leftarrow\mathbb{Z}_q$ and $y\leftarrow\mathbb{Z}_q$ at random. Set the secret key $sk \leftarrow (x,y)$ and the public key $pk \leftarrow (g_2^x, g_2^y)=(X,Y)$ + \item \emph{Sign.} Given a message $m$, and the secret key $sk$, choose $a$ at random and output the signature $\sigma\leftarrow(a, a^y, a^{x+xym}) = (a,b,c)$ + \item \emph{Verify.} Given message $m$, signature $\sigma$ and public key $pk$, verify, that $a \neq 1_{\mathbb{G}_1}$, $e(a,Y) = e(b,g_2)$ and $e(a,X)\cdot e(b,X)^m = e(c,g_2)$ + \end{itemize} + Camenisch et al.\@ stated in section 4.2 of their paper\cite{camenisch16} that one has to verify the equation against $e(g_1,b)$ and $e(g_1,c)$ which is not correct. + + \subsection{DAA Protocol on LRSW Assumption} + \label{ssec:daa-protocol-on-lrsw-assumption} %TODO extend security properties according to Camenisch + DAA is a group signature protocol, which aims with a supporting TPM to reveal no additional information about the signing host besides content and validity of the signed message $m$. + According to Camenisch et.\@ al.\cite{camenisch16}, the DAA protocol consists of three parties: + \begin{itemize} + \item \emph{Issuer} \issuer. The issuer maintains a group and has evidence of hosts that are members in this group. This role equals the group manager of Bellare's generic definition. + \item \emph{Host} \host. The Host creates a platform with the corresponding TPM \tpm{}. Membership of groups are maintained by the TPM. + Compared to Bellare et.\@ al., the role of a member is split into two cooperating parties, the key owner (TPM, passive) and the message author (Host, active). + \item \emph{Verifier} \verifier. A verifier can check whether a Host with its TPM is in a group or not. Besides the group membership, no additional information is provided. + \end{itemize} + A certificate authority $\mathcal{F}_{ca}$ is providing a certificate for the issuer itself. + The basename \texttt{bsn} is some clear text string, whereas \texttt{nym} represent the encrypted basename $bsn^{gsk}$. + $\mathcal{L}$ is the list of registered group members which is maintained by \issuer. + The paper of Camenisch et.\@ al.\cite{camenisch16} introduces further variables that are necessary for their proof of correctness. + These extensions were omitted in the following to understand the protocol more easily. + \begin{itemize} + \item \emph{Setup.} During Setup \issuer{} is generating the issuer secret key $isk$ and the corresponding issuer public key $ipk$. The public key is published and assumed to be known to everyone. + \begin{enumerate} + \item On input \textsf{SETUP} \issuer + \begin{itemize} + \item generates $x,y \leftarrow \mathbb{Z}_q$ and sets $isk=(x.y)$ and $ipk\leftarrow(g_2^x,g_2^y) = (X,Y)$. Initialize $\mathcal{L} \leftarrow \emptyset$, + \item generates a prove $\pi \sassign SPK\{(x,y):X=g_2^x\wedge Y=g_2^y\}$ that the key pair is well formed, + \item registers the public key $(X,Y,\pi)$ at $\mathcal{F}_{ca}$ and stores the secret key, + \item outputs \textsf{SETUPDONE} + \end{itemize} + \end{enumerate} + \item \emph{Join.} When a platform, consisting of host \host[j] and TPM \tpm[i], wants to become a member of the issuer's group, it joins the group by authenticating to the issuer \issuer. + \begin{enumerate} + \item On input \textsf{JOIN}, host \host[j] sends the message \textsf{JOIN} to \issuer. + \item \issuer\ upon receiving \textsf{JOIN} from \host[j], chooses a fresh nonce $n\leftarrow\{0,1\}^\tau$ and sends it back to \host[j]. + \item \host[j] upon receiving $n$ from \issuer, forwards $n$ to \tpm[i] + \item \tpm[i] generates the secret key: + \begin{itemize} + \item Check, that no completed key record exists. Otherwise, it is already a member of that group. + \item Choose $gsk\sassign\mathbb{Z}_q$ and store the key as $(gsk, \bot)$. + \item Set $Q \leftarrow g_1^{gsk}$ and compute $\pi_1 \sassign SPK\{(gsk):Q=g_1^{gsk}\}(n)$. + \item Return $(Q,\pi_1)$ to \host[j]. + \end{itemize} + \item \host[j] forwards \textsf{JOINPROCEED}$(Q, \pi_1)$ to \issuer. + \item \issuer\ upon input \textsf{JOINPROCEED}$(Q, \pi_1)$ creates the CL-credential: + \begin{itemize} + \item Verify that $\pi_1$ is correct. + \item Add \tpm[i] to $\mathcal{L}$. %TODO what is the representative of the TPM? + \item Choose $r\sassign\mathbb{Z}_q$ and compute $a\leftarrow g_1^r$, $b\leftarrow a^y$, $c\leftarrow a^x\cdot Q^{rxy}$, $d\leftarrow Q^{ry}$. + \item Create the prove $\pi_2\sassign SPK\{(t):b=g_1^t\wedge d=Q^t\}$. + \item Send \textsf{APPEND}$(a,b,c,d,\pi_2)$ to \host[j] + \end{itemize} + \item \host[j] upon receiving \textsf{APPEND}$(a,b,c,d,\pi_2)$ + \begin{itemize} + \item verifies, that $a\neq 1$, $e(a,Y)=e(b,g_2)$ and $e(c,g_2) = e(a\cdot d, X)$. + \item forwards $(b,d,\pi_2)$ to \tpm[i]. + \end{itemize} + \item \tpm[i] receives $(b,d,\pi_2)$ and verifies $\pi_2$. The join is completed after the record is extended to $(gsk, (b,d))$. \tpm[i] returns \textsf{JOINED} to \host[j]. + \item \host[j] stores $(a,b,c,d)$ and outputs \textsf{JOINED}. + \end{enumerate} + \item \emph{Sign.} + After joining the group, a host \host[j] and TPM \tpm[i] can sign a message $m$ with respect to basename \texttt{bsn}. + \begin{enumerate} + \item \host[j] upon input \textsf{SIGN}$(m,\bsn)$ re-randomizes the CL-credential: + \begin{itemize} + \item Retrieve the join record $(a,b,c,d)$ and choose $r\sassign\mathbb{Z}_q$. \\ + Set $(a',b',c',d') \leftarrow (a^r,b^r,c^r,d^r)$. + \item Send $(m, \bsn, r)$ to \tpm[i] and store $(a',b',c',d')$. + \end{itemize} + \item \tpm[i] upon receiving $(m, \bsn, r)$ + \begin{itemize} + \item checks, that a complete join record $(gsk, (b,d))$ exists, and + \item stores $(m, \bsn, r)$. + \end{itemize} + \item \tpm[i] completes the signature after it gets permission to do so. %TODO Why? + \begin{itemize} + \item Retrieve group record $(gsk, (b,d))$ and message record $(m, \bsn, r)$. + \item Compute $b'\leftarrow b^r, d'\leftarrow d^r$. + \item If $\bsn = \bot$ set $\nym \leftarrow\bot$ and compute \\ + $\pi \sassign SPK\{(gsk):d'=b'^{gsk}\}(m, \bsn)$ + \item If $\bsn \neq \bot$ set $\nym\leftarrow H_1(\bsn)^{gsk}$ and compute \\ + $\pi \sassign SPK\{(gsk):\nym=H_1(\bsn)^{gsk}\wedge d'=b'^{gsk}\}(m, \bsn)$. + \item Send $(\pi,\nym)$ to \host[j]. + \end{itemize} + \item \host[j] assembles the signature $\sigma \leftarrow (a', b', c', d', \pi, \nym)$ and outputs \textsf{SIGNATURE}$(\sigma)$ + \end{enumerate} + \item \emph{Verify.} + Given a signed message, everyone can check whether the signature with respect to \bsn\ is valid and the signer is member of this group. + Furthermore a revocation list \RL\ holds the private keys of corrupted TPMs, whose signatures are no longer accepted. + \begin{enumerate} + \item \verifier\ upon input \textsf{VERIFY}$(m, \bsn, \sigma)$ + \begin{itemize} + \item parses $\sigma\leftarrow(a,b,c,d,\pi,\nym)$, + \item verifies $\pi$ with respect to $(m,\bsn)$ and \nym if $\bsn\neq\bot$. + \item checks, that $a\neq 1$, $b\neq 1$ $e(a,Y)=e(b, g_2)$ and $e(c,g_2)=e(a\cdot d,X)$, + \item checks, that for every $gsk_i \in \RL: b^{gsk_i} \neq d$, + \item sets $f\leftarrow 1$ if all test pass, otherwise $f\leftarrow 0$, and + \item outputs \textsf{VERIFIED}$(f)$. + \end{itemize} + \end{enumerate} + \item \emph{Link.} + After proving validity of the signature, the verifier can test, whether two different messages with the same basename $\bsn \neq\bot$ are generated from the same TPM. + \begin{enumerate} + \item \verifier\ on input \textsf{LINK}$(\sigma, m, \sigma', m', bsn)$ verifies the signatures and compares the pseudonyms contained in $\sigma, \sigma'$: + \begin{itemize} + \item Check, that $\bsn\neq\bot$ and that both signatures $\sigma, \sigma'$ are valid. + \item Parse the signatures $\sigma\leftarrow(a,b,c,d,\pi,\nym)$, $\sigma'\leftarrow(a',b',c',d',\pi',\nym')$ + \item If $\nym = \nym'$, set $f\leftarrow 1$, otherwise $f\leftarrow 0$. + \item Output \textsf{LINK}$(f)$ + \end{itemize} + \end{enumerate} + \end{itemize} + + Camenisch et.\@ al.\cite{camenisch16} extend with their concept the general group concept scheme. + The feature of linking messages together requires further security features within the DAA scheme, which the authors also prove in their paper along with the other properties of the scheme: + \begin{itemize} + \item \emph{Non-frameability}: No one can create signatures that the Platform never signed, but that link to messages signed from that Platform. + \item \emph{Correctness of link}: Two signatures will link when the honest platform signs it with the same basename. + \item \emph{Symmetry of Link}: Id does not matter in which order the linked signatures will be proven. The link algorithm will always output the same result. + \end{itemize} \chapter{Concept} \label{cha:concept} diff --git a/thesis/MAIN.pdf b/thesis/MAIN.pdf index bfd149299fb0553648f1deaccd4b34f1f4567ecb..a14c15b47e41a53221cd74b17c21cb22c449f33a 100644 GIT binary patch delta 248108 zcmY(KQ*b80*0uA-wr$(VBoo`VZF7>mv2EM7ZCev#V%wQ-&N=_hfALiH#j5JA>Z<&Q%|H?n#=>vQ z{r2#*JSgMh6+@+EO#a#WdtaY3T!oaPPVpl!nKU~^vN4n$HHjvNf*dabnyn~xxwvDsUf;L%^SR>T`A}s^M!c z-0bTaxs!#*x(WvOC6$Q?Wh+@;Jxg*=mb(l8jOq>u3bP92WNA~i(JQMkJNQ0}ivwH6 zF-YL^_f^b;BZP_T+$z#9NA_uGyPC?RCcWXEneN~(og7~<$;<_91q^S+hTOW{t?4IBnOC-m%CpX4bc_;kO3kYjD;X?~;xv{XLpMFRPs=W$EEYn)ESHcN zJy)zk91Hl(AY%>Xyp2nNH9_bTSTlQ57uU2fZ7js5u3S_I)T%<`Reg)|Re82i_7N4?r4~D77o$VX%`U$P6cVy9AQ?m)IXLKsvy; zCrJ){Piz4HO-LSJ65N5uOSDY^E1B4-BD(1Qdg%-ZDj@tc{`Su!vaLq@0EQgQN@FDr z{MJc@geH$B!IiZKGh#aMH;OMNMxb2UGkFbSwANZydmQ_7QuDSAj!X^;ZAk@UPLU}{ zpLsJ#9STx#+gLsYU0RUK_@I4eY*)Ky5=|mDxV7CUI@u{Bm}(drgnba4=$*y9|Kz#1Xk|1kTV-;|(MDUilVx`XXMKc8IkULC3BGStbonXn1@w~(jmr18zM 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