\documentclass{article}
\usepackage{../style}
\usepackage{../langs}
\usetikzlibrary{patterns,decorations.pathreplacing}

\begin{document}

\section*{Handout 5 (Protocols)}

Protocols are the computer science equivalent to fractals and
the Mandelbrot set in mathematics. With the latter you have a
simple formula which you just iterate and then you test
whether a point is inside or outside a region, and voila
something magically
happened.\footnote{\url{http://en.wikipedia.org/wiki/Fractal},
\url{http://en.wikipedia.org/wiki/Mandelbrot_set}} Protocols
are similar: they are simple exchanges of messages, but in the
end something ``magical'' can happen---for example a secret
channel has been established or two entities have
authenticated themselves to each other. The problem with magic
is of course it is poorly understood and even experts often
got, and get, it wrong with protocols. 

To have an idea what kind of protocols we are interested, let
us look at a few examples. One example are (wireless) key 
fobs which operate the central locking system and the
ignition in a car.

\begin{center}
\includegraphics[scale=0.075]{../pics/keyfob.jpg}
\quad
\includegraphics[scale=0.2025]{../pics/startstop.jpg}
\end{center}

\noindent The point of these key fobs is that everything is
done over the ``air''---there is no physical connection
between the key, doors and engine. So we must achieve security
by exchanging certain messages between the key fob on one side
and doors and engine on the other. Clearly what we like to
achieve is that I can get into my car and start it, but that
thieves are kept out. The problem is that everybody can
``overhear'' or skim the exchange of messages between the key
fob and car. In this scenario the simplest attack you need to
defend against is a person-in-the-middle attack. Imagine you
park your car in front of a supermarket. One thief follows you
with a strong transmitter. A second thief ``listens'' to the
signal from the car and wirelessly transmits it to the
``colleague'' who followed you and who silently enquires about
the answer from the key fob. The answer is then send back to
the thief at the car, which then dutifully opens and possibly
starts. No need to steal your key anymore.

But there are many more such protocols we like to consider.
Other examples are wifi---you might sit at a Starbucks and
talk wirelessly to the free access point there and from there
talk with your bank, for example. Also even if your have to
touch your Oyster card at the reader each time you enter and
exit the Tube, it actually operates wirelessly and with
appropriate equipment over some quite large distance. But
there are many many more examples (Bitcoins, mobile
phones,\ldots). The common characteristics of the protocols we
are interested in here is that an adversary or attacker is
assumed to be in complete control over the network or channel
over which you exchanging messages. An attacker can install a
packet sniffer on a network, inject packets, modify packets,
replay old messages, or fake pretty much everything. In this
hostile environment, the purpose of protocols (that is
exchange of messages) is to achieve some security goal, for
example only allow the owner of the car in but everybody else
should be kept out.

The protocols we are interested here are generic descriptions
of how to exchange messages in order to achieve a goal, be it
establishing a mutual secure connection or being able to
authenticate to a system. Unlike the distant past where for
example we had to meet a person in order to authenticate him
or her (via a passport for example), the problem we are facing
on the Internet is that we cannot easily be sure who we are
``talking'' to. The obvious reason is that only some electrons
arrive at our computer; we do not see the person, or computer,
behind the incoming electrons (messages). 

To start, let us look at one of the simplest protocols that
are part of the TCP protocol (which underlies the Internet).
This protocol does not do anything security relevant, it just
establishes a ``hello'' from a client to a server which the
server answers with ``I heard you'' and the client answers 
in turn with something like ``thanks''. This protocol
is often called a \emph{three-way handshake}. Graphically it
can be illustrated as follows

\begin{center}
\includegraphics[scale=0.5]{../pics/handshake.png}
\end{center}

\noindent On the left-hand side is a client, say Alice, on the
right-hand side is a server, say. Time is running from top to
bottom. Alice initial SYN message needs some time to travel to
the server. The server answers with SYN-ACK, which will
require some time to arrive at Alice. Her answer ACK will
again take some time to arrive at the server. After the 
messages are exchanged Alice and the server simply have 
established a channel to communicate over. Alice does
not know whether she is really talking to the server (somebody 
else on the network might have intercepted her message
and replied in place of the server). Similarly, the
server has no idea who it is talking to. That this can be 
established depends on what is exchanged next and is the
point of the protocols we want to study in more detail.

Before we start in earnest, we need to fix a more
convenient notation for protocols. Drawing pictures like
the one above would be awkward in the long-run. The
notation already abstracts away from a few details we are
not interested in: for example the time the messages
need to travel between endpoints. What we are interested
in is in which order the messages are sent. For the SYN-ACK
protocol we will therefore use the notation 


\begin{equation}
\begin{array}{l@{\hspace{2mm}}l}
A \to S: & SYN\\
S \to A: & SYN\_ACK\\
A \to S: & ACK\\
\end{array}\label{SYNACK}
\end{equation}


\noindent The left-hand side specifies who is the sender and
who is the receiver of the message. On the right of the colon
is the message that is send. The order from top to down
specifies in which order the messages are sent. We also
have the convention that messages like above $SYN$ are send
in clear-text over the network. If we want that a message is 
encrypted, then we use the notation

\[
\{msg\}_{K_{AB}}
\]  
  
  
\noindent for messages. The curly braces indicate a kind of
envelope which can only be opened if you know the key $K_{AB}$
with which the message has been encrypted. We always assume
that an attacker, say Eve, cannot get the content of the
message, unless she is also in the possession of the key. We
explicitly exclude in our study that the encryption can be
broken.\footnote{\ldots{}which of course is what a good
protocol designer needs to ensure and more often than not
protocols are broken. For example Oyster cards contain a very
weak encryption mechanism which has been attacked.} It is also
possible that an encrypted message contains several parts. In
this case we would write something like

\[
\{msg_1, msg_2\}_{K_{AB}}
\] 

\noindent But again Eve would not be able to know 
this unless she also has the key. We also allow the 
possibility that a message is encrypted twice under 
different keys. In this case we write

\[
\{\{msg\}_{K_{AB}}\}_{K_{BC}}
\] 

\noindent The idea is that even if attacker Eve has the
key $K_{BC}$ she could decrypt the outer envelop, but
still do not get to the message, because it is still
encrypted with the key $K_{AB}$. Note, however,
while an attacker cannot obtain the content of the message
without the key, encrypted messages can be observed
and be recorded and then replayed at another time, or
send to another person!

Another very important point is that the notation for
protocols such as shown in \eqref{SYNACK} is a
\underline{schema} how the protocol should proceed.
It could be instantiated by an actual protocol run
between Alice, say, and the server Calcium at King's. In this 
case the specific instance would look like

\[
\begin{array}{l@{\hspace{2mm}}l}
\text{Alice} \to \text{Calcium}: & SYN\\
\text{Calcium} \to \text{Alice}: & SYN\_ACK\\
\text{Alice} \to \text{Calcium}: & ACK\\
\end{array}
\]

\noindent But a server like Calcium of course needs to
serve many clients. So there could be the same protocol
also running with Bob, say

\[
\begin{array}{l@{\hspace{2mm}}l}
\text{Bob} \to \text{Calcium}: & SYN\\
\text{Calcium} \to \text{Bob}: & SYN\_ACK\\
\text{Bob} \to \text{Calcium}: & ACK\\
\end{array}
\]

\noindent And these two instances of the protocol could be
running in parallel or be at different stages. So the protocol
schema shown in \eqref{SYNACK} can be thought of how two 
programs need to run on the side of $A$ and $S$ in order to 
successfully complete the protocol. But it is really just a 
blue print how the communication is supposed to proceed. 

This is actually already a way how such protocols can fail. 
Although very simple the $SYN\_ACK$ protocol can cause 
headaches for system administrators where an attacker
starts the protocol, but does not complete it. This looks 
graphically like

\begin{center}
\includegraphics[scale=0.4]{../pics/synflood.png}
\end{center}

\noindent The attacker sends lots of $SYN$ requests which the
server dutifully answers, but needs to keep track of such
protocol exchanges. So every time a little bit of memory
resource will be eaten away on the server side until all
resources are exhausted and when Alice tries to contact the
server then the server is overwhelmed and does not respond
anymore. This kind of attack are called \emph{SYN
floods}.\footnote{\url{http://en.wikipedia.org/wiki/SYN_flood}}

After reading four pages, you might be wondering where the
magic is. For this let us take a closer look at authentication 
protocols.

\subsubsection*{Authentication Protocols}

The simplest authentication protocol between principals
$A$ and $B$, say is

\begin{center}
$A \to B: K_{AB}$ 
\end{center}

\noindent It can be sought of as $A$ sends a common secret to
$B$ like a password. The idea is that if only $A$ and $B$ know
the key $K_{AB}$ then this should be sufficient for $B$ to
infer it is talking to $A$. But this is of course too naive,
if the message can be observed by everybody else on the
network. Eve could just record this message $A$ just send, and
next time send the same message to $B$ and $B$ would believe
it talked to $A$. But actually it talked to Eve which now
clears out $A$s back account if $B$ had been a bank.

A more sophisticated protocol which tries to avoid the
replay attack is as follows

\begin{center}
\begin{tabular}{l@{\hspace{2mm}}l}
$A \to B:$ & $HELLO$\\
$B \to A:$ & $N$\\
$A \to B:$ & $\{N\}_{K_{AB}}$\\
\end{tabular}
\end{center} 

\noindent With this protocol the idea is that $A$ first sends 
a message to $B$ saying ``I want to talk to you''. $B$ sends 
then a challenge in form of a random number $N$. In protocols 
such random numbers are often called \emph{nonce}. What is the
purpose of this nonce? Well, if an attacker records $A$ 
answer, it will not make sense to replay this message, because
next time this protocol is run the nonce $B$ sends will be
different. So if we run this protocol, what can $B$ infer:
it has send out an (unpredictable) nonce to $A$ and
received this challenge back, but encoded under the key 
$K_{AB}$. If $B$ assumes only $A$ and $B$ know the key $K_{AB}$
and the nonce is unpredictable, then $B$ is able to
infer it must be talking to $A$. Of course the implicit 
assumption on this inference are that nobody else knows
about the key $K_{AB}$ and nobody else can decrypt the
message. $B$ of course can decrypt the answer from $A$
and check whether the answer corresponds to the challenge
(nonce) $B$ has send earlier.

But what about $A$? Can $A$ make any assumptions about who it
talks to? It dutifully answered the challenge and hopes its
bank, say, will be the only one to understand her answer. But
is this the case? No! Lets consider an attacker Eve who has
control over the network. She could have intercepted the
message $HELLO$ and just replied herself to $A$ using a random
number\ldots{} for example one which she observed in a
previous run of this protocol. Remember that if a message is
send without curly braces it is sent in clear text. Then
$A$ would encrypt the nonce with the key $K_{AB}$ and send
it back to Eve. She just throws the answer away. $A$ would
hope that she talked to $B$ because she followed the protocol,
but unfortunately she cannot be sure who she is talking to. 

The solution is to follow a \emph{mutual challenge-response}
protocol. There $A$ already starts off with a challenge (nonce)
on her own.

\begin{center}
\begin{tabular}{l@{\hspace{2mm}}l}
$A \to B:$ & $N_A$\\
$B \to A:$ & $\{N_A, N_B\}_{K_{AB}}$\\
$A \to B:$ & $N_B$\\
\end{tabular} 
\end{center}

\noindent As seen, $B$ receives this nonce, $N_A$, adds his
own nonce, $N_B$ and encrypts it with the key $K_{AB}$. $A$
receives this message, is able to decrypt it since we assume
she has the key $K_{AB}$, and sends back the nonce of $B$.
Let us analyse which assumptions $A$ and $B$ can make after 
the protocol has run. $B$ received a challenge and answered 
correctly to $A$ (in the encrypted message). An attacker
would just not be able to answer this challenge correctly 
because the attacker is assumed to not be in the possession of
the key $K_{AB}$; so could not have formed this message.
It could also not have just replayed an old message, because
$A$ would send out each time a fresh nonce. So with this
protocol you can ensure also for $A$ that it talks to $B$.
I leave you to argue that $B$ can be sure to talk to $A$.
Of course these arguments will depend on the assumptions that
only $A$ and $B$ know the key $K_{AB}$ and that nobody can
break the encryption unless they have this key and that the
nonces are fresh each time the protocol is run.

There might be something mysterious about the nonces, the
random numbers, that are sent around. They need to be
unpredictable and in this way fulfil an important role in
protocols. Suppose

\begin{enumerate}
\item I generate a nonce and send it to you encrypted with a
      key we share
\item you increase it by one, encrypt it under a key I know
      and send it back to me 
\end{enumerate}

\noindent In our notation this would correspond to the 
protocol

\begin{center}
\begin{tabular}{l@{\hspace{2mm}}l}
$I \to Y:$ & $\{N\}_{K_{IY}}$\\
$Y \to I:$ & $\{N + 1\}_{K_{IY}}$\\
\end{tabular} 
\end{center}

\noindent What can I infer from this simple exchange:

\begin{itemize}
\item you must have received my message (it could not just be
      deflected by somebody on the network, because the
      response required some calculation; doing the
      calculation and sending the answer requires the key
      $K_{IY}$)

\item you could only have generated your answer after I send
      you my initial message (since my $N$ is always new, it
      could not have been a message that was generated before
      I myself knew what $N$ is)

\item if only you and me know the key $K_{IY$, the message
      must have come from you
\end{itemize}

\noindent Even if this does not seem much information I can
glean from such an exchange, it is in fact the basic building 
blocks for establishing some secret or achieving some 
security goal (like authentication).

While the mutual challenge-response protocol solves already
the authentication problem, there are some problems. One is of
course that it requires a pre-shared secret key. That is
something that needs to be established beforehand. Not all
situations allow such an assumption. For example if I am a
whistle blower (say Snowden) and want to talk to a journalist
(say Greenwald) then I might not have a secret pre-shared key.


Another problem is that such mutual challenge-response systems
often work in the same system in the ``challenge mode'' but
also in the ``response mode''. For example if two servers want
to talk to each other---they would need the protocol in
response mode, but also if they want to talk to other servers
in challenge mode. Similarly if you in an military aircraft
you have to challenge everybody you see, in case there is a
friend amongst the targets you like to shoot, but you also
have to respond to any of your own anti-aircraft guns on the
ground lest they shoot you. In these situations you have to be
careful to not decode, or answer, your own challenge. Recall 
the protocol is

\begin{center}
\begin{tabular}{l@{\hspace{2mm}}l}
$A \rightarrow B$: & $N_A$\\  
$B \rightarrow A$: & $\{N_A, N_B\}_{K_{AB}}$\\
$A \rightarrow B$: & $N_B$\\
\end{tabular}
\end{center}

\noindent but it does not specify who is $A$ and who is $B$.
If, as supposed, the protocol works in response and in 
challenge mode, then $A$ will be $A$ in one instance, but $B$
in the other. I hope this makes sense. Let us look at the 
details and lets assume our adversary is $E$ who just deflects
our messages back to us. 

\begin{center}
\begin{tabular}{lllll}
& \multicolumn{2}{l}{challenge mode:} & 
\multicolumn{2}{l}{response mode:}\smallskip\\
1) & $A \rightarrow E$: & $N_A$\\ 
2) & & & $E \rightarrow A$: & $N_A$\\ 
3) & & & $A \rightarrow E$: & $\{N_A, N_A'\}_{K_{AB}}$\\
4) & $E \rightarrow A$: & $\{N_A, N_A'\}_{K_{AB}}$\\
5) & $A \rightarrow E$: & $N_A'$\\
\end{tabular}
\end{center}

\noindent In the first step we challenge $E$ with a nonce we
created. Since we also run the protocol in ``response mode'',
$E$ can now feed us the same challenge in step 2. We do not
know where it came from (it's over the air), but if we are in
an aircraft we should better quickly answer it, otherwise we
risk to be shot. So we add our own challenge $N'_A$ and
encrypt it under the secret key $K_{AB}$ (step 3). Now $E$
does not need to know this key in order to form the correct
answer for the first protocol. It will just replays this
message back to us in the challenge mode (step 4). I happily
accept this message---after all it is encrypted under the
secret key $K_{AB}$ and it contains the correct challenge from
me, namely $N_A$. So I accept that $E$ is a friend and send
even back the challenge $N'_A$. The problem is that $E$ now
starts firing at me and I have no clue what is going on. I
might suspect, erroneously, that an idiot must have leaked the
secret key. Because I followed in both cases the protocol to
the letter, but somehow $E$, unknowingly to me with my help,
managed to disguise as a friend. As a pilot, I would be a bit
peeved at that moment and would have preferred the designer of
this challenge-response protocol had been a tad smarter. For
one thing they violated the best practice in protocol design
of using the same key, $K_{AB}$, for two different
purposes---challenging and responding. They better had used
two different keys. This would have averted this attack and
would have saved me a lot of trouble.

\subsubsection*{Trusted Third Parties}

One limitation the protocols we discussed so far is
that they pre-suppose a secret shared key. As already 
mentioned, this is a convenience we cannot always assume.
How to establish a secret key then? Well, if both parties,
say $A$ and $B$, mutually trust a third party, say $S$, 
then they can use the following protocol:

\begin{center}
\begin{tabular}{l@{\hspace{2mm}}l}
$A \to S :$ & $A, B$\\
$S \to A :$ & $\{K_{AB}\}_{K_{AS}}$ and $\{\{K_{AB}\}_{K_{BS}} \}_{K_{AS}}$\\
$A \to B :$ & $\{K_{AB}\}_{K_{BS}}$\\
$A \to B :$ & $\{m\}_{K_{AB}}$\\
\end{tabular}
\end{center}

\noindent The assumption in this protocol is that $A$ and $S$
share a secret key, and also $B$ and $S$ ($S$ being the
trusted third party). The goal is that $A$ can send $B$ a
message $m$ under a shared secret key $K_{AB}$, which at the
beginning of the protocol does not exist yet. How does this
protocol work? In the first step $A$ contacts $S$ and says
that it wants to talk to $B$. In turn $S$ invents a new key
$K_{AB}$ and sends two messages back to $A$: one message is
$\{K_{AB}\}_{K_{AS}}$ which is encrypted with the key $A$ and
$S$ share, and also the message
$\{\{K_{AB}\}_{K_{BS}}\}_{K_{AS}}$. which is encrypted with
$K_{AB}$ but also a second time with $K_{BS}$. The point of
the second message is that it is a message intended for $B$.
So a receives both messages and can decrypt them---in the
first case it obtains the key $K_{AB}$ which $S$ suggested to
use. In the second case it obtains a message it can forward to
$B$. $B$ receives this message and since it knows the key it
shares with $S$ obtains the key $K_{AB}$. Now $A$ and $B$ can
start to exchange messages with the shared secret key
$K_{AB}$. What is the advantage of $S$ sending $A$ two 
messages instead of contacting $B$ instead? Well, for one
there can now be a time-delay between the second and
third step in the protocol. At some point in the past
$A$ and $S$ need to have come together to share
a key, similarly $B$ and $S$. After that $B$ does not need to
be ``online'' anymore until $A$ actually starts sending messages
to $B$. $A$ and $S$ can completely on their own negotiate a
new key. 

The major limitation of this protocol however is that I need
to trust a third party. And in this case completely, because
$S$ can of course also read easily all messages $A$ sends to
$B$. The problem is that I cannot really think of any
institution who could serve as such a trusted third party. One
would hope the government would be such a trusted party, but
in the Snowden-era we know that this is wishful thinking in
the West, and if I lived in Iran or North Korea, for example,
I would not even start to hope for this.

The cryptographic ``magic'' of public-private keys 
seems to offer an elegant solution for this, but as we shall 
see in the next section, this requires some very clever
protocol design.
 
\subsubsection*{Averting Person-in-the-Middle Attacks}

The idea of public-private key encryption is that one can make
public the key $K^{pub}$ which people can use to encrypt
messages for me. and I can use my key $K^{priv}$ to be the
only one that can decrypt them. While this sounds all good, it
relies that people can associate me, for example, with my
public key. That i snot so trivial as it sounds. For example,
if I would be the government, say Cameron, and try to find out
who are the trouble makers in the country, I would publish an
innocent looking webpage and say I am The Guardian newspaper
(or alternatively The Sun for all the juicy stories), publish
a public key on it, and then just wait for incoming messages. 

This problem is supposed to be solved by using certificates.
The purpose of certification organisations is that they verify
that a public key, say $K^{pub}_{Bob}$, really belongs to Bob.
This is also the mechanism underlying the HTTPS protocol. The
problem is that this system is essentially completely
broken\ldots{}but this is a story for another time. Suffice
to say for now that one of the main certification
organisations, VeriSign, has limited its liability to \$100 in
case it issues a false certificate. This is really a joke and
really the wrong incentive for the certification organisations
to clean up their mess.

The problem we want to study closer here is that protocols
based on public-private key encryption are susceptible to
person-in-the-middle attack. Consider the following protocol
where $A$ and $B$ attempt to exchange secret messages using
public-private keys. 

\begin{itemize}
\item $A$ sends public key  to $B$
\item $B$ sends public key  to $A$
\item $A$ sends a message encrypted with $B$'s public 
key,\\ $B$ decrypts it with its private key
\item $B$ sends a message encrypted with $A$'s public 
key,\\ $A$ decrypts it with its private key
\end{itemize}
  
\noindent In our formal notation for protocols, this would
look as follows:

\begin{center}
\begin{tabular}{l@{\hspace{2mm}}l}
$A \to B :$ & $K^{pub}_A$\smallskip\\
$B \to A :$ & $K^{pub}_B$\smallskip\\
$A \to B :$ & $\{A,m\}_{K^{pub}_B}$\smallskip\\
$B \to A :$ & $\{B,m'\}_{K^{pub}_A}$
\end{tabular}
\end{center}

\noindent Since we assume an attacker, say $E$, has complete
control over the network, $E$ can intercept the first two 
messages and substitutes her own public key. The protocol
run would therefore be

\begin{center}
\begin{tabular}{ll@{\hspace{2mm}}l}
1) & $A \to E :$ & $K^{pub}_A$\smallskip\\
2) & $E \to B :$ & $K^{pub}_E$\smallskip\\
3) & $B \to E :$ & $K^{pub}_B$\smallskip\\
4) & $E \to A :$ & $K^{pub}_E$\smallskip\\
5) & $A \to E :$ & $\{A,m\}_{K^{pub}_E}$\smallskip\\
6) & $E \to B :$ & $\{E,m\}_{K^{pub}_B}$\smallskip\\
7) & $B \to E :$ & $\{B,m'\}_{K^{pub}_E}$\smallskip\\
8) & $E \to A :$ & $\{E,m'\}_{K^{pub}_A}$
\end{tabular}
\end{center}

\noindent where in steps 6 and 8, $E$ can modify the
messages by including the $E$ in the message. Both messages
are received encrypted with $E$'s public key; therefore it
can decrypt it and repackage it with new content. $A$ and $B$
have no idea that they talking to an attacker. Because $E$
can modify messages, it seems very difficult to defend 
against this attack. 

But there is a clever trick\ldots{}dare I say some magic.
Modify the protocol above so that $A$ and $B$ send their 
messages in two halves.

\begin{center}
\begin{tabular}{ll@{\hspace{2mm}}l}
1) & $A \to B :$ & $K^{pub}_A$\smallskip\\
2) & $B \to A :$ & $K^{pub}_B$\smallskip\\
3) & & $\{A,m\}_{K^{pub}_B} \;\mapsto\; H_1,H_2$\\
4) & $A \to B :$ & $H_1$\smallskip\\
5) & $B \to A :$ & $\{H_1\}_{K^{pub}_A}$\smallskip\\
6) & $A \to B :$ & $H_2$
\end{tabular}
\end{center}

\noindent The idea is that in step 3, $A$ encrypts the
message (with $B$'s public key) and then splits the encrypted
message into two halves. Say the encrypted message is

\begin{center}
\texttt{\Grid{0X1peUVTGJK0XI7G+H70mMjAM8piY0sI}}
\end{center}
 
\noindent then $A$ splits it up into two halves

\begin{center}
$\underbrace{\texttt{\Grid{0X1peUVTGJK0XI7G}}}_{H_1}$\qquad
$\underbrace{\texttt{\Grid{+H70mMjAM8piY0sI}}}_{H_2}$
\end{center}

\noindent sends the first half $H_1$ to $b$. $B$ (and also any
potential attacker) cannot do much with this half. What $B$ 
does, it encrypts it with $A$'s public key and sends it back
to $A$. Now $A$ can decrypt it and if it matches with what it
had send, it will send $B$ the second half $H_2$. Only after
$B$ received this second part, it will be able to decrypt the
entire message $\{A,m\}_{K^{pub}_B}$ and see what $A$ had 
written.


\begin{enumerate}
\item $C$ generates a random number $r$
\item $C$ calculates $(F,G) = \{r\}_K$
\item $C \to T$: $r, F$
\item $T$ calculates $(F',G') = \{r\}_K$
\item $T$ checks that $F = F'$
\item $T \to C$: $r, G'$
\item $C$ checks that $G = G'$
\end{enumerate}


\subsubsection*{Further Reading}

{\small
\url{http://www.cs.ru.nl/~rverdult/Gone_in_360_Seconds_Hijacking_with_Hitag2-USENIX_2012.pdf}}

\end{document}

%%% Local Variables: 
%%% mode: latex
%%% TeX-master: t
%%% End: 
