From fffc35ad3c397359b29f30949547e2c767198600 Mon Sep 17 00:00:00 2001
From: Dennis Brentjes <dennis@brentj.es>
Date: Mon, 21 May 2018 17:10:57 +0200
Subject: changed results and conclusion stuff.

---
 content/cmix.tex | 25 ++++++++++++++++++++-----
 1 file changed, 20 insertions(+), 5 deletions(-)

(limited to 'content/cmix.tex')

diff --git a/content/cmix.tex b/content/cmix.tex
index ed5fb71..3af780d 100644
--- a/content/cmix.tex
+++ b/content/cmix.tex
@@ -6,20 +6,35 @@
 \label{sec:anon}
 
 \subsection{The onion router}
-We can't talk about anonymity networks without talking about The Onion Router\cite{goldschlag1999onion} or TOR for short. It's a free software project that provides access to an anonymity network. It has some similarities with some classic mix networks but also has some weaknesses which mix networks try to resolve.
+We can't talk about anonymity networks without talking about The Onion Router\cite{goldschlag1999onion} or TOR for short. It's a free software project that provides access to an anonymity network based on Onion Routing.
 
 Tor works by users selecting a path trough the tor network consisting of 3 nodes. When a user wants to send a message it has to encrypt its message with the key of the last node in the network. This yields a result, which needs to be encrypted with the key of the middle node. This results needs to be encrypted with the key of the first node and then can be send out the first node. The first node can peel off the outer layer of encryption and send it to the second node which in turn can peel of the new outer layer. The last node removes the last layer of encryption and reveals the plaintext. This plaintext can be sent to the original destination. This simplified view of TOR reveals that the sender of a certain message remains anonymous so long as at least one of your 3 nodes is not compromised. And you use End to End encryption because the last node will see your plaintext.
 
-However there is something called a correlation attack\cite{Johnson:2013:UGR:2508859.2516651}. This is an attack where the attacker can see incoming traffic of your first node and the outgoing traffic of the last node. It can then try to correlate the entry times, exit times and size of the packets. An attacker can use this data to correlate a packet entering and exiting the network and therefore link a user and a destination with a certain probability. Therefore de-anonymizing the traffic. This attack is highly probabilistic, but could flag users for further targeted investigation. Therefore we really want to prevent this attack from being possible.
+Unfortunately some information is leaked, and this is exploited by a correlation  attack\cite{Johnson:2013:UGR:2508859.2516651}. This is an attack where the attacker sees incoming traffic of your first node and the outgoing traffic of the last node. It can then try to correlate the entry times, exit times, origin, destination and size of the packets. An attacker can use this data to correlate a packet entering and exiting the network and therefore link a user and a destination with a certain probability. Therefore de-anonymizing the traffic. This attack is highly probabilistic, but could flag users for further targeted investigation. Therefore we really want to prevent this attack from being possible.
+
+This attack would be mitigated by the another type of anonymity network called a Mix net.
 
 
 \subsection{Mix networks}
 
-The first mix network was developed by David Chaum \cite{chaum1981untraceable}. this mix network consists of $N$ nodes. Each of these nodes have a public/private key pair. Users that want to use the mix network have to package their message as follows, it prepends the identifier of the destination to the message and encrypts it with the public key of \NODE{N-1}. It then prepends the identifier of \NODE{N-1} and encrypts it with the public key of \NODE{N-2}. The client does this for all the nodes in the network working backwards and sends it to the first node.
+The first mix network was proposed and developed by David Chaum \cite{chaum1981untraceable}. this mix network consists of $N$ nodes. Each of these nodes have a public/private key pair. Users that want to use the mix network have to package their message as follows, it prepends the identifier of the destination to the message and encrypts it with the public key of \NODE{N-1}. It then prepends the identifier of \NODE{N-1} and encrypts it with the public key of \NODE{N-2}. The client does this for all the nodes in the network working backwards and sends it to the first node.
+
+This first node can now unpack the message it receives and retrieve an identifier for the next node and a encrypted message which only \NODE{N+1} can decrypt. The last node can decrypt the original message which contains its destination and sends it the end user. Up until this point this is roughly how the TOR anonymity network operates, but there is a difference. The first node in the \cmix network does not immediately send out the messages it receives. The node first collects up to $P$ messages. When this threshold is achieved it will decrypt all the messages and randomly shuffle the order they were in, otherwise known as mixing. It then sends them to the next node. Another subtle difference is that each message within one mix operation should have the same length, However it is possible to choose a large enough message size and pad all the messages to this length.
+
+This mixing and delaying in the first node causes an arbitrary amount of delay on client connection messages. Furthermore, an outsider analyzing the input and output of the nodes cannot see which packet went where in the mixing operation. So it cannot keep track of a specific message. This is what grants the additional anonymity within mix networks, as it mitigates the correlation attack possible on TOR.
+
+The introduction of Re-encryption mix nets by Park et all \cite{park1993efficient}
+introduces the usage of ElGamal encryption in mix nets. Using it's homomorphic properties to no longer de-encrypt each incoming message but rather just re-encrypt the message which makes it faster to run. It also has the effect that the ciphertext no longer lengthens in the order of the amount of nodes in the mix network. Which does happen in the classic Chaum mix network and in TOR.
+
+The network operates by each node having a public and private ElGamal key. It publishes its public key and a user can use all of the public keys of all of the nodes en encrypt his message. Each node can re-encrypt the message with it's private key. After the last nodes successfully re-encrypts the value the plain text is revealed. In the original paper this is used as a voting scheme and therefore no mention is made of a Receiver as it just needs to aggregate in one place. But is of course extensible to support sending messages to specific recipients.
+
+
+
+A major downside of these classic mix network is the amount of public key operations the client and nodes need to do when sending single message. This may not be an issue on modern day desktop computers and or low volume traffic, but it is an issue for mobile phones' battery life and low-power devices. This is were the precomputation and use of ElGamals homomorphic properties come in to play.
+
+
 
-This first node can now unpack the message it receives and retrieve an identifier for the next node and a encrypted message which only \NODE{N+1} can decrypt. The last node can decrypt the original message which contains its destination and sends it the end user. Up until this point this is roughly how the TOR anonymity network operates, but there is a difference. The first node in the \cmix network does not immediately send out the messages it receives. The node first collects up to $P$ messages. When this threshold is achieved it will decrypt all the messages and randomly shuffle the order they were in, otherwise known as mixing. It then sends them to the next node. Another subtle difference is that each message should have the same length, However it is possible to choose a large enough message size and pad all the messages to this length. Even when unpacking the messages the server nodes should keep padding the messages to the decided size as the network is not fixed and clients can choose their own path trough the network.
 
-This causes an arbitrary amount of delay on client connection messages. Furthermore, an outsider analyzing the input and output of the nodes cannot see which packet went where in the mixing operation. So it cannot keep track of a specific message. This is what grants the additional anonymity within mix networks, as it mitigates the correlation attack possible on TOR. A major downside of this classic mix network is the amount of public key operations the client and nodes need to do when sending single message. This may not be an issue on modern day desktop computers and or low volume traffic, but it is an issue for mobile phones and low-power devices.
 
 \section{\cmix}
 
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