You are raising valid questions and one goal of our posting here is indeed to 
discuss exactly these system issues.

On Thursday 07 August 2014 15:00:11 you wrote:

I think the description at your website leaves out the truly interesting
part: How do you decentralize this securely?
- How do Alice, Bob, Charlie and Dave communicate, i.e. which network is
used for communication and how?

The simplest approach is obviously to use direct connections to a randomly 
elected leader, who is also responsible for the broadcasts.
One advantage of CoinShuffle is that the unlinkability between input and 
output addresses is guaranteed, no matter which underlying network you use. 
(Still, it is a good idea in general to hide your IP address but we can let 
the user decide here.)

Of course, there would be other possibilities, such as overlay networks. 
Coinmux, a CoinJoin prototype by Michael Pearce (http://coinmux.com/) uses 
TomP2P, a distributed hash table, for communication. 

Do you have any hints regarding this point?

- How does Alice know that Bob, Charlie and Dave are not the same person?
(= how do you prevent a Sybil attack?)

Because thats the real problem with mixing it seems - ensuring that your
mixing partners are actually 100 people and not just 1 attacker. There are
probably many mixing algorithms which work if you solve that problem, but I
don't see how you offer a solution for it :(

It's true that there are a few proposals for mixing protocols which all have 
their advantages and disadvantages. However, it's not true that the mixing 
itself becomes simple if you solve the problem of Sybil attacks. Still, mixing 
is difficult to get right: Even if there are no Sybil attacks, you have to 
ensure that the participants (or a server) cannot break unlinkability or steal 
money. Actually that's why there are several proposals for mixing protocols, 
because there is no obvious perfect solution.

Regarding your question:
It is indeed very important to get this right. Fundamentally, there is nothing 
that prevents the attacker from creating a lot of identities participating in 
a lot of CoinJoins. However, there are ways that make it hard for the attacker 
to put an honest user together only with malicious users.

For a moment, assume that you can reliably establish a pool of users that 
would like to participate in the protocol. (I will discuss this later.) 
You have to divide the users to individual groups, i.e., CoinJoins runs. If 
the assignment cannot be influenced by the attacker, then the probability that 
there are also honest users in a run is quite high. Of course, the attacker is 
able to reduce your anonymity set but they cannot just put you together only 
with their malicious identities.

Note that the attacker has to pay transaction fees for joining many 
transaction. One could even increase the required fee depending on the number 
of users in the pool (enforced by honest CoinShuffle participants that would 
not accept CoinJoins that pay a lower transaction fee).

And making sure that the attacker cannot influence the assignment is simple: 
One can use the hash of all users' public keys in the pool to determine the 
assignment for example.
 
For the initial setup step, i.e., creating the pool of participants, you need 
some kind of "bulletin board". 

One possibility is to use an underlying peer-to-peer network. Bitcoin itself 
is the first that comes to the mind but it does not allow arbitrary messages. 
So if we do not want to change the Bitcoin protocol, chans in Bitmessage are a 
very promising possibility. Bitmessage relies basically on the same broadcast 
mechanism as Bitcoin. If you as a peer use enough outgoing connections to 
other peers, it's very difficult for an attacker to ensure that your message 
will not be spread among the network. (Btw, people have used this to do 
CoinJoin  manually already 
https://forum.namecoin.info/viewtopic.php?f=2&t=1694 .)
Solutions like distributed hashtables (TomP2P again) are another possibility. 
We are not sure which of those approaches provides the best robustness against 
malicious nodes that try to stop single participants from reaching the 
network. For the setup step, latency is not an issue, so Bitmessage is indeed 
a promising candidate here.
 
I think that in general, P2P is the way to go here, but there are other 
approaches as well:

 - A possibility is to have a lot of servers acting as bulletin 
boards. The user sends his announcement message to all of the servers and 
the user waits until at some of the servers send back a guarantee to 
include the user. After some time, the servers agree on the pool of the users 
just by taking all the users that have registered with at least one of the 
servers. There are well-understood protocols to achieve this goal or similar 
goals, because essentially the same problem arises in e-voting (see 
http://arxiv.org/pdf/1401.4151 for just one example. this paper provides also 
a detailed discussion of related protocols in section 9).
Of course, the disadvantage of this approach is that the protocol is not 
really decentralized anymore.

 - If you really want to be on the safe side, you can include your 
announcement messages in the Bitcoin blockchain, e.g., by adding your 
announcement message to an unspendable output, at the cost of an additional 
transaction. I know that putting data to the blockchain is discouraged but let 
me explain why it is useful here: If you want to do several CoinJoins in a 
row, you can include your announcement message for the second CoinJoin in the 
transaction of the first CoinJoin, so your announcement is very robust but you 
do not need an additional transaction, because you can piggy-back on the frist 
transaction.

Additionally, it is possible to combine these approaches by joining several 
pools. 

Another interesting point that my co-author Aniket Kate mentioned is that you 
can look at that problem as a social issue: You could combine this with 
information from your friends. You can participate in a CoinJoin only if your 
friends tell you that they also participate in the same run. They do not even 
have to reveal their input address, they just have to reveal that their 
address is in a particular run. Of course, this is not yet a technical 
solution but a very interesting idea.

Don't get me wrong. We don't think that there is a perfect solution the 
two issues that you mentioned but we are pretty sure there are several that 
work well enough in practice if they are implemented correctly. 

Tim

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