\documentclass{article}
\usepackage{../style}
\usepackage{../graphics}
\usepackage{../langs}
\usepackage{../data}


\begin{document}
\fnote{\copyright{} Christian Urban, 2014, 2015}

\section*{Handout 8 (Bitcoins)}

In my opinion Bitcoins are an elaborate Ponzi
scheme\footnote{\url{http://en.wikipedia.org/wiki/Ponzi_scheme}}---still
the ideas behind them are really beautiful and not too
difficult to understand. Since many colourful claims about
Bitcoins float around in the mainstream and not-so-mainstream
media, it will be instructive to re-examine such claims from a
more technically informed vantage point. For example, it is
often claimed that Bitcoins are anonymous and free from any
potential government meddling. It turns out that the first
claim ignores a lot of research in de-anonymising social
networks, and the second underestimates the persuasive means a
government has at its disposal. 

There are a lot of articles, blogposts, research papers
etc.~available about Bitcoins. Below I will follow closely the
very readable explanations from

\begin{center}
\url{http://www.michaelnielsen.org/ddi/how-the-bitcoin-protocol-actually-works/} \;\;and\smallskip\\
\url{http://www.imponderablethings.com/2013/07/how-bitcoin-works-under-hood.html}
\end{center}

\noindent The latter also contains a link to a nice youtube
video about the technical details behind Bitcoins. I will
also use some of their pictures.

Let us start with the question who invented Bitcoins? You
could not make up the answer, but we actually do not know who
the inventor is. All we know is that the first paper

\begin{center}
\url{https://bitcoin.org/bitcoin.pdf}
\end{center}

\noindent is signed by Satoshi Nakamoto, which however is
likely only a pen name. There is a lot of speculation who
could be the inventor, or inventors, but we simply do not
know. This part of Bitcoins is definitely anonymous so far.
The paper above is from the end of 2008; the first Bitcoin
transaction was made in January 2009. The rules in Bitcoin are
set up so that there will only ever be 21 Million Bitcoins
with the maximum reached around the year 2140. Currently there
are already 11 Million Bitcoins in `existence'. Contrast this
with traditional fiat currencies where money can be printed
almost at will. The smallest unit of a Bitcoin is called a
Satoshi, which is the $10^{-8}$th part of a Bitcoin. Remember
a Penny is the $10^{-2}$th part of a Pound.

The two main cryptographic building blocks of Bitcoins are
cryptographic hashing functions (SHA-256) and public-private
keys using the elliptic-curve encryption scheme for digital
signatures. Hashes are used to generate `fingerprints' of data
that ensure integrity (absence of tampering). Public-private
keys are used for signatures. For example sending a message,
say $msg$, together with the encrypted version

\[
msg, \{msg\}_{K^{priv}}
\]

\noindent allows everybody with access to the corresponding
public key $K^{pub}$ to verify that the message came from the
person who knew the private key. Signatures are used in
Bitcoins for verifying the addresses where the Bitcoins are
sent from. Addresses in Bitcoins are essentially the public
keys. There are $2^{160}$ possible addresses, which is such a
vast amount that there is not even a check for duplicates, or
already used addresses. If you start with a random number to
generate a public-private key pair it is very unlikely that
you step on somebody else's shoes. Compare this with the
email-addresses you wanted to register with, say
Gmail, but which are always already taken.

One major difference between Bitcoins and traditional banking
is that you do not have a place, or few places, that record the
balance on your account. Traditional banking involves a
central ledger which specifies the current balance in each
account, for example 

\begin{center}
\begin{tabular}{l|r}
account owner & balance\\\hline
Alice   & \pounds{10.01}\\
Bob     & \pounds{4.99}\\
Charlie & -\pounds{1.23}\\
Eve     & \pounds{0.00}
\end{tabular}
\end{center}

\noindent Bitcoins work differently in that there is no such
central ledger, but instead a public record of all
transactions ever made. This means spending money corresponds
to sending messages of the (oversimplified) form 

\begin{equation}
\{\text{I, Alice, am giving Bob one Bitcoin.}\}_{K^{priv}_{Alice}}
\end{equation}

\noindent These messages, called transactions, are the only
data that is ever stored in the Bitcoin system (we will come
to the precise details later on). The transactions are
encrypted with Alice's private key so that everybody,
including Bob, can use Alice's public key $K^{pub}_{Alice}$ to
verify that this message came really from Alice, or more
precisely from the person who knows $K^{priv}_{Alice}$. 

The problem with such messages in a distributed system is that
what happens if Bob receives 10, say, of these transactions?
Did Alice intend to send him 10 Bitcoins, or did the message
get duplicated by for example an attacker re-playing a sniffed
message? What is needed is a kind of serial number for such
transactions. This means transaction messages shoul look more like 

\begin{center}
$\{\text{I, Alice, am giving Bob Bitcoin \#1234567.}\}_{K^{priv}_{Alice}}$
\end{center}

\noindent There are two difficulties, however, that need to be
solved with serial numbers. One is who is assigning serial
numbers to Bitcoins and also how can Bob verify that Alice
actually owns this Bitcoin to pay him? In a system with a bank
as trusted third-party, Bob could do the following:

\begin{itemize}
\item Bob asks the bank whether the Bitcoin with that serial
      number belongs to Alice and Alice hasn't already spent
      this Bitcoin.
\item If yes, then Bob tells the bank he accepts this Bitcoin.
      The bank updates the records to show that the Bitcoin
      with that serial number is now in Bob’s possession and
      no longer belongs to Alice. 
\end{itemize}

\noindent But for this banks would need to be trusted and
would also be an easy target for any government interference,
for example. Think of the early days of music sharing where
the company Napster was the trusted third-party but also the single point of ``failure'' which
was taken offline by law enforcement. Bitcoins is more like a
system such as BitTorrent without a single central entity that
can be taken offline.\footnote{There is some Bitcoin
infrastructure that is not so immune from being taken offline:
for example Bitcoin exchanges, HQs of Bitcoin mining pools,
Bitcoin developers and so on.}

Bitcoins solve the problem of not being able to rely on a bank
by making everybody the ``bank''. Everybody who cares can have
the entire transaction history starting with the first
transaction made in January 2009. This history of transactions
is called the \emph{blockchain}. Bob, for example, can use his
copy of the blockchain for determining whether Alice owned the
Bitcoin he received, and if she did, he transmits the message
that he owns it now to every other participant on the Bitcoin
network. An illustration of a three-block segment of the
blockchain is (simplified) as follows

\begin{equation}
\includegraphics[scale=0.4]{../pics/bitcoinblockchain0.png}
\label{segment}
\end{equation}

\noindent The chain grows with time. Each block contains a
list of individual transactions, written txn in the picture
above, and also a reference to the previous block, written
prev. The data in a block (txn's and prev) is hashed so that
the reference and transactions in them cannot be tampered
with. This hash is also the unique serial number of each
block. Since this previous-block-reference is also part of the
hash, the whole chain is robust against tampering. I let you
think why this is the case?\ldots{}But does it actually
eliminate all possibilities of fraud?

We can check the consistency of the blockchain by checking
whether all the references and hashes are correctly recorded.
I have not tried it myself, but it is said that with the
current amount of data (appr.~12GB) it takes roughly a day to
check the consistency of the blockchain on a normal computer.
Fortunately this ``extended'' consistency check usually only
needs to be done once. Afterwards the blockchain only needs to
be updated consistently.

Recall I wrote earlier that Bitcoins do not maintain a ledger,
which lists all the current balances in each account. Instead
only transactions are recorded. While a current balance of an
account is not immediately available, it is possible to
extract from the blockchain a transaction graph that looks
like the picture shown in Figure~\ref{txngraph}. Each
rectangle represents a single transaction. Take for example
the rightmost lower transaction from Charles to Emily. This
transaction has as receiver the address of Emily and as the
sender the address of Charles. In this way no Bitcoins can
appear out of thin air (we will discuss later how Bitcoins are
actually generated). If Charles did not have a transaction of
at least the amount he wants to give Emily to his name
(i.e.~send to an address with his public-private key) then
there is no way he can make a payment to Emily. Equally, if
now Emily wants to pay for a coffee, say, with the Bitcoin she
received from Charles she can essentially only forward the
message she received. The only slight complication with this
setup in Bitcoins is that ``incoming'' Bitcoins can be
combined in a transaction and ``outgoing'' Bitcoins can be
split. For example in the leftmost upper transactions in
Figure~\ref{txngraph}, Fred makes a payment to Alice. But this
payment (or transaction) combines the Bitcoins that were send
by Jane to Fred and also by Juan to Fred. This allows you to
``consolidate'' your funds: if it were only possible to split
transactions, then the amounts would get smaller and smaller. 

In Bitcoins you have the ability to both combine incoming
transactions, but also to split outgoing transactions to
potentially more than one receiver. The latter is also needed.
Consider again the rightmost transactions in
Figure~\ref{txngraph} and suppose Alice is a coffeeshop owner
selling coffees for 1 Bitcoin. Charles received a transaction
from Zack over 5 Bitcoins, say. How does Charles pay for the
coffee? There is no explicit notion of \emph{change} in the
Bitcoin system. What Charles has to do instead is to make one
single transaction with 1 Bitcoin to Alice and with 4 Bitcoins
going back to himself, which then Charles can use to give to
Emily, for example.

\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.4]{../pics/blockchain.png}
\end{center}
\caption{Transaction graph that is implicitly recorded in the
public blockchain.\label{txngraph}}
\end{figure}

Let us consider another example. Suppose Emily received 4
Bitcoins from Charles and independently received another
transaction (not shown in the picture) that sends 6 Bitcoins
to her. If she now wants to buy a coffee from Alice for 1
Bitcoin, she has two possibilities: She could just forward the
transaction from Charles over 4 Bitcoins to Alice split in
such a way that Alice receives 1 Bitcoin and Emily sends the
remaining 3 Bitcoins back to herself. In this case she would
now be in the possession of two unspend Bitcoin transactions,
one over 3 Bitcoins and the independent one over 6 Bitcoins.
Or, Emily could combine both transactions (one over 4 Bitcoins
from Charles and the independent one over 6 Bitcoins) and then
split this amount with 1 Bitcoin going to Alice and 9 Bitcoins
going back to herself. 

I think this is a good time for you to pause to let this
concept of transactions to really sink in\ldots{}You should
come to the conclusion that there is really no need for a central ledger and no
need for an account balance as familiar from traditional
banking. The closest what Bitcoin has to offer for the notion
of a balance in a bank account are the unspend transactions
that a person (more precisely a public-private key address)
received. That means transactions that can still be forwarded. 

After the pause also consider the fact that whatever
transaction is recorded in the blockchain will be in the
``historical record'' for the Bitcoin system. If a transaction
says 1 Bitcoin goes from address $A$ to address $B$, then this
is what will be---$B$ has then the possibility to spend the
corresponding Bitcoins, whether the transaction was done
fraudulently or not. There is no exception to this rule.
Interestingly this is also how Bitcoins can get lost: One
possibility is that you send Bitcoins to an address for which
nobody has generated a private key, for example because of a
typo in the address field---bad luck for fat
fingers\footnote{\url{http://en.wikipedia.org/wiki/Typographical_error}}
in the Bitcoin system. The reason is that nobody has a private
key for this erroneous address and consequently cannot forward
the transaction anymore. Another possibility is that you
forget your private key and you had messages forwarded to the
corresponding public key. Also in this case bad luck: you will
never be able to forward this message again, because you will
not be able to form a valid message that sends this to
somebody else (we will see the details of this later). But
this is also a way how you can get robbed of your Bitcoins. By
old-fashioned hacking-into-a-computer crime, for example, an
attacker might get hold of your private key and then quickly
forwards the Bitcoins that are in your name to an address the
attacker controls. You will never again have access to these
Bitcoins, because for the Bitcoin system they are assumed to
be spent. And remember with Bitcoins you cannot appeal to any
higher authority. Once the Bitcoins are gone, they are gone.
This is much different in traditional banking where at least
you can try to harass the bank to roll back the transaction. 

This brings us to back to problem of double spend. Suppose Bob
is a merchant. How can he make sure that Alice does not cheat
him? She could for example send a transaction to Bob. But also
forward the ``same'' transaction to Charlie, or even herself.
If Alice manages to get the second transaction into the
blockchain, Bob will be cheated out of his money. The problem
in such conflicting situations is how should the network
update their blockchain? You might end up with a picture like
this

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

\noindent where Alice convinced some part of the ``world''
that she is still the owner of the Bitcoin and some other part
of the ``world'' thinks it's Bob's. How should such a
disagreement be resolved? This is actually the main hurdle
where Bitcoin really innovated. The answer is that Bob needs
to convince ``enough'' people on the network that the
transaction from Alice to him is legit. 

What does, however, ``enough'' mean in a distributed system?
If Alice sets up a network of a billion, say, puppy identities
and whenever Bob tries to convince, or validate, that he is
the rightful owner of the Bitcoin, then the puppy identities
agree. Bob would then have no reason to not give Alice her
coffee. But behind his back she has convinced everybody else
on the network that she is still the rightful owner of the
Bitcoin. After being outvoted, Bob would be a tad peeved. 

The reflex reaction to such a situation would be to make the
process of validating a transaction as cheap as possible. The
intention is that Bob will easily get enough peers to agree with him
that he is the rightful owner. But such a solution has always
the limitation of Alice setting up an even bigger network of
puppy identities. The really cool idea of Bitcoin is to go
into the other direction of making the process of transaction
validation (artificially) as expensive as possible, but reward
people for helping with the validation. This is really a novel
and counterintuitive idea that makes the whole system of
Bitcoins work so beautifully.

\subsubsection*{Proof-of-Work Puzzles}

In order to make the process of transaction validation
difficult, Bitcoin uses a kind of puzzle. Solving the puzzles
is called \emph{Bitcoin mining}, where whoever solves a puzzle
will be awarded some Bitcoins. At the beginning this was 50
Bitcoins, but the rules of Bitcoin are set up such that this
amount halves every 210,000 transactions or so. Currently you
will be awarded 25 Bitcoins for solving a puzzle. Because the
amount will halve again and then later again and again, around
the year 2140 it will go below the level of 1 Satoshi. In that
event no new Bitcoins will ever be created again and the
amount of Bitcoins stays fixed. There will be still an
incentive to help with validating transactions, because there
is the possibility in Bitcoins to offer a transaction fee to
whoever solves a puzzle. At the moment this fee is usually set
to 0, since the incentive for miners is the 25 Bitcoins that
are currently awarded for solving puzzles. 
 
What do the puzzles that miners have to solve look like? The
puzzles can be illustrated roughly as follows: Given a string,
say \code{"Hello, world!"}, what is the salt so that the hash
starts with a long run of zeros? Let us look at a concrete
example. Recall that Bitcoins use the hash-function SHA-256.
Suppose we call this hash function \code{h}, then we could try
the salt \code{0} as follows:

\begin{quote}
\code{h("Hello, world!0") =}\\
\mbox{}\quad\footnotesize\pcode{1312af178c253f84028d480a6adc1e25e81caa44c749ec81976192e2ec934c64}
\end{quote}

\noindent OK this does not have any zeros at all. We could 
next try the salt \code{1}: 

\begin{quote}
\code{h("Hello, world!1") =}\\
\mbox{}\quad\footnotesize\pcode{e9afc424b79e4f6ab42d99c81156d3a17228d6e1eef4139be78e948a9332a7d8}
\end{quote}

\noindent Again this hash value does not contain any leading 
zeros. We could now try out every salt until we reach

\begin{quote}
\code{h("Hello, world!4250") =}\\
\mbox{}\quad\footnotesize\pcode{0000c3af42fc31103f1fdc0151fa747ff87349a4714df7cc52ea464e12dcd4e9}
\end{quote}

\noindent where we have four leading zeros. If four zeros are
enough, then the puzzle would be solved with this salt. The
point is that we can very quickly check whether a salt solves
a puzzle, but it is hard to find one. Latest research suggest
it is an NP-problem. If we want the output hash value to begin
with 10 zeroes, say, then we will, on average, need to try
$16^{10} \approx 10^{12}$ different salts before we find a
suitable one. 

In Bitcoins the puzzles are not solved according to how many
leading zeros a hash-value has, but rather whether it is below
a \emph{target}. The hardness of the puzzle can actually be
controlled by changing the target according to the available
computational power available. I think the adjustment of the
hardness of the problems is done every 2060 blocks
(appr.~every two weeks). The aim of the adjustment is that on
average the Bitcoin network will most likely solve a puzzle
within 10 Minutes. 

\begin{center}
\includegraphics[scale=0.37]{../pics/blockchainsolving.png}
\end{center}

\noindent It could be solved quicker, but equally it could 
take longer, but on average after 10 Minutes somebody on the 
network will have found a solution. 

Remember that the puzzles are a kind of proof-of-work that
make the validation of transactions artificially expensive.
Consider the following picture with a blockchain and some
unconfirmed transactions. 

\begin{equation}
\includegraphics[scale=0.38]{../pics/bitcoin_unconfirmed.png}
\label{unconfirmed}
\end{equation}

\noindent The puzzle is stated as follows: There are some
unconfirmed transactions. Choosing some of them, the miner
(i.e.~the person/computer that tries to solve a puzzle) will
form a putative block to be added to the blockchain. This
putative block will contain the transactions and the reference
to the previous block. The serial number of such a block is
simply the hash of all the data. The puzzle can then be stated
as the ``string'' corresponding to the block and which salt is
needed in order to have the hashed value being below the
target. Other miners will choose different transactions and
therefore work on a slightly different putative block and
puzzle.

The intention of the proof-of-work puzzle is that the
blockchain is at every given moment linearly ordered, see the
picture shown in \eqref{unconfirmed}. If we don’t have such a
linear ordering at any given moment then it may not be clear
who owns which Bitcoins. Assume a miner David is lucky and
finds a suitable salt to confirm some transactions. Should he
celebrate? Not yet. Typically the blockchain will look as
follows

\begin{center}
\includegraphics[scale=0.65]{../pics/block_chain1.png}
\end{center}

\noindent But every so often there will be a fork

\begin{center}
\includegraphics[scale=0.65]{../pics/block_chain_fork.png}
\end{center}

\noindent What should be done in this case? Well, the tie is
broken if another block is solved, like so:

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

\noindent The rule in Bitcoins is: If a fork occurs, people on
the network keep track of all forks (they can see). But at any
given time, miners only work to extend whichever fork is
longest in their copy of the block chain. Why should miners
work on the longest fork? Well their incentive is to mine
Bitcoins. If somebody else already solved a puzzle, then it
makes more sense to work on a new puzzle and obtain the
Bitcoins for solving that puzzle, rather than waste efforts on
a fork that is shorter and therefore less likely to be
``accepted''. Note that whoever solved a puzzle on the
``loosing'' fork will actually not get any Bitcoins as reward.
Tough luck.


\subsubsection*{Alice against the Rest of the World}

Let us see how the blockchain and the proof-of-work puzzles
avoid the problem of double spend. If Alice wants to cheat
Bob, she would need to pull off the following ploy:

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

\noindent Alice makes a transaction to Bob for paying, for
example, for an online order. This transaction is confirmed,
or validated, in block 2. Bob ships the goods around block 4.
In this moment, Alice needs to get into action and try to
validate the fraudulent transaction to herself instead. At
this moment she is in a race against all the computing power
of the ``rest of the world''. Because the incentive of the
rest of the world is to work on the longest chain, that is the
one with the transaction from Alice to Bob:

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

\noindent As shown in the picture she has to solve the puzzles
2a to 5a one after the other, because the hash of a block is
determined via the reference by all the data in the previous
block. She might be very lucky to solve one puzzle for a block
before the rest of the world, but to be lucky many times is
very unlikely. This principle of having to race against the
rest of the world avoids the ploy of double spend.

In order to raise the bar for Alice even further, merchants
accepting Bitcoins use the following rule of thumb: A
transaction is ``confirmed'' if 

\begin{itemize}
\item[(1)] it is part of a block in the longest fork, and 
\item[(2)] at least 5 blocks follow it in the longest fork. In
           this case we say that the transaction has 6
           confirmations. 
\end{itemize} 

\noindent A simple calculation shows that this amount of
confirmations can take up to 1 hour and more. While this seems
excessively long, from the merchant's point of view it is not
that long at all. For this recall that ordinary creditcards
can have their transactions been rolled-back for 6 months or
so. The point however is that the odds for Alice being able to
cheat are very low, unless she can muster more than 50\% of
the world Bitcoin mining capacity. In this case she could
out-race the rest of the world. The point is however that
amassing such an amount of computing power is practically
impossible for a single person or even a moderately large 
group.

Connected with the 6-confirmation rule is an interesting
phenomenon. On average, it would take several years for a
typical computer to solve a proof-of-work puzzle, so an
individual’s chance of ever solving one before the rest of the
world, which typically takes only 10 minutes, is negligibly
low. Therefore many people join groups called \emph{mining
pools} that collectively work to solve blocks, and distribute
rewards based on work contributed. These mining pools act
somewhat like lottery pools among co-workers, except that some
of these pools are quite large, and comprise more than 20\% of
all the computers in the network. It is said that BTCC, a
large mining pool, has limited its number of members in order
to not solve more than 6 blocks in a row. Otherwise this would
undermine the trust in Bitcoins, which is also not in the
interest of BTCC, I guess. Some statistics on mining pools can
be seen at

\begin{center}
\url{https://blockchain.info/pools}
\end{center}

\subsubsection*{Bitcoins for Real}

Let us now turn to the nitty gritty details. As a participant
in the Bitcoin network you need to generate and store a
public-private key pair. The public key you need to advertise
in order to receive payments (transactions). The private key
needs to be securely stored. For this there seem to be three
possibilities

\begin{itemize}
\item an electronic wallet on your computer
\item a cloud-based storage (offered by some Bitcoin services)
\item paper-based
\end{itemize}

\noindent The first two options of course offer convenience
for making and receiving transactions. But given the nature of
the private keys and how much security relies on them (recall
if somebody gets hold of it, your Bitcoins are quickly lost
forever) I would opt for the third option for anything except
for trivial amounts of Bitcoins. As we have seen earlier in
the course, securing a computer system that it can withstand a
targeted breakin is still very much an unsolved problem.

An interesting fact with Bitcoin keys is that there is no
check for duplicate addresses. This means when generating a
public-private key, you should really start with a carefully
chosen random number such that there is really no chance to
step on somebody's feet in the $2^{160}$ space of
possibilities. Again if you share an address with somebody
else, he or she has access to all your unspend transactions.
The absence of such a check is easily explained: How would one
do this in a distributed system? The answer you can't. It is
possible to do some sanity check of addresses that are already
used in the blockchain, but this is not a fail-proof method.
One really has to trust on the enormity of the $2^{160}$
space for addresses.

Let us now look at the concrete data that is stored in an transaction 
message:

\lstinputlisting[language=Scala]{../slides/msg}

\noindent The hash in Line 1 is the hash of all the data that
follows. It is a kind of serial number for the transaction.
Line 2 contains a version number in case there are some
incompatible changes to be made. Lines 3 and 4 specify how
many incoming transactions are combined and how many outgoing
transactions there are. In our example there are one for each.
Line 5 specifies a lock time for when the transaction is
supposed to become active---this is usually set to 0 to become
active immediately. Line 6 specifies the size of the message;
it has nothing to do with the Bitcoins that are transferred.
Lines 7 to 11 specify where the Bitcoins in the transaction
are coming from. The has in line 9 specifies the incoming
transaction and the \pcode{n} in Line 10 specifies which
output of the transaction is referred to. The signature in
line 11 specifies the address (public key $K^{pub}$) from
where the Bitcoins are taken and the digital signature of the
address, that is $\{K^{pub}\}_{K^{priv}}$. Lines 12 to 15
specify the value of the first outgoing transaction. In this
case 0.319 Bitcoins. The hash in Line 14 specifies the address
to where the Bitcoins are transferred.
 
As can be seen there is no need to issue serial numbers for
transactions, the hash of the transaction data can do this
job. The hash will contain the sender addresses and
hash-references to the incoming transactions, as well as the
public key of the incoming transaction. This uniquely
identifies a transaction and the hash is the unique
fingerprint of it. The in-field also contains the address to
which a earlier transaction is made. The digital signature
ensures everybody can check that the person who makes this
transaction is in the possession of the private key. Otherwise
the signature would not match up with the public-key address.

When mining the blockchain it only needs to be ensured that
the transactions are consistent (all hashes and signatures
match up). Then we need to generate the correct previous-block
link and solve the resulting puzzle. Once the block is
accepted, everybody can check the integrity of the whole
blockchain.

A word of warning: The point of a lottery is that some people
win. But equally, that most people lose. Mining Bitcoins has
pretty much the same point. According to the article below, a
very large machine (very, very large in terms of June 2014)
could potentially mine \$40 worth of Bitcoins a day, but would
require magnitudes more of electricity costs to do so. 

\begin{center}
\url{http://bitcoinmagazine.com/13774/government-bans-professor-mining-bitcoin-supercomputer/}
\end{center}

\noindent Bitcoin mining nowadays is only competitive, or
profitable, if you get the energy for free, or use special
purpose computing devices. 

This about ``free'' energy can actually hurt you very badly in
unexpected ways. You probably have heard about, or even used,
Amazon's Elastic Compute Cloud (EC2). Essentially, Amazon is
selling computing power that you can use to run your web site,
for example. It is \emph{elastic} in the sense that if you
have a lot of visitors, you pay a lot, if you have only a few,
then it is cheap. In order to bill you, you need to set
up an account with Amazon and receive some secret keys in
order to authenticate you. The clever (but also dangerous) bit
is that you upload the code of your web site to GitHub and
Amazon will pull it from there. You can probably already guess
where this is going: in order to learn about Amazon's API, it
gives out some limited computing power for free. Somebody used
this offer in order to teach himself Ruby on Rails with a
mildly practical website. Unfortunately, he uploaded also his
secret keys to GitHub (this is really an easy mistake). Now,
nasty people crawl GitHub for the purpose of stealing such
secret keys. What can they do with this? Well, they quickly
max out the limit of computing power with Amazon and mine
Bitcoins (under somebody else's account). Fortunately for this
guy, Amazon was aware of this scam and in a goodwill gesture
refunded him the money the nasty guys incurred over
night with their Bitcoin mining. If you want to read the
complete story, google for ``My \$2375 Amazon EC2 Mistake''.

\subsubsection*{Multi-Signature Transactions}

To be explained.

\subsubsection*{Anonymity with Bitcoins}

One question one often hears is how anonymous is it actually
to pay with Bitcoins? Paying with paper money used to be a
quite anonymous act (unlike paying with credit cards, for
example). But this has changed nowadays: You cannot come to a
bank anymore with a suitcase full of money and try to open a
bank account. Strict money laundering and taxation laws mean
that not even Swiss banks are prepared to take such money and
open a bank account. That is why Bitcoins are touted as 
filling this niche again of anonymous payments. 

While Bitcoins are intended to be anonymous, the reality is
slightly different. I fully agree with the statement by
Nielsen from the blog article I referenced at the beginning:

\begin{quote}\it{}``Many people claim that Bitcoin can be used
anonymously. This claim has led to the formation of
marketplaces such as Silk Road (and various successors), which
specialize in illegal goods. However, the claim that Bitcoin
is anonymous is a myth. The block chain is public, meaning
that it’s possible for anyone to see every Bitcoin transaction
ever. Although Bitcoin addresses aren't immediately associated
to real-world identities, computer scientists have done a
great deal of work figuring out how to de-anonymise
`anonymous' social networks. The block chain is a marvellous
target for these techniques. I will be extremely surprised if
the great majority of Bitcoin users are not identified with
relatively high confidence and ease in the near future.''
\end{quote}

\noindent The only thing I can add to this is that with the Bitcoin
blockchain we will in the future have even more pleasure hearing
confessions from reputable or not-so-reputable people, like the
infamous ``I did not inhale'' from an US
president.\footnote{\url{www.youtube.com/watch?v=Bktd_Pi4YJw}} The
whole point of the blockchain is that it public and will always be.

There are some precautions one can take for boosting anonymity, for
example to use a new public-private key pair for every new
transaction, and to access Bitcoin only through the Tor network. But
the transactions in Bitcoins are designed such that they allow one to
combine incoming transactions. In such cases we know they must have
been made by the single person who knew the corresponding private
keys. So using different public-private keys for each transaction
might not actually make the de-anonymisation task much harder. And the
point about de-ano\-nymising `anonymous' social networks is that the
information is embedded into the structure of the transition
graph. And this cannot be erased with Bitcoins.

One paper that has fun with spotting transactions made to Silk Road (2.0)
and also to Wikileaks is

\begin{center}
\url{http://people.csail.mit.edu/spillai/data/papers/bitcoin-transaction-graph-analysis.pdf}
\end{center}

\noindent
A paper that gathers some statistical data about the blockchain is

\begin{center}
\url{https://eprint.iacr.org/2012/584.pdf}
\end{center}

\subsubsection*{Government Meddling}

Finally, what are the options for a typical Western government to
meddle with Bitcoins? This is of course one feature the proponents of
Bitcoins also tout: namely that there aren't any options. In my
opinion this is far too naive and far from the truth. Let us assume
some law enforcement agencies would not have been able to uncover the
baddies from Silk Road 1.0 and 2.0 (they have done so by uncovering
the Tor network, which is an incredible feat on its own). Would the
government in question have stopped? I do not think so. The next
target would have been Bitcoin.  If I were the government, this is
what I would consider:

\begin{itemize}
\item The government could compel ``mayor players'' to blacklist
  Bitcoins (for example at Bitcoin exchanges, which are usually
  located somewhere in the vicinity of the government's reach).  This
  would impinge on what is called \emph{fungibility} of Bitcoins and
  make them much less attractive to baddies. Suddenly their
  ``hard-earned'' Bitcoin money cannot be spent anymore. The attraction
  of this option is that this blacklisting can be easily done
  ``whole-sale'' and therefore be really be an attractive target for
  governments \& Co.
\item The government could attempt to coerce the developer
      community of the Bitcoin tools. While this might be a
      bit harder, we know certain governments are ready to
      take such actions (we have seen this with Lavabit, just
      that the developers there refused to play ball and shut
      down their complete operation).
\item The government could also put pressure on mining pools
      in order to blacklist transactions from baddies. Or be a
      big miner itself. Given the gigantic facilities that
      are built for institutions like the NSA (pictures from
      the Utah dessert)
      
      \begin{center}
      \includegraphics[scale=0.04]{../pics/nsautah1.jpg}
      \hspace{3mm}
      \includegraphics[scale=0.031]{../pics/nsautah2.jpg}
      \end{center}
      
      this would not be such a high bar to jump over. Remember it
      ``only'' takes to be temporarily in control of 50\%-plus of the
      mining capacity in order to undermine the trust in the
      system. Given sophisticated stories like Stuxnet (where we still
      do not know the precise details) maybe even such large
      facilities are not really needed. What happens, for example, if
      a government starts DoS attacks on existing miners? They have
      complete control (unfortunately) of all mayor connectivity
      providers, i.e.~ISPs.
      
      There are estimates that the Bitcoin mining capacity
      outperforms the top 500 supercomputers in the world,
      combined(!):
      
      \begin{center}\small
      \url{http://www.forbes.com/sites/reuvencohen/2013/11/28/global-bitcoin-computing-power-now-256-times-faster-than-top-500-supercomputers-combined/}
      \end{center}
      
      But my gut feeling is that these are too simplistic
      calculations. In security (and things like Bitcoins) the
      world is never just black and white. The point is once
      the trust is undermined, the Bitcoin system would need
      to be evolved to Bitcoins 2.0. But who says that Bitcoin
      2.0 will honour the Bitcoins from Version 1.0?
      \end{itemize} 

\noindent A government would potentially not really
need to follow up with such threads. Just the rumour that it
would, could be enough to get the Bitcoin-house-of-cards to
tumble. Some governments have already such an ``impressive''
trackrecord in this area, such a thread would be entirely
credible. Because of all this, I would not have too much hope
that Bitcoins are free from interference by governments \& Co when
it will stand in their way, despite what everybody else is
saying. To sum up, the technical details behind Bitcoins are
simply cool. But still the entire Bitcoin ecosystem is in my
humble opinion rather fragile. 

\subsubsection*{Further Reading}

Finally, finally, the article

\begin{center}\small
\url{http://www.extremetech.com/extreme/155636-the-bitcoin-network-outperforms-the-top-500-supercomputers-combined}
\end{center}

\noindent makes an interesting point: If people are willing to
solve meaningless puzzles for hard, cold cash and with this
achieve rather impressive results, what could we achieve if
the UN, say, would find the money and incentivise people to,
for example, solve protein folding
puzzles?\footnote{\url{http://en.wikipedia.org/wiki/Protein_folding}}
For this there are projects like
Folding@home.\footnote{\url{http://folding.stanford.edu}} 
This might help with curing diseases such as Alzheimer or
diabetes. The same point is made in the article

\begin{center}\small
\url{http://gizmodo.com/the-worlds-most-powerful-computer-network-is-being-was-504503726}
\end{center}

A definitely interesting and worthy use of Bitcoins has been explored 
in the thesis

\begin{center}
\url{http://enetium.com/resources/Thesis.pdf}
\end{center}

\noindent where the author proposes ways of publishing information
that is censor resistant as part of the blockchain. The idea is that
if a government wants to use Bitcoins, it would also have to put up
with plain-text data that can be included in a transaction.

\end{document}

bit coin

A fistful of bitcoins
http://cseweb.ucsd.edu/~smeiklejohn/files/imc13.pdf
http://cseweb.ucsd.edu/~smeiklejohn/files/imc13.pdf

Ross Anderson & Co (no dispute resolution; co-ercion)
http://www.cl.cam.ac.uk/~sjm217/papers/fc14evidence.pdf

http://www.michaelnielsen.org/ddi/how-the-bitcoin-protocol-actually-works/
http://www.imponderablethings.com/2013/07/how-bitcoin-works-under-hood.html

http://randomwalker.info/bitcoin/

Jeffrey Robinson
Bitcon: The Naked Truth about Bitcoin

The Bitcoin Backbone Protocol: Analysis and Applications
https://eprint.iacr.org/2014/765.pdf
