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\section*{Handout 7 (Bitcoins)}

In my opinion Bitcoins are a 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 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 their

disposal. Below I will follow the very readable explanations

about Bitcoins from

\begin{center}

\url{http://www.michaelnielsen.org/ddi/how-the-bitcoin-protocol-actually-works/}\smallskip\\

\url{http://www.imponderablethings.com/2013/07/how-bitcoin-works-under-hood.html}

\end{center}

Let us start with the question who invented Bitcoins? You

could not make up the answer, but we actually do not know who

is the inventor. 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. The first

Bitcoin transaction was made in January 2009. The rules in

Bitcoin are set up so that there will only be 21 Million

Bitcoins with the maximum reached around year 2140. Contrast

this with other fiat currencies where money can be printed

almost at will. The smallest unit of a Bitcoin is called a

Satoshi which is the $10^{-8}$ part of a Bitcoin. Remember a

Penny is the $10^{-2}$ part of a Pound.

The two main cryptographic building blocks of Bitcoins are

cryptographic hashing (SHA-256) and public-private keys using 

elliptic-curve encryption for digital signatures. Hashes are 

used to generate `fingerprints' of data that ensures its

integrity. 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 public key to

verify the message came from the person who knew the private

key. Signatures are used in Bitcoins for verifying the

addresses where the Bitcoins come 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 test

for duplicates\ldots{}or already used addresses.

Traditional banking involves a central ledger which specifies

the current balance in each account, for example 

\begin{center}

\begin{tabular}{l|r}

account & 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

central ledger, but a public record of all transactions. This

means spending money corresponds to sending messages of

the very rough form 

\begin{center}

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

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\noindent They are encrypted with Alice's private key such

that everybody, including Bob, can use Alice's public key

$K^{pub}_{ALice}$ in order to verify the 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 what happens if Bob receives 10, say, of

these messages. Did Alice intend to send him 10 Bitcoins, or

did the message by Alice get duplicated by for example an

attacker re-playing a sniffed message. What is needed is

a kind of serial number for such messages. Meaning transaction 

messages look more like 

\begin{center}

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

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\noindent There are two problems that need to be solved. 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 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 single point of ``failure'' which was taken

offline by law enforcement. 

Bitcoin solves 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 

\emph{blockchain}. Bob can use his copy of the blockchain for 

determining whether Alice owned the Bitcoin and if yes 

transmits the message to every other participant on the 

Bitcoin network. The blockchain looks roughly like a very long 

chain of individual blocks

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\noindent Each block contains a list of individual

transactions. They are hashed so that the data in the

transactions cannot be tampered with. This hash is the unique

serial number of each block. Each block also contains a

reference of the previous block. Since this

previous-block-reference is also hashed, the whole chain is

robust against tampering. We can check this by checking the

entire blockchain whether the references and hashes are

correctly recorded. I have not tried it myself, but it is said

that with the current amount of data in the blockchain it

takes roughly a day to check the consistency of the blockchain

on a ``normal'' computer. Fortunately this consistency test

from the beginning usually only needs to be done once.

Recall I wrote earlier Bitcoins that do not maintain a ledger

listing all the current balances in each account.

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bit coin

https://bitcoin.org/bitcoin.pdf

https://bitcoin.org/bitcoin.pdf

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/