33 video about the technical details behind Bitcoins.

    33 video about the technical details behind Bitcoins. I will

    34 also use some of their pictures.

    70 public key $K^{pub}$ to verify the message came from the

    71 public key $K^{pub}$ to verify that the message came from the

    80 Googlemail, but which are already taken.

    81 Gmail, but which are already taken.

    81 

    82 

    82 One main difference between Bitcoins and traditional banking

    83 One major difference between Bitcoins and traditional banking

   111 including Bob, can use Alice's public key $K^{pub}_{Alice}$

   112 including Bob, can use Alice's public key $K^{pub}_{Alice}$ to

   112 for verifying that this message came really from Alice, or

   113 verify that this message came really from Alice, or more

   113 more precisely from the person who knows $K^{priv}_{Alice}$. 

   114 precisely from the person who knows $K^{priv}_{Alice}$. 

   116 what happens if Bob receives 10, say, of these transactions.

   117 what happens if Bob receives 10, say, of these transactions?

   146 was taken offline by law enforcement. Bitcoins is more a

   147 was taken offline by law enforcement. Bitcoins is more like a

   147 system like BitTorrent without a single central entity that

   148 system such as BitTorrent without a single central entity that

   148 can be taken offline.

   149 can be taken offline.\footnote{There is some Bitcoin

   150 infrastructure that is not so immune from being taken offline:

   151 for example Bitcoin exchanges, HQs of Bitcoin mining pools,

   152 Bitcoin developers and so on.}

   154 is called \emph{blockchain}. Bob, for example, can use his

   158 is called the \emph{blockchain}. Bob, for example, can use his

   171 with. This hash is the unique serial number of each block.

   175 with. This hash is also the unique serial number of each

   172 Since this previous-block-reference is also part of the hash,

   176 block. Since this previous-block-reference is also part of the

   173 the whole chain is robust against tampering. I let you think

   177 hash, the whole chain is robust against tampering. I let you

   174 why this is the case?\ldots{}But does it actually eliminate

   178 think why this is the case?\ldots{}But does it actually

   175 all possibilities of fraud?

   179 eliminate all possibilities of fraud?

   213 But in Bitcoins it is also important to have the ability to

   217 In Bitcoins you have the ability to both combine incoming

   214 split the money from one or more incoming transaction to

   218 transactions, but also to split outgoing transactions to

   215 potentially more than one receiver. Consider again the

   219 potentially more than one receiver. The latter is needed.

   216 rightmost transactions in Figure~\ref{txngraph} and suppose

   220 Consider again the rightmost transactions in

   217 Alice is a coffeeshop owner selling coffees for 1 Bitcoin.

   221 Figure~\ref{txngraph} and suppose Alice is a coffeeshop owner

   218 Charles received a transaction from Zack over 5 Bitcoins, say.

   222 selling coffees for 1 Bitcoin. Charles received a transaction

   219 How does he pay for the coffee? There is no explicit notion of

   223 from Zack over 5 Bitcoins, say. How does he pay for the

   220 \emph{change} in the Bitcoin system. What Charles has to do

   224 coffee? There is no explicit notion of \emph{change} in the

   221 instead is to make one single transaction with 1 Bitcoin to

   225 Bitcoin system. What Charles has to do instead is to make one

   222 Alice and with 4 Bitcoins going back to himself, which then

   226 single transaction with 1 Bitcoin to Alice and with 4 Bitcoins

   223 Charles can use to give to Emily, for example.

   227 going back to himself, which then Charles can use to give to

   228 Emily, for example.

   240 remaining 3 Bitcoins ``back'' to herself. In this case she

   245 remaining 3 Bitcoins back to herself. In this case she would

   241 would now be in the ``possession'' of two unspend Bitcoin

   246 now be in the possession of two unspend Bitcoin transactions,

   242 transactions, one over 3 Bitcoins and the independent one over

   247 one over 3 Bitcoins and the independent one over 6 Bitcoins.

   243 6 Bitcoins. Or, Emily could combine both transactions (one

   248 Or, Emily could combine both transactions (one over 4 Bitcoins

   244 over 4 Bitcoins from Charles and the independent one over 6

   249 from Charles and the independent one over 6 Bitcoins) and then

   245 Bitcoins) and then split this amount with 1 Bitcoin going to

   250 split this amount with 1 Bitcoin going to Alice and 9 Bitcoins

   246 Alice and 9 Bitcoins going back to herself. 

   251 going back to herself. 

   249 concept of transactions really sink in\ldots{}You should see

   254 concept of transactions to really sink in\ldots{}You should

   250 that there is really no need for a central ledger and no need

   255 see that there is really no need for a central ledger and no

   251 for an account balance as familiar from traditional banking.

   256 need for an account balance as familiar from traditional

   252 The closest what Bitcoin has to offer for the notion of a

   257 banking. The closest what Bitcoin has to offer for the notion

   253 balance in a bank account are the unspend transactions that a

   258 of a balance in a bank account are the unspend transactions

   254 person (more precisely a public-private key address) received.

   259 that a person (more precisely a public-private key address)

   255 That means transactions that can still be forwarded. 

   260 received. That means transactions that can still be forwarded. 

   280 forward the Bitcoins that are in your name to an address the

   285 forwards the Bitcoins that are in your name to an address the

   315 coffee. But behind his back, however, she has convinced

   320 coffee. But behind his back she has convinced everybody else

   316 everybody else on the network that she is still the rightful

   321 on the network that she is still the rightful owner of the

   317 owner of the Bitcoin. After being outvoted, Bob would be a tad

   322 Bitcoin. After being outvoted, Bob would be a tad peeved. 

   318 peeved. 

   335 difficult, Bitcoin uses a kind of puzzles. Solving the puzzles

   339 difficult, Bitcoin uses a kind of puzzle. Solving the puzzles

   387 suitable one. In Bitcoins the puzzles are not solved according

   391 suitable one. 

   388 to how many leading zeros a has-value has, but rather whether

   392 

   389 it is below a \emph{target}. The hardness of the puzzle can

   393 In Bitcoins the puzzles are not solved according to how many

   390 actually be controlled by changing the target according to the

   394 leading zeros a hash-value has, but rather whether it is below

   391 available computational power available. I think the

   395 a \emph{target}. The hardness of the puzzle can actually be

   392 adjustment of the hardness of the problems is done every two

   396 controlled by changing the target according to the available

   393 weeks. I am not sure whether this is an automatic process. The

   397 computational power available. I think the adjustment of the

   394 aim of the adjustment is that on average the Bitcoin network

   398 hardness of the problems is done every 2060 blocks

   395 will most likely solve a puzzle within 10 Minutes. 

   399 (appr.~every two weeks). I am not sure whether this is an

   400 automatic process. The aim of the adjustment is that on

   401 average the Bitcoin network will most likely solve a puzzle

   402 within 10 Minutes. 

   407 The validation and the derivation of the puzzle is done as 

   414 Consider the following picture with a blockchain and some

   408 follows:

   415 unconfirmed transactions. 

   415 \noindent There are some unconfirmed transactions. Choosing

   422 \noindent The puzzle is given as follows: There are some

   416 some of them, the miner (i.e.~the person/computer that tries

   423 unconfirmed transactions. Choosing some of them, the miner

   417 to solve a puzzle) will form a putative block to be added to

   424 (i.e.~the person/computer that tries to solve a puzzle) will

   418 the blockchain. This putative block will contain the

   425 form a putative block to be added to the blockchain. This

   419 transactions and the reference to the previous block. The

   426 putative block will contain the transactions and the reference

   420 serial number of such a block is simply the hash of all the

   427 to the previous block. The serial number of such a block is

   421 data. The puzzle can then be stated as the ``string''

   428 simply the hash of all the data. The puzzle can then be stated

   422 corresponding to the block and which salt is needed in order

   429 as the ``string'' corresponding to the block and which salt is

   423 to have the hashed value being below the target. Other miners

   430 needed in order to have the hashed value being below the

   424 will choose different transactions and therefore work on a 

   431 target. Other miners will choose different transactions and

   425 slightly different putative block and puzzle.

   432 therefore work on a slightly different putative block and

   433 puzzle.

   428 blockchain is at every given moment nicely linearly ordered,

   436 blockchain is at every given moment linearly ordered, see the

   429 see the picture shown in \eqref{unconfirmed}. If we don’t have

   437 picture shown in \eqref{unconfirmed}. If we don’t have such a

   430 such a linear ordering at any given moment then it may not be

   438 linear ordering at any given moment then it may not be clear

   431 clear who owns which Bitcoins. Assume a miner David is lucky

   439 who owns which Bitcoins. Assume a miner David is lucky and

   432 and finds a suitable salt to confirm the transactions. Should

   440 finds a suitable salt to confirm the transactions. Should he

   433 he celebrate? Not yet. Typically the blockchain will look as

   441 celebrate? Not yet. Typically the blockchain will look as

   446 \noindent What should be done in this case? The tie is broken

   454 \noindent What should be done in this case? Well, the tie is

   447 if another block is solved, like so:

   455 broken if another block is solved, like so:

   454 the network keep track of all forks. But at any given time,

   462 the network keep track of all forks (they can see). But at any

   455 miners only work to extend whichever fork is longest in their

   463 given time, miners only work to extend whichever fork is

   456 copy of the block chain. Why should miners work on the longest

   464 longest in their copy of the block chain. Why should miners

   457 fork? Well their incentive is to mine Bitcoins. If somebody

   465 work on the longest fork? Well their incentive is to mine

   458 else already solved a puzzle, then it makes more sense to work

   466 Bitcoins. If somebody else already solved a puzzle, then it

   459 on a new puzzle and obtain the Bitcoins for solving that

   467 makes more sense to work on a new puzzle and obtain the

   460 puzzle. Note that whoever solved a puzzle on the ``loosing''

   468 Bitcoins for solving that puzzle, rather than wast efforts on

   461 fork will actually not get any Bitcoins as reward. Tough luck.

   469 a fork that is shorter and therefore less likely to be

   470 ``accepted''. Note that whoever solved a puzzle on the

   471 ``loosing'' fork will actually not get any Bitcoins as reward.

   472 Tough luck.

   473 

   465 Let is see how the blockchain and the proof-of-work puzzles

   477 Let us see how the blockchain and the proof-of-work puzzles

   467 Bob she would need to pull off the following ploy:

   479 Bob, she would need to pull off the following ploy:

   477 validate the fraudulent transaction to herself instead. 

   489 validate the fraudulent transaction to herself instead. At

   490 this moment she is in a race against all the computing power

   491 of the ``rest of the world''. Because the incentive of the

   492 rest of the world is to work on the longest chain, that is the

   493 one with the transaction from Alice to Bob:

   483 \noindent At this moment she is in a race against all the

   499 \noindent As shown in the picture she has to solve the puzzles

   484 computing power of the ``rest of the world''. She has to solve

   500 2a to 5a one after the other, because the hash of a block is

   485 the puzzles one by one, because the hash of a block is

   501 determined via the reference by all the data in the previous

   486 determined by all the data in the previous has. She might be

   502 block. She might be very lucky to solve one puzzle for a block

   487 very lucky to solve one puzzle for a block before the rest of

   503 before the rest of the world, but to be lucky many times is

   488 the world, but to be lucky many times is very unlikely. In

   504 very unlikely. This principle of having to race against the

   489 order to raise the bar for Alice, merchants accepting Bitcoin

   505 rest of the world avoids the ploy of double spend.

   490 use the following rule of thumb: A transaction is

   506 

   491 ``confirmed'' if (1) it is part of a block in the longest

   507 In order to raise the bar for Alice even further, merchants

   492 fork, and (2) at least 5 blocks follow it in the longest fork.

   508 accepting Bitcoin use the following rule of thumb: A

   493 In this case we say that the transaction has ``6

   509 transaction is ``confirmed'' if 

   494 confirmations''. A simple calculation shows that these number

   510 

   495 of confirmations can take up to 1 hour and more. While this

   511 \begin{itemize}

   496 seems excessively long, from the merchant's point of view it

   512 \item[(1)] it is part of a block in the longest fork, and 

   497 is not long at all. For this recall that ordinary credit cards

   513 \item[(2)] at least 5 blocks follow it in the longest fork. In

   514            this case we say that the transaction has ``6

   515            confirmations''. 

   516 \end{itemize} 

   517 

   518 \noindent A simple calculation shows that this amount of

   519 confirmations can take up to 1 hour and more. While this seems

   520 excessively long, from the merchant's point of view it is not

   521 that long at all. For this recall that ordinary creditcards

   500 cheat are very low.

   524 cheat are very low, unless she can muster more than 50\% of

   525 the world Bitcoin mining capacity.

   506 world, which typically takes 10 minutes, is negligibly low.

   531 world, which typically takes only 10 minutes, is negligibly

   507 Therefore many people join groups called \emph{mining pools}

   532 low. Therefore many people join groups called \emph{mining

   508 that collectively work to solve blocks, and distribute rewards

   533 pools} that collectively work to solve blocks, and distribute

   509 based on work contributed. These mining pools act somewhat

   534 rewards based on work contributed. These mining pools act

   510 like lottery pools among co-workers, except that some of these

   535 somewhat like lottery pools among co-workers, except that some

   511 pools are quite large, and comprise more than 20\% of all the

   536 of these pools are quite large, and comprise more than 20\% of

   512 computers in the network. It is said that BTC, the largest

   537 all the computers in the network. It is said that BTC, a large

   519 \ldots

   549 Let us now turn to the nitty gritty details. As a user you 

   550 need to generate and store a public-private key pair. The 

   551 public key you need to advertise in order to receive payments 

   552 (transactions). The private key needs to be securely stored. 

   553 For this there seem to be three possibilities

   554 

   555 \begin{itemize}

   556 \item an electronic wallet on your computer

   557 \item a cloud-based storage (offered by some Bitcoin service)

   558 \item paper-based

   559 \end{itemize}

   560 

   561 \noindent The first two options of course offer convenience

   562 for making and receiving transactions. But given the nature of

   563 the private key and how much security relies on them (recall

   564 if somebody gets hold of it, your Bitcoins are quickly lost

   565 forever) I would opt for the third option for anything except

   566 for trivial amounts of Bitcoins. As we have seen securing a

   567 computer system that it can withstand a breakin is still very

   568 much an unsolved problem.

   569 

   570 An interesting fact with Bitcoin keys is that there is no

   571 check for duplicate addresses. This means when generating a

   572 public-private key, you should really start with a carefully

   573 chosen random number such that there is really no chance to

   574 step on somebody's feet in the $2^{160}$ space of

   575 possibilities. Again if you share an address with somebody

   576 else, he or she has access to all your unspend transactions.

   577 The absence of such a check is easily explained: How would one

   578 do this in a distributed system? The answer you can't. It is

   579 possible to do some sanity check of addresses that are already

   580 used in the black chain, but this is not a fail-proof method.

   581 One really has to trust on the enormity of the $2^{160}$

   582 number.

   583 

   584 Let us now look at the data that is stored in an transaction 

   585 message:

   523 \noindent

   589 \noindent The hash in Line 1 is the hash of all the data that

   524 The hash in Line 1 is the has of all the data that follows. It

   590 follows. It is a kind of serial number for the transaction.

   525 is a kind of serial number for the transaction. Line 2

   591 Line 2 contains a version number in case there are some

   526 contains a version number. Line 3 and 4 specify how many

   592 incompatible changes to be made. Lines 3 and 4 specify how

   527 incoming transactions are combined and how many outgoing

   593 many incoming transactions are combined and how many outgoing

   528 transactions there are. In our example there are 1 each. Line

   594 transactions there are. In our example there are one for each.

   529 5 specifies a lock time for when the transaction is supposed

   595 Line 5 specifies a lock time for when the transaction is

   530 to become active---this is usually set to 0 to become active

   596 supposed to become active---this is usually set to 0 to become

   531 immediately. Line 6 specifies the size of the message; it has

   597 active immediately. Line 6 specifies the size of the message;

   532 nothing to do with the Bitcoins that are transferred. Lines 7

   598 it has nothing to do with the Bitcoins that are transferred.

   533 to 11 specify where the Bitcoins in the transaction are coming

   599 Lines 7 to 11 specify where the Bitcoins in the transaction

   534 from. The has in line 9 specifies the incoming transaction and

   600 are coming from. The has in line 9 specifies the incoming

   535 the \pcode{n} in Line 10 specifies which output of the

   601 transaction and the \pcode{n} in Line 10 specifies which

   536 transaction is referred to. The signature in line 11 specifies

   602 output of the transaction is referred to. The signature in

   537 the address (public key $K^{pub}$) from where the Bitcoins are

   603 line 11 specifies the address (public key $K^{pub}$) from

   538 taken and the digital signature of the address, that is

   604 where the Bitcoins are taken and the digital signature of the

   539 $\{K^{pub}\}_{K^{priv}}$. Lines 12 to 15 specify the value of

   605 address, that is $\{K^{pub}\}_{K^{priv}}$. Lines 12 to 15

   540 the first outgoing transaction. In this case 0.319 Bitcoins.

   606 specify the value of the first outgoing transaction. In this

   541 The hash in Line 14 specifies the address to where the

   607 case 0.319 Bitcoins. The hash in Line 14 specifies the address

   542 Bitcoins are transferred.

   608 to where the Bitcoins are transferred.

   544 \ldots

   610 As can be seen there is no need to issue serial numbers for

   611 transactions, the hash of the transaction data can do this

   612 job. The hash will contain the sender addresses and

   613 hash-references to the incoming transactions, as well as the

   614 public key of the incoming transaction. This uniquely

   615 identifies a transaction and the hash is the unique

   616 fingerprint of it. The in-field also contains the address to

   617 which a earlier transaction is made. The digital signature

   618 ensures everybody can check that the person who makes this

   619 transaction is in the possession of the private key. Otherwise

   620 the signature would not match up with the public-key address.

   621 

   622 When mining the blockchain it only needs to be ensured that

   623 the transactions are consistent (all hashes and signatures

   624 match up). Then we need to generate the correct previous-block

   625 link and solve the resulting puzzle. Once the block is

   626 accepted, everybody can check the integrity of the whole

   627 blockchain.

   628 

   629 A word of warning: The point of a lottery is that some people

   630 win. But equally, that most people lose. Mining Bitcoins has

   631 pretty much the same point. According to the article below, a

   632 very large machine (very, very large in terms of June 2014)

   633 could potentially mine \$40 worth of Bitcoins a day, but would

   634 require magnitudes more of electricity costs to do so. 

   635 

   636 \begin{center}

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

   638 \end{center}

   639 

   549 to pay with Bitcoins? Paying with paper money in the past was

   644 to pay with Bitcoins? Paying with paper money used to be a

   550 quite an anonymous act (unlike paying with creditcards), but

   645 quite anonymous act (unlike paying with creditcards, for

   551 this has changed nowadays. You cannot come to a bank anymore

   646 example). But this has changed nowadays: You cannot come to a

   552 with a suitcase full of money and try to open a bank account.

   647 bank anymore with a suitcase full of money and try to open a

   553 Strict money laundering and taxation laws mean that not even

   648 bank account. Strict money laundering and taxation laws mean

   554 Swiss banks are prepared to take such money and open a bank

   649 that not even Swiss banks are prepared to take such money and

   555 account. With Bitcoins the situation is different, but I fully

   650 open a bank account. That is why Bitcoins are touted as 

   556 agree with the statement by Nielsen from the blog article I

   651 filling this niche again of anonymous payments. 

   557 referenced at the beginning:

   652 

   653 While Bitcoins are intended to be anonymous, the reality is

   654 slightly different. I fully agree with the statement by

   655 Nielsen from the blog article I referenced at the beginning:

   575 will have even more fun with many more confessions like the

   673 will have even more fun hearing confessions like the infamous

   576 infamous ``I did not

   674 ``I did not

   579 always be. There are some precautions that are suggested, like

   677 always be. 

   580 to use a new public-private key pair for every new transaction

   678 

   581 or access Bitcoin only through the Tor network. But the

   679 There are some precautions that are suggested, like to use a

   680 new public-private key pair for every new transaction, and to

   681 access Bitcoin only through the Tor network. But the

   586 keys for each transaction, might not make the de-anonymisation

   686 keys for each transaction might not actually make the

   587 task much harder. And the point about de-anonymising

   687 de-anonymisation task much harder. And the point about

   588 `anonymous' social networks is that the information is

   688 de-ano\-nymising `anonymous' social networks is that the

   589 embedded into the structure of the transition graph. And this

   689 information is embedded into the structure of the transition

   590 cannot be erased with Bitcoins.

   690 graph. And this cannot be erased with Bitcoins.

   594 proponents of Bitcoins tout: namely that there aren't any

   694 proponents of Bitcoins also tout: namely that there aren't any

   595 options. In my opinion this is too naive and far from the

   695 options. In my opinion this is far too naive and far from the

   597 have been able to uncover the baddies from Silk Road 2.0 (they

   697 have been able to uncover the baddies from Silk Road 1.0 and

   598 have done so by uncovering the Tor network, and incredible

   698 2.0 (they have done so by uncovering the Tor network, which is

   599 feat on its own). Would a government have stopped?

   699 an incredible feat on its own). Would a government have

   700 stopped? I think no. The next target would have been Bitcoin.

   701 If I were the government, this is what I would consider:

   603       blacklist Bitcoins (for example at exchanges). This

   705       blacklist Bitcoins (for example at Bitcoin exchanges).

   604       would impinge on what is called \emph{fungibility} of

   706       This would impinge on what is called \emph{fungibility}

   605       Bitcoins and make them much less attractive to baddies.

   707       of Bitcoins and make them much less attractive to

   606       This blacklisting can be easily done ``whole-sale'' and

   708       baddies. Suddenly their hard-earned Bitcoin money cannot

   709       be spent anymore.The attraction of this option is that

   710       this blacklisting can be easily done ``whole-sale'' and

   609 \item They could attempt to coerce developer community of the

   713 \item The government could attempt to coerce the developer

   610       Bitcoin tools. While this might be a bit harder, we know

   714       community of the Bitcoin tools. While this might be a

   611       certain governments are ready to take such actions (we

   715       bit harder, we know certain governments are ready to

   612       have seen this with Lavabit, just that the developers

   716       take such actions (we have seen this with Lavabit, just

   613       there refused to play ball and shut down their complete

   717       that the developers there refused to play ball and shut

   614       operation).

   718       down their complete operation).

   616       in order to blacklist transactions from baddies. Or be

   720       in order to blacklist transactions from baddies. Or be a

   618       are built for institutions like the NSA

   722       are built for institutions like the NSA (pictures from

   723       the Utah dessert)

   626       this would not be such a high bar to jump over.

   731       this would not be such a high bar to jump over. Remember

   627 \end{itemize} 

   732       it ``only'' takes to temporarily be in control of 50\%+

   628 

   733       of the mining capacity in order to undermine the trust

   629 \noindent Finally the government would potentially not need to

   734       in the system. Given sophisticated stories like Stuxnet

   630 follow up with such threads. Just the rumour that it would,

   735       (where we still not know the precise details) maybe even

   631 could be enough to get the Bitcoin-house-of-cards to tumble.

   736       such large facilities are not really needed. What

   632 Because of all this I would not have too much hope that

   737       happens, for example, if a government starts DoS attacks

   633 Bitcoins are free from government \& Co interference when it

   738       on existing miners: They have complete control

   634 will stand in its way.

   739       (unfortunately) of all mayor connectivity providers,

   635 

   740       i.e.~ISPs. 

   741       

   742       There are estimates that the Bitcoin mining capacity

   743       outperforms the top 500 supercomputers in the world,

   744       combined(!):

   745       

   746       \begin{center}\small

   747       \url{http://www.forbes.com/sites/reuvencohen/2013/11/28/global-bitcoin-computing-power-now-256-times-faster-than-top-500-supercomputers-combined/}

   748       \end{center}

   749       

   750       But my gut feeling is that these are too simplistic

   751       calculations. In security (and things like Bitcoins) the

   752       world is never just black and white. The point is once

   753       the trust is undermined, the Bitcoin system would need

   754       to be evolved to Bitcoins 2.0. But who says that Bitcoin

   755       2.0 will honour the Bitcoins from Version 1.0?

   756       \end{itemize} 

   757 

   758 \noindent Finally, a government would potentially not really

   759 need to follow up with such threads. Just the rumour that it

   760 would, could be enough to get the Bitcoin-house-of-cards to

   761 tumble. Some governments have already such a ``impressive''

   762 trackrecord in this area, such a thread would be entirely

   763 credible. Because of all this, I would not have too much hope

   764 that Bitcoins are free from government \& Co interference when

   765 it will stand in its way, despite what everybody else is

   766 saying. To sum up, the technical details behind Bitcoins are

   767 simply cool. But still the entire Bitcoin ecosystem is in my

   768 humble opinion rather fragile. 

   769 

   770 \subsubsection*{Further Reading}

   771 

   772 Finally, finally, the article

   773 

   774 \begin{center}\small

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

   776 \end{center}

   777 

   778 \noindent makes an interesting point: If people are willing to

   779 solve meaningless puzzles for hard, cold cash and with this

   780 achieve rather impressive results, what could we achieve if

   781 the UN, say, would find the money and incentivise people to,

   782 for example, solve protein folding

   783 puzzles?\footnote{\url{http://en.wikipedia.org/wiki/Protein_folding}}

   784 There are projects like

   785 Folding@home\footnote{\url{http://folding.stanford.edu}} which have 

   786 This might help with curing diseases such as Alzheimer or

   787 diabetes, which to a large portion baddies and goodies will

   788 suffer at some point. The same point is made in the article

   789 

   790 \begin{center}\small

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

   792 \end{center}