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Tuesday, Aug 02, 2011 - 02:23 SGT
Posted By: Gilbert

Bitcoins In Them Thar Hills

This came across as so intriguing that I just had to give the lowdown on it, so here it is:


Bitcoins


If it helps, you can imagine them to look like this
(Source: microsreports.com)


So what exactly are these "Bitcoins"? Well, you could scan the official FAQ and Wikipedia entry, but in short, Bitcoin is a digital currency, and a special one at that. What makes it so special is that, unlike implementations like e-gold, which are backed by a physical commodity (gold, in this case), or even stuff like World of Warcraft or other MMORPG items, which at least have utility in some virtual world, Bitcoins are intrinsically quite darn worthless.

Or they would be, had they not had one special property - they are hard to get, and therefore scarce, and as we all know, scarcity (and greed) is the bedrock of all economics.

But let's rewind to the beginning. A couple of years ago, a guy using the pseudonym Satoshi Nakamoto released a paper on a "peer-to-peer electronic cash system", and it didn't even go towards a thesis or anything. Basically, it described how a distributed marketplace with no central authority could be designed, such that privacy is (at least in theory) preserved, even as the security of currency transactions is publicly verifiable (as we have seen, these two objectives are often incompatible).

As to how this is done, what happens in a nutshell is that a public-key cryptography is applied in a sequence, producing a chain which can be followed right till the beginning if required. As each transaction is made, the previous owner uses his private key to generate a signature, which is appended to the end of the current hash-chain file, which can be (very quickly) verified using his public key*.

[*N.B. Public-key cryptography is fascinating in its own right, and revolutionized cryptography by breaking the symmetry of encryption and decryption; previously, nearly all codes were reversible by the same procedure used to encode them.

We shall not delve into the details, but suffice to say that a (for all intents and purposes unique) pair of keys, one public and the other private, can be generated by mathematical wizardry on demand. Then, decoding with a public key (which everybody is assumed to know) proves authorship by the owner of the private key (the use mentioned above), and encoding with a public key provides security (as nobody but the owner of the private key can decode it)]

Then, Nakamoto continued describing how a network of anonymous users could verify that a chain of transactions is valid, i.e. it originated with a legitimate unit of currency. Again, I shall not go into the details, suffice to mention that it was proven to work if honest users controlled at least half of the computing power of the entire network (which, as it happens, is better than the more-than-two-to-one ratio required in the Byzantine Generals Problem).

Now, all this is kind of interesting, but basically it's adapting nested public-key signatures into a networked context (which by the way is still vulnerable to simple expedients like flooding attacks, as with most public networks). It might have gotten into a journal somewhere, I don't know.

So we come to the fun part: what exactly is the original currency that is nested within the encrypted hash-chains?


Mining Thar Hills


Sorry, no Bitcoins found today, better luck tomorrow!
(Source: my-ecoach.com)


Well, basically any block of data could have been used, since verification depends on a (traceable) public trail of transaction records. It should have been entirely possible, if desired, to set up something akin to a central bank, with sole authority over issuing new currency units (probably verifiable using its public key)

That wouldn't have been fun, however, quite aside from the question of what might constitute a legitimate central bank; if the inventor of this system went this route, he might as well have been handing out self-created Monopoly money, endorsed by the Private Bank of Nakamoto or equivalent. As you might verify with an inkjet printer, this sort of scrip is unlikely to be valued (unlike actual local currencies, which have interest vested in them by an entire community).

What was done instead was quite ingenious; it was set up so that literally anybody with a computer could mine for Bitcoins. How this is done is that users generate random blocks of data, which they feed into a hashing function, and check whether the output satisfies certain (rare) properties.

The hashing function used here is basically one-way (or asymmetric) [and is therefore also used in public key cryptography, as mentioned] - putting a value x into the function, it is very simple to check that it returns a value y, but given y, it is extremely difficult to discover that it originated from the value x. Therefore, although users know which values of y are valuable (due to possessing those rare properties), the only known way to obtain x is by brute force, i.e. trying many combinations of x.

Following onto that, since brute forcing is required, computational power is king, though as it happens, graphics cards are much better at repetitive hashing operations than CPUs. Still, anybody with a computer can grab a metaphorical pickaxe (by downloading and running a program) and start cracking some hashes, although since the system was planned to increase the difficulty of generating Bitcoins as time passes, many users have found it convenient to pool their efforts for more regular rewards.

And how big are these rewards? Currently, one Bitcoin trades for about US$13.50. To put that into perspective, my N460GTX graphics card runs at about 50 to 70 million hashes per second, roughly as predicted. This translates to approximately 0.03 Bitcoins mined per day (using the deepbit.net pool), or about 50 US cents, which is not very impressive. This hasn't stopped enthusiastic prospectors from assembling customized rigs (often at cost) to crunch those numbers, or even appropriate entire computer labs.


Fool's Gold?


Image does not actually depict pyrite
(Source: moviewallpaper.net)


Here, my economics training has to kick in. Let's step back and take stock of the situation - people are performing heaps of basically useless computations, and are selling (and therefore buying) the meaningless results, and for quite a bit of money. A couple of months back, a user famously had some 25000 Bitcoins stolen. That came to about half a million bucks (a little less at today's rates), by the way.

Furthermore, performing these useless computations is not free. You would need a computer, to begin with. Fine, you might need a computer anyway, but taxing your graphics cards causes it to draw extra electricity - which costs real money (unless someone else is paying the power bill).

While mining may still be profitable, at least at current exchange rates, and almost certainly when Bitcoin first started since the hashes used were much simpler and faster to discover then, there is no guarantee that Bitcoin value will hold up, as admitted in the FAQ, which incidentally makes a good point about scarcity alone not guaranteeing value.

Unfortunately, to be frank, scarcity is about all that Bitcoin has going for it, the way I see it. While it is true that actual gold is not that useful, and often dug up only to be deposited in an underground vault somewhere, it at least has some practical applications (and is shiny besides)

Try a little thought experiment: what is stopping somebody else from copying Bitcoin's concept (perhaps using a different hashing algorithm)? He would be able to offer much better potential returns (for the same computing resources), since users would have the opportunity to be early adopters (and go up against easy hashes) on a new network. The relative complexity might have deterred many casual entrepreneurs, but given some starving mathematicians and perhaps some external backing (e.g. giving away some incentives in the form of hard cash to kickstart the new system), a Bitcoin clone can quite likely outstrip the original.

Of course, if this happens, those heavily invested in the original Bitcoin (such as by purchasing hardware for the express purpose of mining) would loudly proclaim its (unfortunately non-unique) merits and denounce the clone, while those who switched over to the new clone would do the reverse. Sort of what happens when supporters of opposing multi-level marketing schemes meet, come to think of it.

Anyway, I daresay that Nakamoto, whoever he is, must be laughing all the way to the bank, having literally created value from nothing (and a bit of embellishment). What, you're saying that the creator of the system didn't compute a nice little stash of Bitcoins at the beginning? My apologies. Ponzi? Perhaps not, but I wouldn't advise purchasing Bitcoins with actual cash, unless you're a seasoned speculator - and then it probably comes down more to an understanding of human nature than any academic-style economics.

Whew, I'm at 0.00307240 Bitcoins for the day. Time to pack it in, then.



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