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In these days, Bitcoin is a major topic in small talk and deep geek-only conversations as well. You might have questioned how secure it is to use Bitcoins, or wondered why there are concerns about energy consumption and environmental issues.
It turns out that security is intimately interwoven with energy voracity, and part of the original design of this crypto-currency.
Energy consumption is in fact related to the computational difficulty in mining and transaction validation. These are in fact conceived as an always-increasing function, so that the computational power which will be predictably available in say 10 years will be still not enough to crack the system by brute-force, because the bar will have risen in parallel.
This aspect will hold true irrespective of how fast the future CPUs will be: the faster the CPUs, the harder the competition for mining and transaction validation. When all blocks will have been mined, the computational market will be regulated by the sole validation of transactions.
Hash rate difficulty from February 2006 to 2018. Source: bitcoinwisdom
A direct implication of this is that there will always be an increasing power consumption related to the Bitcoin market as adoption get more and more widespread. The darkest projection foresee an enormous, reckless power consumption, more than any current-day nation.
This is of course not a sustainable course.
To be fair, other estimates are more gentle on Bitcoin-related Energy estimates, but still foresee a whopping consumption of 2% of the whole planet’s energy requirement.
This will be in addition to the estimated 6% of global energy consumption tied to banking and the financial world.
We still need to solve a pressing Climate Change problem before we can afford this kind of energy risk.
On the other hand, the vastness of the Bitcoin address space (i.e. the set of all addresses valid for Bitcoin transactions) is a security requirement.
At any moment, in fact, all mined (i.e. existing) Bitcoins are tied to Bitcoin addresses, i.e. Bitcoin (and Bitcoin fractions) cannot exist without a valid address.
While any payment (bot in the digital and in the real world) must identify from- and to- addresses in order to be valid, it is not enough to know an address to retrieve its goodies.
Just as it is not enough to know the address of a bank to get its money, also in the Bitcoin word you need a key to unlock the value hidden behind an address.
If the key of your bank is lost, all you can do is to go at the right street address, sit in front of it and stare. Or try your luck by lock-picking with all possible keys.
A Bitcoin key is made secure by the fact that there are an even larger number of possible keys, and while it is immediate to use a key to “unlock” a Bitcoin address, the reverse is considered impossible on a mathematical basis.
A professional keymaker at work in his natural Matrix environment.
Still, you can try to B&E (Break & Enter, as made famous by Breaking Bad) by demolishing the walls.
Similarly, if the key to your Bitcoin address is lost you have basically simultaneously lost also your virtual money.
You can use brute force and try all possible key combinations until you find the right key, kinda lock-picking in its digital form.
Also, if you are the lucky possessor of a mighty mind, you could try to break the walls of the elliptic-curve algorithm, upon which the strong encryption system of Bitcoin is based. In that case you would gain access not only to the “bank” at your legitimate address but also to all the Bitcoins behind any other known address.
Speaking of which, there is an even more adventurous middle ground: find all possible addresses and then try to brute force them.
Let me introduce a little spoiler for the TL;DR folk: this is an impossible task. And we are going to see why.
Until now we have spoken in a figurative, metaphorical way. Let dive now a little deeper and see the numbers from a more human perspective.
We are talking about digital, after all, and the word “digital” derives from Latin “digitus”, meaning “finger”, intended as a primitive way to count numbers.
So dive with me into the blue sea of numbers.
The creator, the mystical creature, of Bitcoin defined the address space as composed by 2¹⁶⁰ possible combinations. A short notation hideously concealing an inconceivably large number.
2¹⁶⁰ is in fact equal to1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976
I know you don’t believe me, so try googling it.
We can write that number in another form, called exponential notation: 1.4615e⁴⁸, meaning a 1 followed by 48 zeros, and then multiplied by 1.4615.Written like that it starts looking intimidating, but not as humbling as it actually is.
Counting towards 2¹⁶⁰
If I take my time, I can mentally count at an approximate rate of one number per second. Much quicker for small numbers (I actually tried and counted from one to 100 in 25 seconds. Without subvocalizing, I think higher speeds could be achieved.), but around that speed for numbers in the order of one million. With larger numbers, I would become slower and slower, but let’s take as a basis for our calculations 1 number per second.
In a day there are 86,400 seconds, so I could count up to 86,400. Not a lot, I would have hoped for something more.
In a year there are 365.25 days, and working night and day, with no excuses, without pauses to drink, eat, sleep, go to the toilet and -God forbid- not even to read the latest Medium articles, I could count up to 31,557,600. Only thirty million and counting. Gee, that is still peanuts!
OK, I will dedicate my whole life, 142 years (yes, I know I will live exactly 100 more years, because I have a sacred mission, now!) to counting. This multiplication is easy, just add two zeros to the right: 3,155,760,000.
What? 3 billions? Is that all? In 100 years I could not even count half of the people on this planet? C’mon: is this a life worth living?
I am relieved to know that at this point you will abide to the same scared mission, along with every other fellow on the planet, won’t you? In doing so, you will be granted a free bonus of 100 additional years, an offer you can’t refuse.
Great! We have now 7 billion people to chant, ahem, to count along: in just 100 years we will have counted 2.2e¹⁹ different numbers. Note that working in parallel, we would not be counting from zero to 2.2e¹⁹, but we could use a little trick and assign to each telly counter, ahem, person a different starting number, basically partitioning the sequence in chunks of 3 billions numbers each.
However: writing 2.2e¹⁹, with the exponential notation, at least starts looking cool.
How far are we from the 1.4615e⁴⁸ we preach to reach?
2.2e¹⁹ is one part in 6e²⁸, or one in 60,000,000,000,000,000,000,000,000,000.
Duh. Carbon-based beings are slow, you know. Let’s invite to the party the tough guys made of silicon!
An average smart phone can sport 4 GIPS (billion instructions per second), i.e. it can count 4 billion numbers in a second. More than I could do in my 100 bonus years (Sir? Where do I sign to waive for that 100-year-life-extension thing?).
Now, the whole computational power nowadays available on the world can be estimated to be 10 EFLOPS, an EFLOPS (Esa Floating Point Operation Per Second) representing 1e¹⁸ operations per second.
Approximating “counting” as a single operation, 1e¹⁹ means that all the computers in the world would take 2.2 seconds to count up to the same number that the whole humanity would reach in 100 years.
Scaling up into the realm of Sci Fi
In a year (always 31,536,000 seconds, even if computers are involved) all the CPUs and GPUs would count up to 3e²⁶. If they had been running since the Big Bang (13.8 billion years ago. I can still remember the sensation during the inflationary epoch: ah, the good old days!), the tally counter would be at 4.4e36.
Still a long way to go, Daenerys.Want to go wild?An artist’s concept for a Dyson Sphere (Image: Levy Wang)
OK, consider this: we are on an anonymous planet of a peripheral star (the Sun) among the 250 billion (± 150 billion) of the Milky Way.
250 billion ± 150 billion means that there could be between 100 and 400 billion stars in our own Galaxy. That is how much we know of our own home. Time to become serious about astrophysics, President Trump.
Let’s pretend that every star in the Milky Way has had a computer-filled planet like ours since the beginning of time, and that all of them have been counting during all this time.
We would have finally reached 1.1e⁴⁸, just only above three-fourths of the addresses available in the Bitcoin space.
To recap, if each and every every star in the Milky Way had a planet with the same total computational power as the Earth has today, and had been counting numbers since the Big Bang, as of today we would have only covered 75% of the Bitcoin address space.
In this respect, we can confidently say 2¹⁶⁰ is a vast number, and the set of Bitcoin addresses is unfathomably immense.
The actual breaking of the keys is a much, much more complex task than just counting to 2¹⁶⁰.
Sorry, Daenerys, we will have to find other, simpler chains to break.
Disclaimer
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