The Incredible Math of Bitcoin’s Private Keys

Create a new Earth for every grain of sand on Earth, and there are 26 billion unique Bitcoin addresses for each grain of sand on each of those Earths.

It’s not easy to slow down hackers and provide equal access to everyone in the world. However, Bitcoin’s solution is to employ outrageously large numbers, and this solution is devilishly simple. Bitcoin’s private keys are made of numbers, which are called quindecillions.

These numbers are so big that they literally choke the best computers. In fact, these numbers would still be too big even if all the world’s computers were able to work together. We will dive into this math by using an analogy to drawers and pirates. We will reveal not only how simple the idea is, but how well it works.

Today we are going to be looking at the incredible math of Bitcoin’s private keys, which is one of the main reasons why it’s absolutely impossible to hack Bitcoin. And for all you technophobes out here don’t get confused because this incredible new technology and these humongous numbers don’t mean it’s going to be hard to understand. This is remarkably simple math, very easy to understand.

 

We are positive that you will be able to explain this phenomenal new technology to your techie friends after reading this article.

Let’s get started then. Don’t worry, we are going to have a little bit of fun. This is the website bitaddress.org.

bitadress

It instantly creates brand new Bitcoin addresses and private keys. So, down here you have your Bitcoin public address and you have your private key, and it will create new ones as fast as you can click.

However, the real incredible thing that has to do with today’s topic is that when you generate this number and these are really just numbers and sort of a Hex 58 format. These are the numbers that you have never seen before, in fact, you can take this number right here, pop it in the Google and you won’t get any search results.

This means that every time you generate a new address you’re actually generating something that the world has never seen before that second that you generate it, and it will never be seen again unless you show it to someone. So, if the numbers are erased right away, those are numbers that were just for a fleeting second and they will never be seen again.

I’m sure that many of you right now are going, “What are you talking about? I don’t understand this.” This is the power of large numbers.

So today we are mostly going to be working with this part. This is the public key

adress

and this is the private key.

priv key

However, remember that your private key is all you need in Bitcoin, the only number you need in Bitcoin.

Your private key can be stuffed into a simple equation and generate the public key every time, so, every time you stuff this through elliptic curve SHA256 RIPEMD it will always generate this number right here. It is important to note that you can’t go backwards because those equations use clock math, which has been shown forever that it’s impossible to go backwards.

So every time, every day, you’ll be able to generate this public key from this private key (see images above).

 

How does this actually work? Let’s take a step back to talk about this. Bitcoin private key is just a number in the Hex 58 format. After that, they do a little of Bitcoin coding to add a number 5 there. This way they let you know it’s a private key.

 

Now, public key is generated by having private key.

And you can see this is a very, very large number, in fact, these digits here are called Quindecillions. And it’s likely that you’ve never heard of a Quindecillion, and you’ve never had to deal with Quindecillions, unless you fiddle with Bitcoin.

In fact, you probably never had to deal with any of these units all the way up here, and these are all just a new range of numbers that we’ve never had to deal with. I think that the US federal budget and all of world income is somewhere in this area right here, billions and trillions of dollar.

So you should start thinking about how much larger a Quindecillion is from billions, trillions, quadrillions etc.

There is one more thing that’s important. The same number, the same decimal number you just saw can also be put in computer format, in binary format, so you can do it in ones and zeros.

This means that using these binary digits right here, you can generate that same decimal number from the page before. Also, it is possible to create private keys just by flipping a coin where someone says one is heads and zero equals tails. Also, by just flipping a coin 160 times and putting those numbers together, you can create a perfect private key. So, if you flip at the first time, you get a heads you put it there, second time you get a heads you put it there then tail, tail and you just keep putting in order till you’ve got a 160.

So, a perfect private key can be created just by flipping a coin. And this is how many people do it. This can also be done by rolling dice or any other way that is used to generate random numbers.

 

Now we are getting to the fun part of this article! Bitcoin relies on these private keys to store value, and it also relies on the fact that these are the numbers that no one has ever used before or seen before and never will see again or generate again.

So, what Bitcoin suggests is that if you flip a penny 160 times, so that number that you’ve generated is a brand new number, one that has never been seen and will never be seen again, unless you show it to someone. It’s really outrageous to start thinking about this. So what Bitcoin saying is that you will end up with something that we can start using for security if you flip a coin 160 times and you put all your ones and zeros together.

This can be a code for security because it won’t be generated again. I know that this sounds completely preposterous right now. This is really unsettling the first time you hear this. I mean, is it really possible for one number to provide security? Well, what Bitcoin is suggesting is that this one number is so secure that no hacker, no combination of hackers, not all the hackers in the world teamed up will ever be able to hack this, huh!

It is more secure than banks or more secure than buried treasure. It is very important to find out now how this works.

We’re going to use a metaphor because the human brain is really bad at visualizing just straight numbers. We’re going to use this idea of drawers, which is a really good metaphor for Bitcoin. So, here is your drawer (we’ll call it your Bitcoin private key), and you’re going to put some value inside it. Here we’ve got some of the little treasure map. However, you can put so many different things inside it.

We’re just putting Bitcoins in Bitcoin’s case. However, those Bitcoins can be shaped to prove access to patents, deeds, contracts and so many other things. So, the real power here is being able to put something in these Bitcoin drawers.

Let’s start now with the big question. If you were only given one single drawer with no locks, is that security? Well, most people in the world would probably say no, not a single drawer, open drawer like that. Is that secure? No, of course not.

But what if I now multiply the number of drawers by four and I put my wealth in the drawer number two. Many people would look at this and go, well, it’s four times longer. However, I would still be able to pull out the treasure map or whatever’s inside there in just a couple of seconds. As you can see, this isn’t much more secure.

However, some people might have noticed well that this set of drawers here is in a house, and that the house had some security, right? So to find the treasure map, you might have to break in, find the drawers and rifle through the drawers.

 

So let’s be fair to Bitcoin because it is public and can be accessed by anyone in the world. This means that we must put our drawers in public. So, our metaphor is not getting better. In fact, it is getting seemingly worse. Suppose I put some value in this drawer right here. Would anyone on Earth feel that this is security?

Suppose you put some coins, some value, or a $2,000 in drawer number two right here, Would you actually go to work in this office for the day and then come back after work and think that your money is still going to be there? Of course not, that’s not security at all. What about now? Suppose we put some money right here in drawer number 61, would you go to work here, start the day and think the money is still going to be there?

Well, no. But you might start to think that perhaps you could play football with these guys over there, and that if you just leave your valuables here on the grass, they would be safer. To find drawers number 61 and pull your money out of that, someone is going to have to rifle through all these drawers. And remember, there are no locks and these are just open drawers. So, that’s what Bitcoin is – open drawers.

 

You can get the money out of any of the drawers if you have the private key. So, if there’s Bitcoins associate with private key you can just yank it out, and there are no locks. We call it cryptocurrency. However, it’s not super crypto.

So, would you feel safe with this setup and would you actually go to work here? You probably wouldn’t. What about now? This is the Boston skyline. There are millions and millions of drawers behind it and we decide that we’re going to stick our $2,000 right here in the drawer number 6786226. Would you now think about maybe going to work for the day, and then at the end of the day go right to your drawer, since you know which drawer it is, to pull your money out as long as no one saw you.

To get your money, they’d have to start pilfering all these drawers. Things are starting to be ok for you. However, let’s start thinking about the issues here. When my two nephews Kevin and Tom are looking for candies, they can open two drawers per second. And maybe they could even open three drawers per second if you told them that you had thousands of dollars that can buy them lots of candies.

 

So, if people knew that you’re actually hiding wealth inside these drawers, they’d be trying to open them nonstop. It’s even possible that millions of drawers might not be enough. The question is, is this secure? Well, we are not sure. But it’s starting to get a little interesting. We’re going to start to have to ask ourselves a question.

If we wanted to build a set of drawers that would provide perfect security, how many drawers would we need to make it safe? Is there a number of drawers that would make it not just okay safe, but perfectly safe?

Are 300 billion drawers enough for perfect security? No, they aren’t because there are 7 billion people on Earth, and they could just randomly pull out a bunch of drawers. So you had your $2000 right here in this, I don’t know, 226 billion drawer blah, blah, blah whatever numbers. Is this safe? Well, it might be safe for an hour.

However, it’s probably not going to be safe for a year. I mean, we really have to think about storing value and security.

 

Bitcoin is public and accessible by everyone with computers. So let’s make our problem even more difficult. We need something that’s going to make sense for our drawer analogy. What if hackers had drawer opening drones that could pen thousands of drawers every day? These drones just fly around and they are able to open any drawer in our system. Suddenly, our 300 billion drawers don’t seem to be nearly enough.

Remember, Bitcoin can be accessed by computers and computers do things very fast. So let’s make it even more difficult. So, what if each person in the world had an app that could control those drones. What if each person in the world could open 1 billion drawers a day using this app? Is our system now safe? Well, there are 300 billion drawers and everyone in the world opens a billion drawers a day.

No, our 300 billion drawers system is not safe. However, this leads us back to the question is there a number of drawers that would start to provide people with perfect security? The security where they could go to bed at night knowing that their money would still be there in the morning. Let’s look at the difficulty of that.

So, let’s think about our drawer system. Imagine all these issues like people actually making drones that would do it and people had this phone app and they really could open a billion drawers a day. Let’s look at the big and crazy numbers of that now. There are 7 billion people on earth, each with drones that are opening one billion drawers per day and they’re going to keep this up for 365 days.

We’ll just say everyone lives to be a 100 and their drone lives to be a 100, so they get 100 years, which means that all these combined over the course of a 100 years you would be able to dig through 260 times 10 to the 21. That’s 260 sextillion. Let’s talk about a sextillion. Sextillion is pretty large and sexy number, and Wolfram suggests that 260 sextillion is on the order of the number of grains of sand on earth. So, the grains of sand on the earth are in the order of 10 to the 20.

Remember this is 260 times 10 to the 21. So, the amount of drawers that all the hackers on the earth with their phone apps and their drones, everybody in the world equally attacking at the same time would be able to open as many drawers as there are grains of sand on the earth.

And remember, this isn’t just the grains of sand. You can see all the grains of sand on the earth – grains of sand under the sand and grains of sand under the ocean. It’s approximate guess. However, these are fun numbers to think about.

So, if everyone in the world can open all these drawers would just seems impossible, we’d never be able to come up with a number of drawers that would give us security. Or can we? What if there are 10 to the 29 drawers in our system. This is really like a million times as many drawers as everyone in the world can open over the course of 100 years using these special drones with their phone apps.

 

So, literally everyone in the world working together for a 100 years would have a one in a million chance of finding our $2,000 that were randomly placed. Well, that’s interesting – $2,000 for a 100 years, one in a million chance that it’s going to happen.

 

What if there were 10 to the 35 drawers, and all of a sudden there were trillion times as many drawers as everyone could open together. So suddenly we went to one in a trillion over one 100 years, instead of one in a million chance over 100 years.  So, you put your $2,000 in one of the drawers, and there’d be one in a trillion chance of finding if all the drones worked furiously for a 100 years. Let’s raise the number even larger and make it 10 to the 38, one in a quadrillion.

Human brains are really bad at calculating odds. Some people are going well one in a quadrillion that’s not enough for me, and we start to think about numbers like one in a quadrillion. What are the odds of that happening? And it’s really difficult for humans to imagine these types of numbers.

However, we need to realize how low a number that is, and what’s even more incredible is that the numbers that Bitcoin deals with, this is tiny.

As it was already mentioned, Bitcoin deals with Quindecillions. And here’s the sextillion of all the iPhones, all the computers and all the drones working together, and everyone in the world is trying to hack the system. What are the odds that one address is going to be hacked from Bitcoin in 100 years? We’re talking odds that are lower than any odds ever calculated on earth.

To put this into perspective here, we have a recent Powerball odds, which just recently had a winning prize of a 149 million and your odds of winning that were one in 175 million. So, trying to hack one address of Bitcoin makes Powerball look like a sure thing, makes it look like a lock.

 

These numbers are just so much larger, and it’s really important to think about how computers can be destroyed by large numbers. They make all the world’s computers together look like a snail, look like a snail in a glue trap, a frozen snail, a dead snail. Here’s the hacker who is trying to yell faster faster with all the world’s computers together. Large numbers destroy the hacker. That is the reason why Bitcoin is relying heavily on these huge numbers, numbers that have never been seen before.

Let’s compare, just for fun, sort of the same idea to pirates back in the day. And we like to think that pirates could bury treasure. This treasure would be safer than ever before, and indeed in many ways it was. Some pirate treasures are still being found, and perhaps the original pirate who knew where it was or the map that had the location on it got destroyed.

 

That’s why the pirate couldn’t get back and find his money and so no one was able to find it now. Imagine someone’s building a house and stumble on some nice little bounty of treasure. So even though these things were worth lots of money, they stayed for hundreds of years because someone buried it underground. And that is what pirates do – they have this nice little gold chest, they dig a couple of feet down, they place the treasure chest in there and now they can sleep pretty well at night after killing off this guy.

But as we’re talking about the power of large numbers let’s start thinking about the math of this. Remember, the earth’s surface is absolutely enormous but it’s not unlimited. So, there’s going to be a finite number of treasure chests that can be buried a couple of feet down under the ground.

So, a simple math can be done here. We have 510 million kilometers square, which is the Earth’s surface. We also have this treasure chest and to be fair they’re kind of small. So, let’s say it’s got a two foot square foot prints. This means that the bottom takes up about two square feet, which is pretty small. How many of these treasure chests could be put on the earth? Here we go – we transfer kilometers to meter squared multiplying by one million.

You get 5.1 times 10 to the 14 meter squared multiply it by 9 to get a round number for about how many square feet there are on the earth. We get 4.59 times 10 to the 15 square feet on the Earth’s surface, so we’re talking about a two square foot footprint, which means that we basically can put half as many chests of gold and we’d have a chest of gold underneath the ground everywhere on Earth, including the oceans.

 

So what is the number of chests of gold that can be put everywhere on the earth? We can bury 2.3 times 10 to the 15 chests of gold on earth, which is surprisingly small when you think about these Bitcoin numbers.

Remember Bitcoins in the order of 10 to the 48, and to get the amount of locations that Bitcoin offers, you’d actually have to cube this number. So, all the possible places, just think of all of New York City covered with treasure chests, the entire desert, every stretch of highway, every place you’ve ever been, treasure chests everywhere and you have to cube that, not multiply by three but cube it to get the amount of different locations and places where you can put Bitcoins.

Putting your money into a Bitcoin address and letting computers hack at it like crazy nonstop is beginning to approach the outrageous security of just placing treasure underground in an undisclosed location with no ability for anyone to find it using a metal detector. I know that some of you are now thinking: Okay, so what if all the computers were programmed to hack Bitcoin. We all know that computers are fast.

I’ll just make a database of all those numbers, all the Quindecillions addresses for Bitcoin, all the possible addresses. After that, I’ll just query my database for which of those have Bitcoins in it. So, I’ll just make this really large database.

After that, I’ll just pull out all the money in all the Bitcoin accounts. Well, what’s really crazy is that we’re so used to thinking of computers as capable of doing everything. However, the truth is that computers can’t even touch this problem, and we’ll look at why.

All the storage, all of China storage, all of Google storage, all hard drives in the world today make up what’s called a zettabyte. One yottabyte is larger than a zettabyte by a factor of one thousand. You would require hard drives that are five yottabytes squared to store all the addresses in Bitcoin. 

So, 5000 times the current hard drives on earth squared, and you’d begin to wonder if all the iron in the world would even be able to make an enclosure for the drives that you would need. So, say you build those drives and you really put those drives together. There isn’t enough gas and coal to make the electricity to even turn those drives up, and this is a problem that makes the world’s computers look like a snail.

And this is the reason why Bitcoin uses these large numbers – it makes it really hard to conceive of hacking Bitcoin because there’s just not enough computational power in the known universe all together trying to solve this issue.

So, we can start to think that this simple math is basically just using large numbers, now that we’re kind of blown away by how these large numbers can make computers look retarded.

Where your Bitcoins were at this number?

adress

I can pull out those Bitcoins if I put that number in.

priv key

Can we make a form of security by using this large number of math and would people keep their money in a system like this is new form of public ledger? Well, it’s already happening. In fact, it’s happening in dramatic fashion.

It’s important to note that Bitcoin is only 8 years old. However, in numerous addresses you have well more than a million dollars in a single address. So, you could pull out millions from this account if you could just roll the dice and come up with that number.

btc adress

And say you messed up and you rolled the wrong number and you came up with this one.

However, you can pull out more millions from this account and the list goes on and on and on.

btc adress 2

For 8 years people have just parked money in there and today there are millions and millions of dollars waiting to be taken by someone who could hack Bitcoin. However, this is actually kind of proof that no one’s able to hack it.

You should remember that you don’t need a password, you don’t need any sort of biometrics and you don’t need to put your thumbprint on.

All you need is the number and you can pull out millions. So, if you have nothing better to do and you just feel like rolling dice the rest of your life you can try. However, you’re going to need a gazillion lives. You’re not going to roll this number. Also, you’re not going to roll this number.

And if I generate a new one and send money to it you’re not going to roll this number. You are not going to roll this one either. So, you can convert it to binary, or you convert it to decimal. Whatever you want. All formats are accepted. However, you’re still not going to roll that number. These are the numbers that you have never seen before, and I can pop them into Google and it’s not going to have any search results and it will not match any documents.

Every time you do this with Bitcoin, you will generate a new address. These are new numbers, and they are not stored anywhere by anybody.

What goes inside these Bitcoin addresses?

What goes inside these Bitcoin addresses? Well, nothing really goes in it. It’s really important to note that Bitcoins don’t truly exist and that they’re just units of accounts on the Bitcoin ledger – blockchain. Some people talk about intrinsic value on a currency.

Well first of all, the whole idea of intrinsic value starts to look like an oxymoron and there is no intrinsic value necessary in a currency. We start to realize that when we look at dollars because there really is no intrinsic value in the paper of the dollars.

For thousands of years, people are using cowry shells over a really broad geographic area. There’s no intrinsic value. The snails themselves didn’t even want them, they chucked them and they were garbage. However, the cowry shells were uniform, difficult to copy.

There was a limited amount and that gave it value. It gave a tradable value, and gave it value in exchange, and that’s exactly what’s going on with Bitcoin.

Bitcoin is not a bunch of drawers. It’s actually a ledger that is protected by huge numbers more than anything else. It’s the fact that you can generate a number with a coin that no one’s ever generated before, and you can send Bitcoins to that number and no one will ever find that number. And the beauty of this is that it basically allows equal and full access to banking to anyone who’s got a coin to flip.

This is also one of the reasons why this is so revolutionary. You can flip a coin a 160 times and you can start to get involved in Bitcoin. Better off if you have a computer and the Internet. However, you don’t need a lot of access to the computer and a lot of access to the Internet to do this. You can set up your account. After that, you can send that public address that you generate from your private key to anyone. After that, they can start to send you money for the products you make.

This is a revolution. It is all a result of large numbers. So, I hope you find that this math is really compelling and really beautiful. But many of you are going to be very unsettled by this and you’re not going to feel comfortable with it right away.

However, over time over the next five to ten years as people start to move towards blockchain technology, our kids and others will start to see that this is more secure than putting money in banks in Cyprus.

I think that this is more secure that even putting money in banks under any government umbrella. You know that your value will be there the next day, and you’re not so sure with anything else.

So that’s it for this article. I hope you enjoyed it while reading this. I also hope you learnt something new.

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