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What I would like to do is describe an imaginary, or a fictitious, Bitcoin transaction. And then talk about how somebody might try to game or defraud the system. And why that's not only mathematically hard to do, but why there's actually an incentive-- actually an economic incentive in the Bitcoin system for different people to behave honestly. So let's suppose that there is someone out there named Dan, and that Dan wants to order a pizza-- maybe a cheese pizza, from Pete's Pizza Shop. And let's say that Pete's Pizza Shop accepts Bitcoins as payment, and that it costs 1 Bitcoin for a pizza pie. And imagine that Dan receive previously-- let's say he received 5 Bitcoins from his cousin, Carol. So maybe Carol, who I'm going to label by C, gave to Dan 5 Bitcoins, which we can label as a B with a circle around it. And that he wants to use 1 of these 5 Bitcoins to buy a pizza from Pete. And so what Dan's Bitcoin client will do is it will create a transaction record that includes information about how Dan got these Bitcoins. In this case, it includes information about this transaction between Carol, who we've marked by C, and Dan for 5 Bitcoins. And then it specifies that Dan wants to give one of these Bitcoins to Pete-- and we'll label Pete by a P. And also that Dan is going to take the remaining 4 Bitcoins. And that will be basically change to himself. And the way that Bitcoin is built is that you have to actually specify the change, because you need to have a way-- whatever goes into the Bitcoin system has to come out at the other end. And so you can't have a transaction where the numbers don't add up. And so whatever is remaining is either change, or part of it can be used as a transaction fee. And so on. But for this example, to keep things simple, I'll assume that there is no transaction fee in place. The transaction fee is just 0. And we'll focus only on the situation in which everything is being accounted for in the transaction. Now, this transaction record is going to be broadcast out to the entire Bitcoin world. And so in particular, Pete is going to receive a copy of this transaction. But in addition to Pete receiving it, so too will the other people on the Bitcoin system. And if you recall, there are these special nodes, the special entities or people in Bitcoin, that are known as Bitcoin miners. And these Bitcoin miners are going to be responsible for making sure that everything checks out in the transaction from a global perspective. What they do is they look at the full record of transactions. And this transaction record is public. It's known as a transaction block chain, and I've put a description of the transaction block chain right here. And this transaction block chain contains the history of every single transaction that's ever occurred within the Bitcoin system from the beginning of time-- the time of the first block, which is known in Bitcoin as the genesis block. And everyone can verify the details of any transaction if they want to because that information is public. And in particular, what these Bitcoin miners will look at is they'll look at whether or not Dan previously received five Bitcoins from anybody else. In this particular case, it was his cousin, Carol. Whether or not Dan has tried to spend those Bitcoin previously. And so on and so forth. And these Bitcoin miners are all collectively trying to take all these recent transactions that haven't yet been recorded, and that includes not only the transaction between Dan and Pete, but there may be other transactions floating out there that took place on the same time. And the Bitcoin miners will basically look at all these different transactions at once. And they're going to basically try to figure out how to form a transaction block out of these transactions. And they want to add this transaction block to the end of the current transaction block chain. Now, if you might recall from previous videos, that for a Bitcoin miner to add a transaction block to a transaction block chain, they have to solve what's known as a proof-of-work puzzle. And the Bitcoin system is designed-- or maybe calibrated is a better word-- so that on average one miner will solve a puzzle in about 10 minutes. I think it's actually worth stressing here that it could take a long time for any one individual miner solve the puzzle. It could even take maybe a year, or even two years. But because there are so many of these miners working at the same time, one of them is bound to get lucky and solve the puzzle quickly. Now, each of these proof-of-work puzzles that is associated with a transaction block happens to have a difficulty score associated with it. And this difficulty basically represents how hard it was to solve that proof-of-work puzzle. So imagine that there are some numbers, and we'll call these numbers D sub N. For the most recent difficulty score, they'll be D sub N minus 1. These are just numbers that somehow represent how hard it was to solve this proof-of-work. And when you look at an overall chain, what the Bitcoin is interested in is it's interested in how hard was it to construct that entire chain. And the reason it's important for someone to understand how hard the entire chain is constructed is because this is overall score for this chain-- this difficulty score for the chain is what's used by Pete or by other people who are receiving Bitcoins to figure out whether or not they trust that transaction. The more work that went into the overall chain, the more trust they'll have in that transaction. And the reason for that is that the way Bitcoin works is that if there was for more than one transaction block chain out there-- let's say there was a bad user out there, or maybe somebody didn't receive a particular message in time, or whatever reason-- if there's somehow more than one transaction block chain out there, according to the Bitcoin protocol, everyone is just supposed to work off of the chain that had the most work put into it. So we ignore chains that have a lot less work and only consider the chain that had the most work put into it. And in the Bitcoin system, that particular chain is often referred to as the longest chain in the system. And this is actually a confusing piece of terminology. Because by longest here, we don't mean that this change is long in any physical sense. We really just mean-- and I'm going to put three equal bars to say what it means. By the longest chain, we mean the change that has the most work. And the way that the work is defined is that you look at all these different difficulty scores, and these are difficulty numbers, and you add them up, and that gives you a difficulty score for the entire chain. And now we're going to be interested in the chain that had the most work put into it. And we call that the longest chain. Now let's imagine that Dan is dishonest and that after he eats the pizza-- let's say Pete's convinced and he gets his Bitcoin from Dan. He waits a bit. He sees that there is a long chain after that contains a transaction. He sends the pizza over to Dan. Dan eats the pizza and then decides that he doesn't want to behave honestly and he wants to somehow cheat Pete, or he wants to defraud the system. And the way that Dan is going to try to defraud the system is by attempting to create another transaction in which he assigns the 5 Bitcoins he got from Carol to somebody else. And it could be-- let's call this person Fred. And let's say Fred is basically-- Fred could be Dan's alter ego. It could be a friend of Dan's. It doesn't matter who Fred is because we know that Fred isn't the rightful owner of these Bitcoins. But what Dan is going to try to do is he's going to try to take those 5 Bitcoins that he got from Carol. And he's going to now try to take those 5 Bitcoins and assign them over to Fred. And we know that this is something that we don't want to allow because that would mean that somehow Dan was able to spend these 5 Bitcoins twice over. He's effectively double-spent those Bitcoins, and obviously one of these transactions should be considered fraudulent, the other one should be allowed to go through. Now, it's important to keep in mind that if Dan just tried to spend these same coins again without trying to cover his tracks or anything of that nature, then everybody out there would know that Dan is up to no good. Because they can see from the existing longest transaction block chain-- namely this existing chain from the beginning-- they can see that, hey, Dan already spent these coins before, he shouldn't be allowed to spend these coins again. And so what Dan has to do is actually-- on his own-- he has to create a different transaction block chain that contains just this second bogus transaction in it. This would be the transaction to Fred. And that would leave out the other transaction to Pete and hope that everybody else will start to accept or believe this newer chain. And remember that since everyone in Bitcoin ultimately goes with the transaction block chain that contains the most work, namely this longest chain that we talked about, Dan has a fighting chance. He has a hope, potentially, of being able to pull off this type of a fraudulent scheme. And the real question now is, how likely is it for Dan to succeed? So for Dan to be able to pull this off, he has to start off with the transaction block chain that existed previously. And he has to try to add to that transaction block chain a different transaction. So rather than having this previous transaction where he gave money to Pete, he's going to try to create a new transaction and add it to the transaction block chain that contains this other fraudulent transaction between Dan and his friend Fred. OK. So this is going to be the bad transaction between Dan and Fred-- will be in this new block. And in Bitcoin lingo, this idea is known as a fork in the chain. And all we mean by fork is that somehow there is more than one version of history. Somebody tried to rewrite their tracks, or to cover their tracks, and to revise history the way we know it. And what that really means is there's now somehow more than one version of what happened out there. So in this example, one branch in this fork is legitimate, and the other branch is bogus. And the legitimate branch with the one, in our minds, where Dan paid his friend Peter this vendor, Pete, for a pizza. And the bogus one is this follow on transaction where Dan attempted to pay his friend Fred with those same exact Bitcoins. But now remember that any transaction block that's added to this transaction block chain has to contain within it a proof-of-work puzzle-- or solution, rather, to a proof-of-work. Otherwise, no one will accept the chain. And so if Dan wants to cheat the system, he has to secretly solve a new proof-of-work puzzle himself. But the challenge for Dan is that he's starting off with a bit of a handicap because there's already this longer chain out there that people have started accepting. And keep in mind that because this chain is out there, other nodes may have started to build on top of this chain. Every 10 minutes, somebody's adding to this change, on average. And so there's this longer transaction block chain out there. And Dan wants to create his own fake chain. And so he has to create a chain. In order for that chain to be believable, it has to now be the longest chain out there. And he has to basically do all these proof-of-works to create a chain that is longer. And to come up with this longer chain on his own, Dan has to outrun the existing proof-of-work chain. And that means he has to solve not just typically one proof-of-work puzzle, but he may need to solve several proof-of-work puzzles to create another chain that he hopes will be longer than the chain that's out there. And if he can get the longest chain, he can get people to start using that chain instead. And that the chain that he might want people to use because it contains this fake transaction. But it removes the previous transaction where he gave money to Pete. And to solve a proof-of-work, Dan has to basically take whatever computing power he has access to. And he has to start working on solving the proof-of-work puzzle. And there are no known shortcuts for solving these puzzles. If you recall from any of the proof-of-work videos, to succeed in a proof-of-work is kind of like winning the lottery. There are ways to do it. But it really depends on how much computing power you have. The more computing power you have access to, the more lottery tickets you have. And if somebody has even one lottery ticket, they do have a chance to win the lottery. But they are far less likely to succeed compared to somebody who has a lot of lottery tickets in hand. And even if you succeed once in winning the lottery with a small number of tickets, the likelihood of repeating that feat over and over again, several times in a row, becomes much smaller. But that's exactly Dan has to do. He has to basically win this lottery multiple times until he has a bigger chain. And so the key metric here-- the key thing you have to look for is how much computing power Dan has versus how much computing power all the honest nodes in the system have together. And if it the case that all the honest nodes-- we'll call this the honest computing power. And when I say honest computing power, I mean the total computing power for all the nodes who are honest. All the Bitcoin mining nodes who are honest in the network. If that total computing power that they have access to is greater than the power that Dan has access to-- so Dan's computing power-- then the Bitcoin system will be safe, because it'll be hard for Dan to be able to create this fraudulent transaction chain because he won't be able to outrun the honest people. The honest people will win the lottery more frequently and they'll create a longer chain. And Dan's attempt is going to be very much an uphill battle. Now, it's theoretically possible that Dan could have access to a lot of computing power. Maybe he's very wealthy or he has a lot of resources. But he'll really need a lot to be able to that. More than everyone else who's legitimate combined. So that's one aspect of why the transaction block chain is secure. Because it's unlikely for any one individual to have access to just that much computing power. And here I should point out that there is also another aspect to the security of Bitcoin. If Dan has access to that kind of computing power to solve these proof-of-work puzzles, then rather than trying to fight this uphill battle of forking the transaction block chain, and creating fake transactions, and so on, Dan is probably much better off just using that computing power he has for legitimate Bitcoin mining himself. You might remember that Bitcoin miners who solve proof-of-work puzzles get both a reward for succeeding-- they get some number of Bitcoins-- and they also get a transaction fee for all the transactions in the block that they validated. So there's this economic incentive for Dan to behave honestly. So maybe I should just recapping in closing the video that the security of Bitcoin transactions comes from, first of all, this mathematical barrier that makes it hard for Dan to fork the transaction block chain in a dishonest way, as well as an economic incentive for Dan to just act honestly and mine Bitcoins for himself.