But how does bitcoin actually work?
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But how does bitcoin actually work?

October 9, 2019


What does it mean to have a bitcoin? Many people have now heard of bitcoin, that’s
it’s a fully digital currency, with no government to issue it and no banks needed to manage
accounts and verify transactions. That no one actually knows who invented it. Yet many people don’t know the answer to
this question, at least not in full. To get there, and to make sure the technical
details underlying this answer feel motivated, we’re going to walk through step-by-step
how you might have invented your own version of Bitcoin. We’ll start with you keeping track of payments
with your friends using a communal ledger. Then, as you trust your friends and the world
less and less, and if you’re clever enough to bring in a few tools of cryptography to
help circumvent the need for trust, what you end up with what’s called a “cryptocurrency”. Bitcoin is just the first implemented example
of a cryptocurrency, and there are now thousands more on exchanges with traditional currencies. Walking the path of inventing your own can
help set the foundation for understanding some of the more recent players in the game,
and recognizing where there’s room for different design choices. In fact, one of the reasons I chose this topic
is in response to the unprecedented leap in attention, investment and…well.. hype directed
at these currencies in just the last year. I won’t comment or speculate on the current
or future exchange rates, but I think we’d all agree that anyone looking to buy a cryptocurrency
should really know what it is. Not just in terms of analogies with vague
connections to gold-mining, I mean an actual direct description of what computers are doing
when sending, receiving and creating cryptocurrencies. One thing worth stressing, by the way, is
that even though you and I will dig into the underlying details here, which takes some
meaningful time, you don’t actually need to know those details to use a cryptocurrency,
just like you don’t need to know the details of what happens under the hood when you swipe
a credit card. Like any other digital payments, there are
plenty of user-friendly applications that let you send and receive these currencies
very easily. The difference is that the backbone underlying
this is not a bank verifying transactions, but a clever system of decentralized trustless
verification based on some of the math born in cryptography. To start, set aside the thought of cryptocurrencies
for a few minutes. We’re going to start the story with something
more down to earth: Ledgers, and digital signatures. If you and your friends exchange money pretty
frequently, paying your share of the dinner bill and such, it can be inconvenient to exchange
cash all the time. So you might keep a communal ledger that records
payments you intend to make in the future. Alice pays Bob $20, Bob pays Charlie $40,
things like that. This ledger will be something public and accessible
to everyone, like a website where anyone can go and just add new lines. At the end of every month, you all look through
the list of transactions and tally everything up. If you’ve spent more than you received,
you put that money into the pot, and if you’ve received more than you spent, you take that
much money out. So the protocol for being part of this system
looks something like this: Anyone can add lines to the ledger, and at the end of every
month everyone gets together to settles up with real money. One problem with a public ledger like this
is that when anyone can add a line, what’s to prevent Bob from going in and writing “Alice
pays Bob $100” without Alice approving? How are we supposed to trust that all these
transactions are what the sender meant for them to be? This is where the first bit of cryptography
comes in: Digital signatures. Like a handwritten signature, the idea here
is that Alice should be able to add something next to a transaction that proves that she
has seen it, and approved of it. And it should be infeasible for anyone else
to forge her signature. At first it might seem like digital signatures
shouldn’t even be possible, since whatever data makes up the signature can just be read
and copied by any computer, so how do you prevent forgeries? The way this works is that everyone generates
what’s called a public key/private key pair, each of which looks like some string of bits. The private key is sometimes also called the
“secret” key, so that we can abbreviate it to sk while abbreviating the public key
as pk. As the names suggest, the secret key is something
you should keep to yourself. In the real world, your handwritten signature
looks the same no matter what document you’re signing. A digital signatures is much stronger, because
it changes for different messages. It looks like a string of 1’s and 0’s,
commonly something like 256 bits, and altering the message even slightly completely changes
what your signature on that message should look like. Formally, producing a signature involves some
function that depends both on the message itself, and on your private key. The private key ensures that only you can
produce the signature, and the fact that it depends on the message means no one can just
copy one of your signatures to forge it on another message. Hand-in-hand with this is a function to verify
that a signature is valid, and this is where the public key comes into play. All it does it output true or false to indicate
if this was a signature created by the private key associated with the public key you use
for the verification. I won’t go into the details how how exactly
these functions work, but the idea is that it should be completely infeasible to find
a valid signature if you don’t know the secret key. Specifically there is no strategy better than
just guessing and checking if random signatures are valid using the public key until you hit
one that works. There are 2^{256} possible signatures with
256 bits, and you’d need to find the one that work. This is a stupidly large number. To call it astronomically large would be giving
way to much credit to astronomy. In fact, I made a supplemental video devoted
just to illustrating what a huge number this is. Let’s just say that when you verify a signature
against a given message and public key, you can feel extremely confident that the only
way someone could have produced it is if they knew the secret key associated with the public
key. There’s one slight problem here: If Alice
signs a transaction like “Alice pays Bob $100”, even though Bob can’t forge Alice’s
signature on new messages, he could just copy that same line as many times as he wants,
since the message/signature combination is valid. To get around that, we make it so that when
you sign a transaction, the message has to include some unique id associated with that
transaction. That way, if Alice pays Bob $100 multiple
times, each transaction requires a completely new signature. Alright, great, digital signatures remove
a huge aspect of trust in our initial protocol. But even still, this relies on an honors system
of sorts. Namely, you’re trusting that everyone will
actually follow through and settle up in cash at the end of each month. But what if, for example, Charlie racked up
thousands of dollars in debt, and just refuses to show up? The only real reason to revert to cash to
settle up is if some people, I’m looking at you Charlie, owe a lot of money. So maybe you have the clever idea that you
never actually have to settle up in cash as long as you have some way to prevent people
from spending too much more than they take in. What you might do is start by having everyone
pay $100 into the pot, and have the first few lines of the ledger will read “Alice
gets $100, Bob gets $100, etc. Now, just don’t accept transactions when
someone is spending more than they have on the ledger. For example, after starting everyone off with
$100, if the first two transaction are “Charlie pays Alice $50” and “Charlie pay Bob $50”,
if he were to try to add “Charlie pays You $20”, that would be invalid, as invalid
as if he never signed it. Notice, this means you need to know the full
history of transactions to verify that a new one is valid. And this is, more or less, going to be true
for cryptocurrencies as well, though there is a little room for optimization. What’s interesting here is that this step
somewhat removes the connection between the Ledger and physical cash. In theory, if everyone in the world used this
Ledger, you could live your whole life just sending and receiving money on this ledger
without ever converting to real US. To emphasize this point, let’s start referring
to quantities on the ledger as “LedgerDollars”, or LD for short. You’re of course free to exchange LedgerDollars
for real US dollars, for example maybe Alice gives Bob a $10 bill in the real world in
exchange for him adding and signing the transaction “Bob pays Alice 10 LedgerDollars” to the
communal ledger. But exchanges like this are not guaranteed
in the protocol. It’s now more analogous to how you might
exchange Dollars for Euros or any other currency on the open market, it’s just its own independent
thing. This is the first important thing to understand
about Bitcoin, or any other cryptocurrency: What it is is a ledger; the history of transactions
is the currency. Of course, with Bitcoin money doesn’t enter
the Ledger with people buying into using cash, I’ll get to how new money enters the ledger
in just a few minutes. Before that, there’s an even more significant
difference between our current system of LedgerDollars how cryptocurrencies works. So far, I’ve said that this ledger is some
public place, like a website where anyone can add new lines. But this requires trusting a central location. Namely, who hosts that website? Who controls the rules of adding new lines? To remove that bit of trust, we’ll have
everyone keep their own copy of the ledger. Then to make a transaction, like “Alice
pays Bob 100 LedgerDollars”, you broadcast into the world for people to hear and record
on their own private Ledgers. But unless we do something more, this system
would absurdly bad. How can you get everyone to agree on what
the right ledger is? When Bob receives the transaction “Alice
pays Bob 10 LedgerDollars”, how can he be sure that everyone else received and believes
that same transaction? That he’ll be able to later use those 10
LedgerDollars to make a trade with Charlie. Really, imagine yourself just listening to
transactions being broadcast. How can you be sure that everyone else is
recording the same transactions in the same order? Now we’ve hit on an interesting puzzle:
Can you come up with a protocol for how to accept or reject transactions and in what
order so that you can feel confident that anyone else in the world following the same
protocol has a personal ledger that looks the same as yours? This is the problem addressed in the original
Bitcoin paper. At a high level, the solution Bitcoin offers
to trust whichever ledger has the most computational work put into it. I’ll take a moment to explain what exactly
that means, which involves this thing called a “Cryptographic hash function”. The general idea we’ll build to is that
if you use computational work as a basis for what to trust, you can make it so that fraudulent
transactions and conflicting ledgers would require an infeasible amount of computation. Again, this is getting well into the weeds
beyond what anyone would need to know just to use a currency like this. But it’s a really cool idea, and if you
understand it, you understand the heart of bitcoin and other cryptocurrencies. A hash function takes in any kind of message
or file, and outputs a string of bits with a fixed length, like 256 bits. This output is called the “hash” or “digest”
of the message, and it’s meant to look random. It’s not random; it always gives the same
output for a given input. But the idea is that when you slightly change
the input, maybe editing just one character, the resulting hash changes completely. In fact, for the hash function I’m showing
here, called SHA256, the way that output changes as you slightly change the input is entirely
unpredictable. You see, this is not just any hash function,
it’s a cryptographic hash function. That means it’s infeasible to compute in
the reverse direction. If I show you some specific string of 1’s
and 0’s and ask you to find an input message so that the SHA256 hash of that message gives
this exact string of bits, you will have no better method than to guess and check. Again, if you want a feel for just how much
computation would be needed to go through 2256 guesses, take a look at the supplement
video. I actually had way too much fun writing that
thing. You might think you could reverse engineer
the desired input by really digging through the details of how the function works, but
no one has ever found a way to do that. Interestingly, there’s no proof that it’s
hard to compute in the reverse direction, yet a huge amount of modern security depends
on cryptographic hash functions. If you were to take a look at what algorithms
underlie the secure connection that your browser is making with YouTube right now, or that
it makes with a bank, you will likely see a name like SHA256 in there. For right now, our focus will just be on how
such a function can prove that a particular list of transactions is associated with a
large amount of computational effort. Imagine someone shows you a list of transactions,
and they say “I found a special number so that when you put this number at the end of
list of transactions, and apply SHA256 the entire thing, the first 30 bits of the output
are zeros”. How hard do you think it was for them to find
that number? For a random message, the probability that
the hash happens to start with 30 successive zeros is 1 in 230, which is about 1 in a billion. Because SHA256 is a cryptographic hash function,
the only way to find a special number like this just guessing and checking. So this person almost certainly had to go
through about a billion different numbers before finding this special one. And once you know the number, you can quickly
verify that this hash really does start with 30 zeros. In other words, you can verify they they went
through a large amount of work without having to go through that same effort yourself. This is called a “proof of work”. And importantly, all this work is intrinsically
tied to that list of transactions. If you change one of the transactions, even
slightly, it would completely change the hash, so you’d have to go through another billion
guesses to find a new proof of work, a new number that makes it so that the hash of the
altered list together with this new number starts with 30 zeros. So now think back to our distributed ledger
situation. Everyone is broadcasting transactions, and
we want a way for everyone to agree on what the correct ledger really is. As I said, the core idea behind the original
bitcoin paper is to have everybody trust whichever ledger has the most work put into it. The this works is to first organize a given
ledger into blocks, where each block consists of a list of transactions, together with a
proof of work. That is, a special number so that the hash
of the whole block starts with a bunch of zeros. For the moment let’s say it has to start
with 60 zeros, but later I’ll return back to how you might choose that number. In the same way that a transaction is only
considered valid if it is signed by the sender, a block is only considered valid if it has
a proof of work. Also, to make sure there is a standard way
to order of these blocks, we’ll make it so that a block has to contain the hash of
the previous block. That way, if you change any block, or try
to swap the order of two blocks, it would change the block after it, which changes that
block’s hash, which changes the next block, and so on. That would require redoing all the work, finding
a new special number for each of these blocks that makes their hashes start with 60 zeros. Because blocks are chained together like this,
instead of calling it a ledger, this is commonly called a “Blockchain”. As part of our updated protocol, we’ll now
allow anyone in the world to be a “block creator”. What this means is that they’ll listen for
the transactions being broadcast, collect them into a block, then do a whole bunch of
work to find the special number that makes the hash of this block start with 60 zeros,
and broadcast out the block they found. To reward a block creator for all this work,
when she puts together a block, we’ll allow her to include a special transaction at the
top in which she gets, say, 10 LedgerDollars out of thin air. This is called the block reward. It’s a special exception to our usual rules
about whether or not to accept transactions; it doesn’t come from anyone, so it doesn’t
have to be signed. It also means that the total number of LedgerDollars
in our economy increases with each new block. Creating blocks is often called “mining”,
since it requires a lot of work, and it introduces new bits of currency into the economy. But when you hear or read about miners, keep
in mind that what they’re really doing is creating blocks, broadcasting those blocks,
and getting rewarded with new money for doing so. From the miners perspective, each block is
like a miniature lottery, where everyone is guessing numbers as fast as they can until
one lucky individual finds one that makes the hash of the block start with many zeros,
and gets rewarded for doing so. The way our protocol will now work for someone
using this system is that instead of listening for transactions, you listen for new blocks
being broadcast by miners, updating your own personal copy of the blockchain. The key addition is that if you hear of two
distinct blockchains with conflicting transaction histories, you defer to the longest one, the
one with the most work put into it. If there’s a tie, wait until you hear of
an additional block that makes one longer. So even though there is no central authority,
and everyone is maintaining their own copy of the blockchain, if everyone agrees to give
preference to whichever blockchain has the most work put into it, we have a way to arrive
at decentralized consensus. To see why this makes for a trustworthy system,
and to understand at what point you should trust that a payment is legitimate, it’s
helpful to walk through what it would take to fool someone in this system. If Alice wants to fool Bob with a fraudulent
block, she might try to send him one that includes a her paying him 100 LedgerDollars,
but without broadcasting that block to the rest of the network. That way everyone else thinks she still has
those 100 LedgerDollars. To do this, she’d have to find a valid proof
of work before all other miners, each working on their own block. And that could happen! Maybe Alice wins this miniature lottery before
anyone else. But Bob will still be hearing broadcasts made
by other miners, so to keep him believing the fraudulent block Alice would have to do
all the work herself to keep adding blocks to this special fork in Bob’s blockchain
that’s different from what he’s hearing from the rest of the miners. Remember, as per the protocol Bob always trusts
the longest chain he knows about. Alice might be able to keep this up for a
few blocks if just by chance she happens to find blocks more quickly than all of the rest
of the miners on the network combined. But unless Alice has close to 50% of the computing
resources among all miners, the probability becomes overwhelming that the blockchain that
all the other miners are working on grows faster than the single fraudulent blockchain
that Alice is feeding Bob. So in time Bob will reject what he’s hearing
from Alice in favor of the longer chain that everyone else is working on. Notice that means you shouldn’t necessarily
trust a new block that you hear immediately. Instead, you should wait for several new blocks
to be added on top of it. If you still haven’t heard of any longer
blockchains, you can trust that this block is part of the same chain everyone else is
using. And with that, we’ve hit all the main ideas. This distributed ledger system based on a
proof of work is more or less how the Bitcoin protocol works, and how many other cryptocurrencies
work. There’s just a few details to clear up. Earlier I said that the proof of work might
be to find a special number so that the hash of the block starts with 60 zeros. The way the actual bitcoin protocol works
is to periodically change that number of zeros so that it should take, on average, 10 minutes
to find a block. So as there are more and more miners on the
network, the challenge gets harder and harder in such a way that this miniature lottery
only has about one winner every 10 minutes. Many newer cryptocurrencies have much shorter
block times. All of the money in Bitcoin ultimately comes
from some block reward. These rewards 50 Bitcoin per block. There’s a great site called “block explorer”
where you can look through the bitcoin blockchain, and if you look at the very first few blocks
on the chain, they contain no transactions other than the 50 Bitcoin reward to the miner. Every 210,000 blocks, which is about every
4 years, that reward gets cut in half. So right now, the reward is at 12.5 Bitcoin
per block, and because this reward decreases geometrically over time, there will never
be more than 21 million bitcoin in existence. However, this doesn’t mean miners will stop
earning money. In addition to the block reward, miners can
also pick up transactions fees. The way this works is that whenever you make
a payment, you can optionally include a small transaction fee with it that will go to the
miner of whatever block includes that payment. The reason you might do this is to incentivize
miners to actually include the transaction you broadcast into the next block. You see, in Bitcoin, each block is limited
to about 2,400 transactions, which many critics argue is unnecessarily restrictive. For comparison, Visa processes an average
of around 1,700 transactions per second, and they’re capable of handling more than 24,000
per second.Slower processing on Bitcoin means higher transactions fees, since that’s what
determines which transactions miners choose to include in new blocks. This is far from a comprehensive coverage
of cryptocurrencies. There are many nuances and alternate design
choices I haven’t touched here, but hopefully this can provide a stable Wait-but-Why-style
tree trunk of understanding for anyone looking to add a few more branches with further reading. Like I said at the start, one of the motivations
behind this video is that a lot of money has started flowing towards cryptocurrencies,
and even though I don’t want to make any claims about whether that’s a good or bad
investment, I do think it’d be healthy for people getting into this game to at least
know the fundamentals of the technology. As always, my sincerest thanks those of you
making this channel possible on Patreon. I understand not everyone is in a position
to contribute, but if you’re still interested in helping out, one the best ways to do that
is simply to share videos that you think might be interesting or helpful to others. I know you know that, but it really does help. I also want to thank Protocol Labs for their
support of this video. This is an organization that runs a number
of research and development projects, and if you follow the links I’ve left in the
description to read into the details of these projects, you’ll notice some strong parallels
with the concepts covered in this video. The challenges and benefits of decentralization
are by no means limited to currency and transaction histories, and the usefulness of tools from
cryptography like hash functions and digital signatures are likewise much more general. For example, a couple of Protocol Lab’s
projects, such as IPFS and Filecoin, center on distributed filestorage, which opens a
whole field of interesting challenges and possibilities. For any developers out there, Protocol labs
places a high value on open source, so if you’re interested you can join what’s
already a very strong community of contributors. They’re also looking to hire more full-time
developers, so if you think you might be a good fit for some of these projects, definitely
apply.

Only registered users can comment.

  1. What's gonna happen when two miners manage to mine and broadcast their own block almost at the same time?
    Both are valid at the moment, would it be a situation that some miners work on one and other miners work on the other?
    One of them might become untrusted in the future, but before that, how miners decide which one to work on?

  2. This video is simply incredible. I've been trying to learn about Bitcoins for a year now but this video honestly made me feel like I actually know how it works for the first time. Grant, you're an amazing teacher and wonderful mathematician 🙂

  3. So basically the necessity for computation power increases as the number of transactions increases. This means that only people who had heavily invested in computation power could do the mining. In the end, only the ones with the most expensive equipment will prevail because they are going to be the ones that will get all the transaction fees. So as long as I manage to corrupt this small number of miners I will be able to corrupt the system. It seems to be the same as the modern banking system in disguise of "decentralization". Basically, becoming a crypto miner in the future will be as hard as becoming a bank owner which means that the former will be as corruptable as the latter.

  4. Is there any way you could do a explanation on the XRPL-XRP (Ripple) since its a decentralized premined crypto,which is a 80% majority consensus algorithm using avalanche to solve this. id love to see a in depth explanation from your viewpoint.

  5. I am a person who never writes comments on videos. But after watching this, I simply had no other option than to appreciate the quality of this video. Everything about this video is incredible, the research done and the way of explaining. I am definitely sharing this video with everyone I know and becoming a regular at this channel!

  6. Perhaps I missed something, but as I understand it, a new block is verified if a value is appended such that when that value is input into the hash function, the output begins with X 0s, where X is updated constantly. Because this cannot be done methodically, or in a computationally feasible amount of time for any given X, how does this happen often enough that the block chain is updated frequently? Does this depend on there being a large number of miners? Large enough that the negligible probabilities of each individual miner mining in parallel leads to a low expected time for frequent updates?

    Furthermore, can one not store values which when input into the hash function produce a number with X leading 0s, so if there is a repeat of X being the required number of leading 0s (which must happen since there are only 256 values and X is updated frequently), one can forge new block chains quickly? The list of stored values could be fuelled by previous valid block signatures for previous Xs found by other miners.

    Really enjoyed the video!

  7. Thank you for the great video.

    However, what is the justification for the high price of bitcoin, save for its scarcity and utility? What is the fundamental value to the bitcoin?

    Also, due to the high volatility and lack of consistency in the price of bitcoin, I am not able to imagine how bitcoin could be use to replace the traditional currency.

  8. I am quite confused on the Ledger illustration at 3:14. "If you have spent more than you received, you put money on the pot and if you received more than you spent, you take that money out". Also, I think the Ledger illustration is not a transaction history list but more like a debt or credit list on who owes who. Can someone simplify this illustration?

  9. What if 500 different block creators just assign one Bitcoin user to receive the block reward? Is that what happens in Bitcoin mining groups? They work together and then pool/split the reward? You could invest that with compounding interest and gain a whole load of money?

  10. finally understood this shit. thx
    Usual "bitcoins explainers" are only explanations of "how to have bitcoin" or "what is it" in 5 minutes videos. You hear some "blockchains", some "proof of work", some "mining". But this is nonsense until the demonstration is complete. Thanks for that, you simplified, but not so much, Satochi's paper.

  11. You are on a whole next level when it comes to teaching. Exceptional. The way you teach and the way you present any topic is simply commendable. hats off.

  12. Is it possible to have an economic system where you only have a cryptocurrency? If yes, could it be possible to trace your transfers? So would people have a bank account etc? Or how would it work?

  13. What if Alice cuts off Bob's connection to the others in the network and then makes her own chain longer? When Bob comes back online, does he see that others have even longer chains and reject the chain from Alice? Even if he accepts Alice's block before coming back online?

  14. Why can’t we just ask people in the peer-to-peer network if they have the transaction in their list? Instead of doing an insane amount of computational work, wecan just send out a message saying ”do you have this transaction recorded” to random people in the network, they all reply withtheir signed answers, thus you know it’s really their answers and not a fraudulent claim from someone else.

  15. 7:00 I felt that this explanation was a bit insufficient, expanding on the "has to". How so? Should've added something like, "If a duplicated message is not changed with a variance token and re-signed, it is treated as the same transaction, so everyone will know it's a duplicate, and they'll just toss it out."

  16. 13:31 the message is "Challenge". You can try it yourself by looking up an online sha-256 tool, and then converting the output from hex to binary.

  17. best video on the internet that actually explains what's going on. I wonder if you could make some cryptography videos explaining the processes used and why they're so hard to crack.

  18. 19:26 as the miner, how would you know which of the chains is the one you should add your newly created block to? If they're of equal length, therefore equal trust-worthiness, how would you know which of the chains to trust?

  19. A programmer i am, you talk of your other video 2^256, this next generation of asics miners are going to fire 60t/hs 60 terahashes !!!! At what point, will guessing private keys be more feasible, than solving harder blocks for crypto as difficulty increases.

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  25. I was look for an explanation, which was informative, techy and well visualized

    This is the best video regarding the mentioned requirements. Thank you for your efforts!

  26. 3Blue 1Brown ;….I have no understanding @ all about this sorta thing, I've just seen, no way I was to be able to understand all that was said, k,……let – a – lone, how I want to see how ligit bitcoin is to be able to send my man in Nigeria who wants to be able to come to N.Z. to work, but can't cos this dear man I have is a genuine man I've been dating for 2 &1/2 yrs now, & He can't get work, to be able to pay for his visa & passport update for himself, & all I wana do is send him $2000, so he can finally apply for his visa & update his passport to come to work & help his poor lol family back in Nigeria cos his wife left him with the two lil children, cos he had a 15 ft fall off a mast @ His job he had as an engineer, cos he cudnt return to work after he recooperated in hospital, his wife never wanted him cos of no money to richly, so she lives in Duibai, with her flash rich patents keeping her,….this man I met is a true genome Christian man, whom I've managed to send some money by a miracle in the passed, but can't send him money thru a friend who passed it on to him anymore, it's so sad how the banks control people wen there's someone that lives in a he'll hold of a place in the world & wants to come to my homeland to work for his family back in Nigeria, & now I can't send money, to help him, & I thort this video was gona help me understand how to help this man I love soo much, how to go about it in a ligit way to know how bitcoin works so I can send him money to this very caring man, whom since I met him online, has never asked me for a solitary bit of money, & refers to me as his Angel sent from God to get money to help his lil daughter to go back to school, for her bees & other bits of importance of need for his family,…..can I please get a reply from 3blue 1Brown, about my mans plight to help his family, by myself sending him bitcoin, as he has a bitcoin account in Nigeria, i don't have one myself,….I wud appreciate to here a comment back from you, in a very simplified very easy to understand way, how I would go about this using bitcoin currency, please & thankyou, 3Blue 1Brown.

  27. The last two months, I have made over $60,000 from Bitcoin, but my success never started that way as I had made substantial losses before my turning point in the Crypto space. I  bought 2Btc last year which quickly rose in the bull run but eventually lost most of it and sold off what was left. That was the last I would ever have to do with bitcoins until I was introduced to Evan Winter first of, he asked to know my trade experience. He then gave me a quick insight on what to look out for when choosing a platform and a bunch of other things most experienced traders may never tell you. Most importantly, he introduced me to his specially designed layout and provided me with professional advice and accurate trade signals. With his system, trading has become easy and profitable, and I want to spread the word and thereby help as many that are in my previous unfortunate situation. For all questions, you can reach by {[email protected]}

  28. thank you for the video! there's one thing i don't understand yet:

    each block of the blockchain can be verified by proof of work as part of the blockchain
    but each block contains lots of individual transactions. how is every single transaction verified so that it will be included in the next 'block' of the blockchain?

    is it just the digital Signature you mentioned in the beginning of the video?

  29. It is worthy of note that Bitcoin is not a get rich quick scheme , its a don't get poor/rich slowly scheme using the right strategy and profitable trading platform like apextradecapital.com to grow your profit gradually by trading and managing your account with the right trading strategy/techniques.

  30. Oh, so bitcoin security scales with time? So the better PCs average ppl have the more secure bitcoin is?
    But does that not mean that quantum computers can hack it?

  31. Well technically stolen bitcoins end up in the wallet of the Scammer or person who stole them. But that doesn’t have to be the end of your bitcoins. In recent times, there has been good reviews on C|EH recovery experts like michael @ btc-recovery. com who are able to recover stolen cryptocurrencies, and I personally have been a victim to a scam on Bitfinance.

  32. Trading and investment becomes way risky if you're not following the right parts or using the right strategy. I can attest for Max Neil Li Lung, investment management and his strategy. I was able to contact him while (GOOGLE SEARCHING) his strategy.

  33. Wait, so if we get quantum computers. this system goes to…
    I mean if we can get solutions to very large problems monumentally faster this protocol of using a function no longer works or is no longer secure right?

  34. Bitcoin truly is the only way to make money in the Crypto sphere, However, Tokoin is a top notch project that can give a handsome reward within a very short period of time, it has shown it potentials with what it raised in its IEO and its superb volume i urge us to invest in it as Tokoin is the future.

  35. i'm here to pass this information to you i have a friend he's into hacking of bitcoins, mining btc and generating more of it. contact him on whatsapp + 1 8 4 5 6 0 5 9 0 2 4

  36. Very informative. Our clients, CoinSmart actually created a software to simplify the process of trading cryptocurrency online. We would love to know your thoughts!

  37. It is very powerful that the Tokoin project has had great success in its IEO on Kucoin exchange.

    They were one of eight IEO projects being traded above the price they sold.

    Right now you can also buy TOKO on Kucoin through this link:

    https://www.kucoin.com/trade/TOKO-USDT

    https://www.tokoin.io/ #Tokoin #MSME #Blockchain #Crypto #cryptotrading #BTC #EmergingMarkets #Ecommerce #retail

  38. Do you want to earn bitcoin I recommend Philip to everyone he really changed my life you can text him for more details [email protected],com or WhatsApp +1 (239) 579‑6274 he’s the best I made 7BtC into my wallet

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