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The unsolved math problem which could be worth a billion dollars. - YouTube
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What's the world's most popular computer algorithm?
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Maybe the SHA 256 hash function.
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I want to show you what it does,
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and tell you about a problem that no one
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on Earth knows how to solve,
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and explain why billions of dollars are at stake.
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[Intro Music]
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The SHA 256 algorithm is a deterministic
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one-way hash function.
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Now, what it the world
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do those words even mean?
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An algorithm is just a process,
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or list of steps for doing something.
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A hash function is a mathematical function
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that takes any size of input
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but has an output of a fixed size.
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You can think of it as a digital fingerprint
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for the file.
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It's deterministic
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which means whenever you start with the same input,
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you always get the same output.
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And SHA 256 stands for
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"Secure Hash Algorithm" and it outputs 256 bits.
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What does "one-way" mean?
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Well, that's just a function
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that's hard to do backwards.
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Some functions are easy to do backwards,
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like for example the function of adding 30.
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You just subtract 30 to do the reverse.
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But the function of multiplying
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two large primes together is really hard
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to do backwards.
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Take a look
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at my follow-up video for more details.
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Okay, back to SHA 256.
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It's an algorithm for a one-way
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hash function that takes any kind of
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digital input and any length of input and
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always outputs exactly 256 bits,
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or 256 ones and zeros,
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which is basically a big long number,
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usually written as 64 hex digits, like this.
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Let me tell you about two things that make
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this function really interesting and useful.
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First of all, the only time you ever end up
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with the same hash, or the same fingerprint,
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is if you started with the exactly identical input.
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There are so many different possible
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fingerprints that no two inputs have ever
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ended up with the same fingerprint,
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and I mean never, in the history of the world.
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How many different hashes are there?
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Two to the 256th,
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which means two multiplied by itself 256 times,
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or to be specific, 115 quattourvigintillion,
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792 tresvigintillion, 89 duovigintillion,
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230, you get the idea.
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Another interesting property of this funciton
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is that it's designed to have
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the butterfly effect built in such that changing
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the input just a little bit
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completely changes the output.
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Let me show you an example.
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Here's a picture I took.
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It's 1000 by 1000 pixels,
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and the file is 24 million bits long.
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When I run this through the SHA 256 algorithm,
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it outputs this hash.
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Now watch what happens when I change
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one single bit in the input.
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I'm going to zoom in to this pixel
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on the telephone pole and change
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the green value by changing this zero to a one.
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Now I re-run the algorithm, and I get a
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completely different output.
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And that's from changing just one single bit
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out of more than 24 million bits.
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So these properties make SHA 256 useful
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for all kinds of applications:
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cryptography, digital signatures, authentication.
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Oh, and there's bitcoin.
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More in a minute.
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Beyond the usefulness of this algorithm,
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I think some of the philosophical consequences
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are amazing to think about.
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First of all it's possible for you
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to see a number that literally no one else
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in human history has ever seen before.
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All you have to do is take a picture
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with some randomness in it,
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and calculate the SHA 256 hash.
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So ladies and gentlemen, here's the world premiere
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of this number that I just made
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from that picture.
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It's never been seen before.
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Also, I think it's cool that
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here's a mathematical function that
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anyone can do on their computer but
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no one has any idea how to do the reverse
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of this function.
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How do we know?
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Because there are billions of dollars at stake.
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You see, SHA 256 is a key part
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of the bitcoin protocol.
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If you could reverse the algorithm,
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you could mine bitcoin faster than
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anyone else and make a lot of money.
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In order to mine bitcoin, all you have to do
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is find an input that produces a SHA 256 output
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with 70-something zeros at the beginning.
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But, since there's no known formula,
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the best anyone can do, is to do it
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by brute force, which means just
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trying a bunch of different inputs
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until they find something that works.
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Now I said before it's impossible
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to find an input that matches a specific
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hash fingerprint.
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And that's true.
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But bitcoin mining only requires that
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you find a hash that's close, not an exact match.
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In fact, the difficulty can be adjusted up or down,
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to make it such that about every ten minutes,
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someone, somewhere finds a match,
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earning themselves 12.5 bitcoins,
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which is worth somewhere between
12 dollars and 12 million dollars.
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Also, that's why I think it's the
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most popular algorithm on Earth,
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or maybe I should say the most "commonly computed"
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algorithm on Earth.
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In this race to mine bitcoin,
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special computers have been built just for
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running SHA 256 as fast as possible.
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How fast?
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Well, if you add up all of the bitcoin miners
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in all of the world, they're currently
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doing 60 trillion hashes,
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no wait, 60 quadrillion,
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no 60 quintillion hashes per day mining bitcoin.
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Oh, wait, I'm wrong again,
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not 60 quintillion per day,
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not per hour, not per minute,
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but per second.
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That's right, SHA 256
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is run 60 quintillion times per second,
all day, every day.
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So yes, I think it's fair to say
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that SHA 256 is the most popular algorithm.
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I mean, unless you count adding and multiplying,
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which are parts of SHA 256.
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Maybe it's the most popular "big" algorithm?
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Actually, I suppose there might be some
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digital signal processing algorithms
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like Fourier transforms that beat it?
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But more than 60 quintillion times per second?
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I don't know.
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Anyway, all of this is good evidence
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that no one has figured out a shortcut,
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because there's a huge financial
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incentive to do so.
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Or maybe they have,
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but they know not to kill the goose
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laying the golden eggs,
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and they're just slowly collecting bitcoins.
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Or maybe there's some kind a secretive government
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organization, hiding the truth from the populace.
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Let's see, who invented bitcoin?
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Nobody knows, what?
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And who designed SHA 256?
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Let's see, the NSA?
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Who are they?
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United States National Security Agency!
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Uh-Oh.
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I think I better go now.
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Thanks for watching.
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