2. Proof of Work and Mining


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visit MIT OpenCourseWare at ocw.mit.edu. NEHA NARULA: So to
start, we’re going to recap what
happened last class. And last class we were talking
about how traditional payment systems work and
some of the downsides when you had a
bank in the middle even if you were using
techniques like Chaumian e-cash to try to manage what
the bank was doing. So just as a quick reminder,
we had this kind of setup where there was Alice
and there was Bob. In order to actually
make transfers, Alice had to interact
with the bank. And in the case of the
traditional payment system, we saw that the bank could
basically just say no, right? That it was always possible
that a bank could decide that it didn’t like
Alice and it didn’t want to process
Alice’s transactions. We got a little better than
this with Chaumian e-cash, but even with Chaumian
e-cash, the bank was required to do something. They were the ones
minting the tokens, and they were the ones
redeeming the tokens. So the banks still played an
integral part in this system. And that actually really
does make a difference. It’s not just a
theoretical problem. There are many accounts of
people with, for example, PayPal accounts, who
have their funds frozen, so they can’t access the money
that they have in PayPal. So this often happens
to merchants, actually, who end up accepting customers
from different countries, or things like this. They can get flagged
by people’s algorithms as being potentially
fraudulent, and that can put a hold on their funds. In the case of
Chaumian e-cash, you’ll notice that we’re not
all running around using digital tokens issued by banks. Chaumian e-cash didn’t
really work out. And that was in
part due to the fact that banks weren’t really
interested in implementing this technique. So– OK. So this is where we
ended last class, which was we’re in this
situation where the bank has a lot of
control over payments and how payments happen. And something I want to
emphasize here, as well, is this isn’t– it’s not just that
we worry about this because we want to
do illegal activity. Having an institution in
the middle of payments and being able to
facilitate payments can be a problem in other ways,
as well, because it can just simply make things slower. It can make things–
it’s harder to innovate. It’s harder to
introduce new features. There’s a sign up process. So there are
reasons why we don’t want to have an
institution in the middle, even if we’re totally
honest actors. So the question–
so where we ended up was how do we build a
decentralized digital token transfer? So we ended with
Chaumian e-cash. And now we’re in this position
where what we want to do is we want to figure
out how to make payments without a bank in the middle. So there’s a few
problems that we’re going to have to address in
order to make this happen, OK? So first of all, we
really don’t want it to be possible
for other users to intercept a transfer of
payment and steal funds. If our system can’t support
this very basic thing, then no one’s going to use it. No one’s going to trust it. No one’s going to rely on it. So it’s very important that
we have security, right? Another aspect of
security is that we don’t want to allow
people to spend money without authorization. There has to be some
mechanism by which we’re really sure it’s Alice when
Alice wants to make a payment. Another problem that
we want to avoid is the double spend problem. So what is the
double spend problem? Well– oh, and an
equivocation problem. So what is a double
spend problem? Well, when you have
digital tokens, the problem with
digital information is that it can really
easily be replicated, right? So you actually need to
think pretty carefully. The naive solution of just
having a unique string that you blast around
as your a digital token doesn’t really work. You have to do something extra
to think about how to ensure that these– once a token is spent,
it cannot be spent again. Now, what I mean by the
equivocation problem is you want to make sure
that once a spend happens, it can’t be taken back
very easily, right? So if I’m being paid by
Alice, I have some confidence that once I actually receive the
money I’ve received the money. Alice can’t renege
on that promise, OK? So these are some
of the problems that we want to solve with a
decentralized digital payment system. And here are some of the
features that we want to have, which is kind of related
to some of the problems. So first of all, we want to make
sure that anyone can use it. That’s what we mean by
the word decentralized. There’s no single
point of control. There’s no one metering
access to this system. If you want to make payments,
if you want to join the system, you can join the system. So anyone can use it. We need authoritative transfer
so that we can be sure that when Alice produces a
transaction it’s really her, and we believe that. And we want to make it so
that you can’t equivocate. You can’t undo spends. So that translates into
the following terminology that we often use
with these systems. We want it to be
permission-less. It doesn’t require permission
to enter the system. Anyone can join. Authoritative
transfer, no double spends, and you can’t undo. We call that being tamper-proof. So we don’t want it to
be the case that someone could go back and undo a spend. Another way to think
about that is we don’t want people
tampering with history. Something that would
be really useful here, and something that the bank
was keeping implicitly, was a database of who
is transferring money to whom, right? That was sort of the little
thing in the corner which said how much was
in Alice’s account and how much was
in Bob’s account. There are actually
techniques out there for maintaining a
decentralized database among a set of participants. This problem of needing
to agree on a value amongst many
different participants is a problem known as
distributed consensus. So here’s what distributed
consensus means. And if you’ve taken
A24, then you’ve probably seen this before. But distributed
consensus is the problem of multiple computers
agreeing on a value, particularly in the
presence of faults. So some of these computers
might fail or go away. You can use this technique,
distributed consensus, to build a log of operations
with something called state machine replication, and
essentially what you have when you do this is a
distributed database, which is what we’re trying
to obtain here. We need to keep
track of accounts and who’s spending
what, and what payments have happened in the system. And so distributed consensus
is a tool that we might be able to use to do this. So the reason that we might
be able to use distributed consensus to do this
is we could keep a log of all of the
transactions in the system. So Alice pays Bob. David pays Charlie. And what this log provides
is it provides ordering. So if Alice tries to pay Carol
the same thing that Alice pays Bob, because we have
this primitive, this log, this globally
ordered log, everyone can see that this came
after that one, right? Everyone can see that Alice
was trying to double spend. Alice was trying to spend
the same coin twice. So this primitive is
going to be really useful. This idea of this
globally-ordered log of transactions is
what fundamentally underlies all of these things. So we could say, if we
were to see this log and we were to see this
transaction pop up, we can decide that this
doesn’t really count. That this is– Alice already spent her coin. A property that we want to
maintain with these things is that you can only
spend a coin once. So therefore, we’re not really
going to allow this to happen. So as I said, the problem
of distributed consensus is that when you have
a whole bunch of people working on this log,
you can tolerate faults. So if some of the
people go away, if it’s only up to a
certain number, it’s OK. You still have a consistent,
globally-ordered log. So there’s a lot of
existing systems that actually provide this property. Some of them are Paxos,
ZooKeeper, and Raft, if you’ve ever heard of them. So the way that
these protocols work is that all of
these participants are executing the protocol
to agree on the log. If a few fail, the
protocol can still operate. Usually they can tolerate
up to a minority failing. So these protocols, the
ones that I just listed, operate in something called the
crash fault tolerance model, meaning they can handle
computers going away, but not really much else. And when we’re operating in
decentralized digital payment land, we want to be able to
tolerate more than crashes. We want to be able to tolerate
actively malicious behavior. Because if you’re going to
create a digital payment system, and it’s
money, then people are going to try to
steal that money. So like I said, if people go
away, if it’s up to a minority, you can still have the log. So there’s stuff
from the literature that actually supports
something close to this. There’s something called
Byzantine fault tolerance. And Byzantine fault tolerance
tolerates more than crashes. It actually tolerates actively
malicious participants. It can tolerate a smaller
number of actively malicious participants,
up to a third. So here, nodes
might not just fail. They might actually try
to subvert the protocol to keep from landing on a
single globally-ordered log. And like I said,
we have protocols that can tolerate this. Great. However, and these protocols
are very, very old, OK? Like the Byzantine
general’s problem, which was a basic
formulation of what led to Byzantium
fault tolerance, was formulated in 1982. Paxos and view-stamped
replication also came about in the ’80s. Those were two distributed
consensus program protocols. Practical Byzantine
fault tolerance, so an actual, very practical
protocol that you can implement and that you can use to create
a globally-ordered log, that was in the ’90s. And ever since then we’ve had
a lot of different protocols. So– And then in 2009, Bitcoin. So this idea, this idea
of a globally-ordered log that can tolerate malicious
participants, the thing I want to impress upon you
is that it’s an old idea. Decades old. So what’s new? What happened with Bitcoin? Well, a downside that
all of these systems have is that you need to know
exactly who is participating in the protocol. So the way that
these systems work is that the protocol
works based on identity. So you have to know
who is involved. You need to know
everybody in the system. You know everybody
in the system. You can tell who’s
sending you messages and who’s not
sending you messages, and you can make
decisions about what everybody else thinks the
globally-ordered log looks like. The thing that these
protocols did not tolerate was when you don’t know
everybody in the system. And the problem when you don’t
know everybody in the system, and you’re not
doing participation based on identity, is that
an attacker could create a whole bunch of identities. Well, there’s nothing
preventing an attacker from creating identities. And remember, we want a
permission-less, decentralized system. We don’t want to have some
gatekeeper saying who can enter into and out of the system. And given that we don’t want
to have that gatekeeper, we can’t just let
people join willy-nilly and manufacture their own
identities, because if they do, all of these protocols, all
of a sudden, no longer work. This is what’s known
as a Sybil attack, OK? When an attacker can
create identities, essentially for free, and
can swarm the good guys and take over the protocol. So where I’m going to leave
you is with this problem, which is we want to figure out how
to address the Sybil attack problem when creating
a globally-ordered log. And one way of doing
that is to think about making identities costly. So good guys can
create new identities and can join the system and
can execute the protocol. Bad guys could potentially
create identities and join the system and
execute the protocol, but because identities
actually cost something, there’s a limit. There’s an inherent limit. They don’t come for free. The bad guys can
only create so many. And that’s where I want to end. Are there any
questions about that as we transfer over to Tadge? AUDIENCE: I have a question. NEHA NARULA: Yeah? AUDIENCE: Does that
model you presented to deal with distributed
consensus assume you have synchronicity
in the system? NEHA NARULA: Not necessarily. So that problem is
unsolvable in the case where there is a totally
asynchronous system. But there’s a lot
of different ways to create a model
where, for example, if you have random
coins, then it is solvable in an
asynchronous system. So this is something that– you
might have heard of something called the CAP theorem. This is sort of a
predecessor to that, which indicates that in a
totally asynchronous system, without random coins, consensus
is actually impossible. But that’s– there’s different
ways to get around that. And oftentimes, people
assume that the system is semi-synchronous. AUDIENCE: Awesome. TADGE DRYJA: Neha. AUDIENCE: I have
one more question. NEHA NARULA: What? Oh, sorry. Yeah. AUDIENCE: So with
Bitcoin, in the paper they mentioned that they moved
away from IP-based identity to CPU [INAUDIBLE] identity. Is that where the
cost comes from? NEHA NARULA: Exactly. And that’s what Tadge
is going to talk about. AUDIENCE: OK. NEHA NARULA: Yeah. TADGE DRYJA: Anything else? Cool. OK. Hi, everyone. I’m going to talk about
proof of work, which is, in my estimation, sort
of the thing that started all of this, that, you know, there’s
all sorts of cool cryptography involved in Bitcoin and
different cryptocurrencies, but it was the proof
of work consensus that kicked all this off, and
that was the big difference. So we want a cost,
Neha was mentioning. We want some kind of cost
to create identities or cost to participate in the system. How do we prevent Sybil attacks? And this is a very hard
problem, because it tends to be an arms
race in many ways, where Twitter or
Facebook or things like that have tons of bots. Because as soon as Twitter
makes a cool new algorithm to identify what’s a bot and
kick them off the system, the various people
who were trying to make millions of Twitter
bots start to figure it out. They’re like, hey, they
banned all these bots. Ah, well, I’ll
switch this around, and make my bots more
human-like and better. I was actually kicked off
of Twitter for being a bot, and I am not. I totally am not. [LAUGHTER] They said I exhibited
automated activity. So this is a hard
problem, and this sort of gets into like Turing test,
CAPTCHA-kind of thing as well. But Bitcoin’s a fairly
different solution. And as Neha said, you don’t
want really anyone in charge. You don’t want a set
identity list of people who can participate. So that rules out things that
other system use, like let’s use social security numbers. Let’s use phone numbers. Let’s use CAPTCHAs. Well, those don’t really apply. Like, what’s a social
security number? What if I’m in Germany
and I want to use it? What if I’m in somewhere
else, you know? Phone numbers as well. Phone numbers are
just administrated by a phone company
who would then become the de facto
controller of the system. And CAPTCHAs are kind of an
interesting idea, but they– you know, the identify
the signs in this picture or the cars in this
picture or whatever. But it doesn’t really
apply, because it’s not easy for people to
verify, and not easy for computers to verify,
that the people were actually doing it. So those don’t work. So what does work is work. So I don’t know if– I think some people
have said they’ve– some people said the first
day, oh, I did problem set one. I was, like, oh, OK. Cool. Some people have yet to
start, which is fine as well. But if you have started
and looked into problem set one, great. I will talk about it a little
bit in the next few minutes. The problem set needs many
attempts to forge a signature. So if you’ve done it, you’ve– I don’t know what the fastest– probably someone got
it to work really fast. When I completed
it, I got it to run on eight cores of a
fairly fast machine, and I got it to run
in like three minutes. And it took me something
like 2 billion attempts. Which it should, right? 2 billion is a run. So this is because the hash
functions have random output, right? I’m looking for a string
where certain bits are set and certain bits are free. And since the hash functions
have random output, I have no shortcut
to be like, well, I want an output where
these bits are ones and these bits are zeros,
and the rest I don’t care. I can’t really specify that as
the input to my hash function. So I just have to keep trying
different numbers, all right? We know what we want, but the
only way to get it is just keep throwing in different
numbers to this hash function, getting the output, and checking
if it matches our criteria. So what do you want out
of work in this case? You want it to be
time-consuming, kind of like the homework. But the example in the
homework has some problems, because it’s this weird
trusted setup, right? In fact, it’s– so
in the homework case, you’re trying to forge
a signature where I have the private key. I’ve made four
signatures, and you want to forge a fifth signature
without my private key. The problem is it
seems like I would have an advantage in this work. I actually don’t, because
you can verify that I haven’t revealed any new bits. But it’s a weird setup, right? Where it’s like,
OK, well, there’s one certain actor that like
sets up this whole work, and we shouldn’t have
that kind of thing. So you want it to
be deterministic. You also want it to be scalable. And you want it
to be memory-less, where everyone gets a chance
and you’re not making progress. Because if you are– I’ll get to that later, but
if you’re making progress, it tends to be that the fastest
person always wins, right? If there’s no
randomness involved. Like, if it’s, you
know, let’s have a race between a bicycle
and someone running. It’s like, well,
that’s not really race. The bicycle is
always going to win. Whereas in this case,
if it’s memory-less, every attempt is a new
shot at getting it, and so someone
who is 10% as fast will still win 10% of the time. OK. So in the case of the homework. So here’s an example where five
bits of eight are constrained. So let’s say these
first two, you’ve got the pre-images for both. This is the zero row. This is the one row. And the signatures
I’ve revealed– OK, you get both bits here. However, here, in
this place, you only have the one bit,
the one pre-image. Here you only have a zero. Here you only have the one. Here you’ve got both, and then
you’re also here, one, zero. So the idea is these
three bits are like x. Like, don’t care. Either a one or
a zero will work. These five bits are constrained. So it must match
101 and then 10. So you’re going to have
to keep trying messages. And since five bits
are constrained, you’re going to have to try
2 to the 5 messages, which is, what, 64? I think? Yeah. Which is totally doable, right? 64 tries, and you’ll
probably get it. So for example, you
try once, and you say, OK, I got, 11001100. Doesn’t work. These are OK, because
they’re OK no matter what. This one’s wrong. This one’s OK. This one’s OK. This one’s wrong. Let me try again. OK, I got it, right? These can be anything. I got a 0 and a 1. Sure. These all line up. The red ones all line up, so
I’ve found a valid solution. And so that works as a proof
of work, and in this case, I found a solution, which
was Tadge forge 1 154262107. And that’s a message that can
be forged, given those four signatures in the problem set. And anyone can, you know,
whatever homework solution you have, you can probably
copy and paste that string and check that if
you hash that, you’ll get a hash that matches up and
can be signed with those four signatures. So then the question is,
did I do 154 million tries to get that? Like did I start at zero? Maybe I did more. Maybe it was random. Maybe I got lucky and I started
counting at 150 million. So it’s not really a
proof, is the thing. Like, you’re not exactly sure
how many attempts someone did. Not quite a proof, right? There’s a lot of chance. However, over many
proofs, it averages out and you can be pretty sure that
someone’s doing all the work, right? So if– you know, if someone
gets lucky once, fine. Like, maybe they
tried a couple times and got a valid proof
of work, but eventually, if they keep doing proof of
work and they’re iteratively showing them, then
you can be pretty sure that they’re not going to be
lucky the whole time, right? And so you have to estimate
the collision difficulty. The best way to estimate the
difficulty and the amount of work that people have done
isn’t to look at their proof, isn’t to look at their
nonce, but to look at the constraints of the
system before they start, right? So in the case of the homework,
31 bits are specified, right? So with four
signatures, you’d guess that about 32 bits would
be– and in this case, there’s 1 bit difference. So in the case of
the homework, there’s 31 bits that are
specified, so that means you’re going to have to do
about 2 billion hashes, right? 2 to the 31 is like 2.1
billion, or something. And so that’s the best
estimate of how long it took, regardless of what the
nonce is, regardless of what it looks like they
did, you could say, well, it’s going to take on
average 2 to 31 attempts. Let’s just– and so if any
valid solution they give me, I’m going to credit that
with 2 to the 31 work. So actually, in
the case of mine, the one is the thread number,
and there were eight threads, so this Tadge forge
1 154 million. So I had eight threads
going in parallel, and that happened
to be thread one. And so they all went
about the same speed. So it’s really like,
154 million times eight, which is
about 1.2 billion. And so that’s actually
kind of lucky, right? Like, it should–
you would estimate on average you would
take 2 billion, and I got it at 1.2 billion,
so pretty good luck, but within 2x of
what you’d expect. And since you can look at
the probability distributions of like– that might be kind of
interesting with the homework, like OK, everyone’s attempt,
some people it takes 2 billion. Some people get lucky
and it takes 1 billion. Some people get unlucky
and it takes 5 billion. And you’re going to have
this curve to see it. But this is– that’s a
kind of weird application of this signature forging
algorithm, all right? It’s not what it’s made for. We can have a
simpler proof of work that has a specific target
that’s reused forever, and it’s more universal
in that it’s not, like, oh, here’s
this private key. Here’s this key pair and here
are these four signatures. Where are these
things coming from? That’s weird. We have to match these weird
strings of bits and stuff. That’s kind of annoying. So it’s better to do something
similar, but much simpler. We’ll just try to collide
with a fixed string. So there’s some defined
string of ones and zeros, and we just say,
OK, well let’s try to have a collision with this. And the simplest is
collide with zero, or you could also
collide with like FFFF. But in the case of
Bitcoin and the case of many of these
systems, we say, well, let’s just try to
have a low number. So let’s interpret the hash
output as an actual number. In most cases– do we
have any hashes out here? No. You know, it’s a 32 byte string,
and we think of it as just, like, here’s a blob of bytes. But you could cast that
into an integer, right? You could say, oh,
let’s interpret these 32 bytes as a uint 256. Right? A 256-bit unsigned integer. And let’s look for
really low ones. And you can do that. I think with some
CPUs, they’ll actually let you do giant
integers that way. But even if not,
you have some kind of big int library in your
computer, which just interprets it that way and
says, OK, let’s try to find collisions with zero. Basically, let’s try
to find low numbers. Yeah, OK. So this idea– there’s
a paper before hashcash, but I don’t think hashcash
was the first software. This idea is
actually really old. In 1997, Adam Back, who still
works on this kind of stuff now with Bitcoin, the idea was
to stop email spam, which– I don’t if– you know,
in the late ’90s, was actually a huge problem. They didn’t have all the
cool like different machine learning stuff, and
there’s tons of spam. And the idea was,
OK, put a nonce. And a nonce is this– we call this a nonce,
right, the random number you’re throwing in to
keep changing things. Put a nonce in
your email header, and you try to get
a low hash output when you hash the whole thing. So within the UI for email,
you don’t necessarily have to see, OK, what’s
this person’s nonce? The computer just does it
all automatically for you. But the idea is you need a
partial collision with zero. You need a low hash
output for your email, before your email, the receiving
person, will display the email. And since the header includes
the destination address, if you’re a spammer
and you want to spam a million different
people, you’re going to have to come up with
a million different proofs of work. And that could
take quite a while. Like, let’s say an
average CPU can do it in two or three seconds. That means you’re going to
have to be waiting months to spam all these emails. However, for a normal
person, if you’re just sending an email to your friend,
takes a few seconds, right? Takes two seconds for your CPU
time, which is not a huge deal. So this was a cool idea. It never really
got off the ground just because, I don’t
know, Gmail happened, Hotmail happened. A lot of web mail
things happened. People don’t really use– AUDIENCE: I think there was a
paper that the economics of it doesn’t work. TADGE DRYJA: Yeah, I mean,
spammers often have bot nets. So, yeah, there’s a lot
of other issues, right? Like there’s– it didn’t
take off for various reasons. But yeah, also,
spammers have botnets, which also sort of hurts the
whole idea of proof of work, in some cases, which we’ll
talk about in a second. OK. So the simpler proof of work. So for example, if you
go onto your computers, and you say, echo Tadge
4233964024, and pipe that to sha256sum, you
will get this output. And that’s eight zeros in
the front, so that’s 4 bytes. I did 2 the 32 work, and it’s–
you know, that’s me, right? And so that proves
that I’m a hard worker, and I’m going to put
this nonce on my resume, and everyone can
see that I do work. That is kind of silly, but it’s
a really easy universal way to have a proof of work. Anyone can put their name or any
message, and any kind of nonce, and we all just pipe it
into the sha256 function and see how low the output is. In this case, it’s
actually 2 to 33, right? Because the first digit
is a 7, so that’s 0111. But this is what
we use in Bitcoins. It’s what they use in
a lot of these things. I mean, it’s really
straightforward. OK. So partial collision work. It has a lot of the
properties that we’re looking for when we want
this consensus system, right? It increases the
costs of equivocation and helps with Sybil resistance,
in that if I want to fool you, I’m still going to have
to do a lot of work. And I need time to do that. I need electricity to do that. I need a bunch of
computers to do that with. Also scalable,
because a ton of work still takes the same
amount of time and space to verify as a little
bit of work, right? So I can do O of n work, right? I can put as many
zeros as I want, and the nonce doesn’t
really get any bigger. The nonce never has to get
bigger than the hash output, certainly. And the time to
verify is the same no matter what, so
that’s really cool. So why do we do work,
in the case of Bitcoin? The idea is you use a
chained proof of work as a distributed time
stamping mechanism. So it’s to determine
what happened first. So in the case of a double
spend, where someone is saying, oh, transaction
A happened first. And someone else
says, well, I think transaction B happened first. You can’t just rely on what
other people are telling you, because who are
these other people? There’s no real identities here. So you look at what got into
the chain of hashes first. And you say, OK,
well, that one– this one, this data,
has a hash of this data, so it must have happened
after it, right? And the things that
happened before are pointed to by the
things that happened after. Because the idea is I can’t
include the hash of something that I haven’t seen yet, right? It should be
impossible to do that. So the idea of the blockchain. You’ve got some
message m, some nonce. Let’s call it r,
and some target, t. And this actually changes,
but we’re not going to talk about the changes yet. So you tack the hash of
your message and the nonce– like I was doing with Tadge– and the number, and
you say, OK, that’s h. And h has to be less
than some number t. So in the case where
I just said my nonce, I had 2 to the 33 work. So say the same thing here. In the example, I’m
going to only require 2 bytes for the
target, so that target needs to be fairly large. And then the message for block
n includes some data, and also the hash of block m minus 1. You refer to your previous
block hash in your current block data. So for example,
message number two would be data 2 concatenated
with the hash of data 1 and r– well, there should be r1 there. OK. So I’ll show you a
little diagram this. So the idea of a
blockchain, which– yeah? AUDIENCE: You’ll
need to back up. Could you explain
why it’s less than? TADGE DRYJA: In this
case, we want low numbers as the hash outputs. AUDIENCE: Does it
have to be less than? TADGE DRYJA: You
could do greater than. You could have, I want something
that starts with a lot of Fs. It would work the
same, you know? You could– yeah? AUDIENCE: The idea here is
you want to constrain, right? TADGE DRYJA: Yeah. AUDIENCE: So you can
do that with less than or you can do that
with greater than. You could do that
with a fixed sort of– TADGE DRYJA: Yeah, you could– AUDIENCE: Little
bits have to be– TADGE DRYJA: Well,
there’s something– OK, so less than and
greater than are actually nicer than just fixed bit. So you could say, I want it
to start with the repeating pattern 10101010. That would work,
too, but then you’re constrained in
how fine tuned you can turn the knob,
in that you’re going to either have to add
another bit of constraint or remove a bit of constraint. And so that, you
know, you’re going to have to go in 2x jumps. What’s nice with this is you
actually have very fine-grained control over how much
work you’re requiring, because you don’t– so in this example, I said,
hey, I have this many zero bits. But I can also
say, well, I needed to have a number less than 7f– dah, dah, dah, dah, dah. Like, less than 7f 000 here. And this satisfies it,
because hey, that’s 7e. That’s less than 7f. right? So I can actually have
a pretty specific thing, not just in terms of
number of bits specified. So greater than or less than
is kind of nice in that sense, because you can have very
small changes to the target. Oh. OK. Any questions about
all this crazy stuff? Cool. OK. Yeah. So you can you can specify. So in the case of the homework,
it’s just number of bits, right? Because they’re all scattered
throughout the field, whereas in this
one, you can say, well, it’s the targets
greater than or less than. In this case, less than. So I have fine-grained control. Which, we’re not going to– we’ll get into later. But, yeah, in the
actual case of Bitcoin, the target can vary, right? So when Bitcoin started, you
needed 4 bytes of zeros, right? You needed to do
2 to the 32 work. Now you need to do
way way, way more, and there’s an algorithm
in Bitcoin that adjusts what that target is. And I’ll show at
the end of this– like a current
Bitcoin proof of work. AUDIENCE: We’ve got
to talk about that. I was going to ask
you, [INAUDIBLE] time? How do you know
[INAUDIBLE] solve? TADGE DRYJA: Right. Right. So time is sort of a tricky,
semi-ugly subject in Bitcoin. It’d be really cool if
they could get rid of it. But time is used, and only
to vary that target, right? So when you mine a
block, you say, I’m going to put what time it is. And you look at the last two– when every two weeks, or
so, every 2016 blocks, you look at them,
and say, OK, what’s the first timestamp
of this 2016 period and the current timestamp? And if that took
two weeks, cool, we don’t have to
vary the target. If it took less than two weeks,
let’s crank up the difficulty, or lower the target. And if it took too
long, let’s make it easier by raising the target. And so really,
you’re only comparing the first and last thing. During the process, when
everyone’s downloading stuff, I think the general rule is if
you see something that’s off by more than two
hours, you reject it, but it’s very lax in terms
of synchronization, right? If someone’s 10 minutes off,
you’re like, yeah, sure. I’ll take it. Even if block eight says it
happened before block seven, refers to block
seven, and yet has a timestamp that’s before it,
you’re still like, yeah, OK. Fine. Whatever. People’s clocks are off. So that the time is fairly lax. AUDIENCE: What happens
if, like, the person who has the last block– who decides– who timestamps it? TADGE DRYJA: You just
time– the person who’s doing the work timestamps it. AUDIENCE: Could an actor
timestamp it wrong to like– TADGE DRYJA: Yeah. To screw around
with the difficulty? Yeah. AUDIENCE: OK. TADGE DRYJA: You’re
fairly constrained, right? So it should be two weeks,
and you can say, well, I bet if I’m off by 20 minutes
everyone will be OK with it. But that’s not a ton
of control, right? If you’re the last one of this
difficulty adjustment thing, you could say, hey,
I’m going to say it’s– I’m going to say– what would you
probably want to do? I’m going to say it’s 20 minutes
in the future, because I want the difficulty to not go
up too much, because I’m trying to get more blocks. So you could try to push it
to 20 minutes in the future from what it actually
is, and people, all the rest of the
nodes in the network will probably accept it. But you get 20
minutes difference over a two week period, which
is way less than a percent, so– AUDIENCE: And you
said two hours is– like, it would not
take a block that says it’s a week in the future? TADGE DRYJA: Yeah. Yeah. So– the thing
is, it’s hard to– you don’t really necessarily
know everyone’s consensus rules in these systems. But I think the default is
two hours from your clock. And every client
I’ve seen will reject something that seems to be
more than two hours off. Which is really lax, right? For most types of distributed
systems, two hours is crazy. Most of the time they’re going
to be within a few seconds. So in general, I
don’t think it ever is a problem in terms of that. So yeah. But what people do– OK. So one of the things they
do, which I can get to here. Since there is a timestamp
in the message being hashed, some chips that are
purpose-built for doing this work, will actually
flip bits in the timestamp, flip the low order bits,
because they’re like, well, no one cares what
second it is, so I have a bit here that I
can just turn on and off and use as a nonce. So the last, the lowest few
bits, they just randomize. They’re like, well, if
I’m off by five seconds, no one cares whether
future, past, so I’ll just use
this as nonce space. OK. So– but I’ll get into
that a little more later. So anyways, so a block. Let’s call this. A block has a bunch of data,
and then we hash it, right? And in this case,
it’s got three things. It’s got a previous
hash, so a pointer. It specifies the thing
it’s building off of. It’s got a message
so that you can add your message that you’re
adding to the blockchain. And it’s got a
nonce, so that you can prove you’re doing work. And then these are the things,
the actual data, but then the block itself
has a hash, right? And this hash is not included
anywhere in the block, because it couldn’t be, right? This is the hash of this data. And so we can compute it, but we
can’t we can’t stick this 00db thing here, because that would
then change the data itself. So the idea is, use these
block hashes as identifiers. And in most of these systems, in
general, the hash of something is its identifiers, its
name, the way to point to it. OK. So the next block includes a
hash of the last block, right? So here you’re saying, OK,
the previous block is 00db. You’re pointing to it. And then you’re adding
your own message, oh hi. And you’re adding your own
nonce to make– you know? And so these two things
you start out with. You start out with the
pointer to the previous block, and then you say,
OK, the message I’m going to try to
add here is oh hi. And then you start grinding
through these, right? You start iterating or randomly
attempting different nonces, until you found one
where it’s low, right? It’s got a bunch of zeros. And so this is the nonce
you need to specify to get a lot of zeros. And in this case, there’s
four characters of nonce. And you only need two
characters of zero, so it’s way more nonce
space than you need. Yes? AUDIENCE: How many
possible nonces are there that would
result in this? TADGE DRYJA: In this
case there would be, on average, 255 nonces
that would work, right? Because– I’m, OK. I haven’t actually
specified these things, but assuming the target here is
must be less than 00ff, right? So you need eight zero
bits in the front, and all the rest can be Fs. And you can have
any nonce you want. And this is an actual hash
function, which is 2 byes long. That means you’ve got 2 bytes
here and only 1 byte specified, so you’ve got two to
the 16 nonce space, and your output is
constrained in 2 to the 8, so you’re going to have 2 to
the 8 different nonces that will work. In the case of Bitcoin,
there’s nowhere near enough nonce space, right? Because your actual constraint
on your proof of work is a lot of bits, and you
only have 4 bytes, or 32 bits, of nonce space. So what you actually
end up doing is using your message as
further nonce space, right? So the thing is, I
could put oh hi 2, and now I’ve changed my message,
which will change my hash. And so if I go through
my entire nonce space and don’t find a valid proof
of work, I can edit my message and then go through it again. So that– it’s a
little ugly, right? It’d be nicer if your nonce
space was big enough that you’d never had to do that. In the case of Bitcoin, we
don’t know who designed it, and whoever designed it
didn’t put enough nonce space, and so it’s kind of annoying. But you can get around it. In theory, you could just
eliminate the nonce space entirely and say, well, just
put it in the message, right? But it’s nice– it’s much easier
to think of when you’re like, here are these separate things. Like, this is random. It has no real meaning. This is the thing
that has meaning that we’re going to use. Anyway. So yeah. The chain keeps building. You add work each
time, right, by finding different nonces that
match up with your message. How are you? Oh, I’m good. OK. And the idea is
if you flip a bit in any block that’s come out. So, for example, you
change oh hi to oh hey, and try to leave
everything the same, you’re going to change the hash. So most likely,
the proof of work will no longer be valid, right? Oh, this starts with a 9 now. No one’s going to use it. And more importantly,
actually, these pointers stop working, right? Because this block
was pointing to 002c. That’s not this. That’s this other one. So basically, you flip any
bit in the entire history of this chain, and
it breaks, right? So you can’t go back
and edit things. You can’t change
messages after the fact. So it gives you the nice
property of immutability that once a message is
included in the system. So in the case of money,
once a transaction has moved funds from
one place to another, you can’t go back and change it. You can’t undo something. Unless. Unless you fork the chain. So the idea is everyone
is running this system. Sometimes inadvertently,
or sometimes on purpose, you can have two
branches, right? You can’t have
something point to two different previous
blocks, right? There’s one specified–
so in this case, when I say previous block, it’s
a single, specific hash that I’m pointing to. And since we’re pretty sure
we can’t find collisions, that means if I’m pointing
to 00db, it’s only this one, which has the message hi. I should not be able to find
two different blocks which hash to 00db, because then it’s
ambiguous, and like, wait, which am I pointing to? So I shouldn’t be
able to do that. However, it’s easy
to have two blocks here that both point
to the same ancestor, that both– we call this a
parent, call this a child, call this a branch. So this is easy to do, right? Two different people can just
come up with their own messages and own nonces and point
to the same ancestor. They could do this
inadvertently, because they’re not aware
of each other’s work, right? Or maybe these two things
happened at the same time, and they’re like, oh, well
we both found the answers at about the same time. Or they could do
it, maliciously, where I saw that
you made this block, and I saw that you
made this block, and I’m going to make these
two, to try to confuse things. So this can happen. And the rule in Bitcoin, and
most all of these systems, is OK, well, the
highest blockchain wins. The most work wins. So that’s just our metric
for what we all determine as the state of the system. So everyone uses the
chain with the most work. And that can change, right? Let’s say we started off with
the 008a being the chain tip. That’s what we call the
current state of the system. And then someone
came along and said, well, I’m want to get
rid of this thing. Something happened in 94
that I want to rewrite. I want to get rid of
the how ru message, and I’m going to replace
it with my own message. And so the way I do it is
I branch off from 002c, make this one, make this one,
and now, I’ve made another one. So now, this branch
here has the most work. And everyone’s going to use it. And they sort of forget
about these two things. They’re like, yeah,
that was the tip. That was the most work state
of the system, but now this is. So now we have to go back. We have to erase
these two messages, and add these three
messages, and now everyone agrees that that’s the
next state the system. And this is called a reorg, a
reorganization of the block. This is sort of bad, but yeah. Yeah? AUDIENCE: How does
the whole process of– so no one realizes they’re in
the wrong chain, [INAUDIBLE],, right? TADGE DRYJA: Mm-hmm. AUDIENCE: How do they say,
OK, I need all the information to build the actual chain? TADGE DRYJA: Yeah. They request it, or
basically, someone says, hey, I have these three. And you’re like, really? What are those three? And they give them to you. And you’re like, OK. Yep. That works. So the actual network– I think in a few weeks we’re
going into the actual network messages that are used in
Bitcoin, but they’re not like– you– actually, if you
wrote it yourself, you’d probably write something
more sensible and better. It’s a little weird. But basically, you sort of– nodes in this network are
all connected to each other, and they report
on what they have. And they say, hey, I have 0061. And you’re like, really? I don’t have 0061. And you think, maybe
0061 builds off here. You request 0061
and you’re like, oh, it builds off of here. And then they’re
like, I have f2. I have a3. And so they build these– you know, they request
them all and build them. And then they actually
keep these in memory for a little while, and then– but I don’t think they
save them on disc. So you can have multiple
different branches, concurrently, in your
software, and you just use this and show this to the UI. Yeah? AUDIENCE: Who specifically
do you ask for the chain? Because if it needs only one,
then you could just sort of– TADGE DRYJA: Needs only– AUDIENCE: If only one
person had a longer chain, and then everyone
starts replicating it, then the network starts
believing it, right? TADGE DRYJA: Yep. Yep. So it’s a gossip network. So basically, there’s
no real identity for all the different
nodes of computers. You also will report all the– you basically do it
by IP address, right? So when I connect to a
node, I don’t think I ask. I think they just
tell me, like, hey, here’s a thousand IP
addresses that I know of, that I’ve connected to, that
are running this software. And you’re like, OK. I’ll add that into my list. And then you just randomly
connect to people. I think the default is randomly
connect to seven peers. And then when you– when anything comes in, you’re
like, hey, I got a new– you know, I got a
new block message. You will tell all
seven of your peers. Hey, I got 00a3. And if they request
what the data is, you’ll give it to them. So in practice, things get
propagated pretty well. But yeah, partition attacks. If you can isolate– so like, if you can isolate
this off the network, you may be able to prevent this
kind of thing from happening. So if someone built
these three blocks but isn’t able to broadcast
it to the network, then people will still think
that this is the most work and build off of this. So yeah, those are
attacks that can happen. Yeah? AUDIENCE: What happens if
you reorg transactions, for instance? Like if the messages
were transactions? TADGE DRYJA: Yeah. They stop being–
they get undone. So this is a very real risk. If you have a– Alice is sending Bob 5
bitcoins in this block. And in this block, you have
a conflicting transaction, Alice is sending Carol 5
bitcoins, the same 5 bitcoins, Bob could think at this
point, hey, I got some money. I have some money. Oh, shoot. I, whoops, don’t have
the money anymore when this gets reorged out. So that’s– that is
an attack, right? And you have to be aware of
that in using Bitcoin, or any of these kinds of systems. They’re not– you
have consensus, but I think it’s like
eventually consensus. So generally, the rule of thumb
people use is wait six blocks. I think that’s in the
original Bitcoin white paper. Which is fairly arbitrary. Like, you know? The longer you wait,
the more certain it is. The more difficult it will be
to perform this kind of attack, because you’re going to
have to do more work, right? And the idea is everyone’s
building off of the one that they think is the tip. So everyone’s going to– you have to get pretty lucky or
outrun everyone else to perform this kind of attack. So. OK. Yeah? AUDIENCE: Are those
known as uncles? TADGE DRYJA: Oh. So like, in Ethereum
and some other systems they have uncles
where you can point to multiple ancestors,
which is weird, because your uncle is not really
your ancestor, but anyway. [LAUGHTER] So that would let– for example, that would let 00f2
to point to both 0061 and 0094. NEHA NARULA: The answer is no. These are not uncles. TADGE DRYJA: Yes. So yes. NEHA NARULA: [LAUGHS] TADGE DRYJA: Sorry. Uncles is a separate thing. This is not uncles,
but related, right? You could draw, like– you
could draw an arrow there, and– I don’t know. OK. So I’ll talk about pros
and cons, and some of this gets into not as objective
and somewhat subjective ideas. But it’s an interesting thing
to talk about, especially in context of money. OK. So pros. Anonymous, member lists,
scalable, non-interactive. I’ll go through all of these. Tied to the real world. Cons. Pretty much all nonces fail. It uses watts. It uses chips. There’s 51% attacks. And people hate it. [LAUGHTER] So the pros. They’re quite good. It is anonymous, right? You can mine without
any kind of identity. Even after you’ve
mined, you don’t really have to say who you are. There’s no pre-known keys. There’s actually no
signatures involved, right? There’s no public
key system at all. You’re just trying
different nonces. Anyone can go for it. Every attempt is equally likely
to succeed, since it’s random, and it’s not limited to humans. So you could have– you don’t need a
social security number. Bots are welcome. Anything can mine. And everyone doesn’t
really care who mined it. It’s not about who. It’s just oh, there’s a nonce. There’s work. OK, this is valid. So that’s really cool. It’s memory-less. This is important, and a little
counter-intuitive in some ways. There’s no progress. So if you have 10
trillion failed nonces, your next nonce is
just as likely to fail, which is extremely likely. So that makes it a
Poisson process, right? Which is– you know, it’s
a certain probability distribution, kind of thing. You will always expect the next
block in 10 minutes from now. So, hey, it’s been 20 minutes
since the last block came out. When’s the next one coming out? Probably 10 minutes. And there’s no–
it’s sort of like– you know, there’s no
progress being made. You always have
no memory of what the last few minutes have had. So the fact that
it’s been 10 minutes, the fact that it’s– or
it’s been two seconds, you still think it’s going
to take about 10 minutes. Which is nice, because
it means there’s a linear trade off between how
many attempts you’re making and what your chances of
finding the next block are. So if you attempt
twice as many, you have twice as good a chance
of finding the next block. Which is good, because if
there is progress, right, if you had some kind of function
where the probability was not just linear number
of chances, but if it was super linear, exponential
or something like that, you– the fastest person
would always win, right? So if it’s like, OK, I
need to compute this thing, and it takes a couple
trillion computations. And so for some computers,
it takes five minutes. For some computers, it
only takes two minutes. The computers that can
do it in two minutes are just always going to
win, because the people who take five minutes to
finish it, well, they just did it in two minutes, and
I can’t keep up with them. So this is really nice, and
it makes it competitive. Otherwise, it would end
up being like whoever is fastest just consistently
can perform the work. Any questions
about memory lists? It’s kind of– this– I mean, you guys actually know
computers, and stuff, and math. You know, MIT. But this is a fairly common
misconception in Bitcoin and other systems like
this, where people get mad. Like, it’s been an hour
and no block’s come out. It’s like well, yeah, you know? Poisson process. On average, every day and a half
there will be a one hour gap. And then people have
been, like, well, the last three blocks came
out in like, two minutes. So there’s going to be a
awhile before the next block. It’s like no, no. There’s– [LAUGHTER] There’s no memory. So there’s a lot
of misconceptions when it’s a purely random
system, that people are not used to this kind of thing. But it’s
counter-intuitive, right? Even I think, like, oh, well– no, no. Memory-less. Got to remember that. Got to remember that
it’s memory-less. OK. So scalability is
actually amazing. So this is a block
hash from this morning, or late last night, that
actually happened in Bitcoin, and there’s a lot of zeros. There’s 18 of them, and 9
bytes, and actually more, because it starts with a three
instead of an f or something. So what’s really cool about
this is it takes just as long to verify this work as it did
with the one with my name, right? Which only had 4 bytes
of work, you know? And the one with my name,
it took my computer, I don’t know, 20 minutes
or whatever to do. This took computer–
you know, this one took 10 minutes, right? But it took the
network 10 minutes, because everyone’s
participating at the same time. So yeah. And it’s a trillion
times more work, and takes no more
time to verify. That’s really cool, and
it is kind of amazing, because this is almost
a mole of attempts. Like, Avogadro’s number. So you’re getting into
numbers that like, you never deal with these
scales of numbers in– I mean, you do in
chemistry, but, like, whoa. So that’s a nice property. Also, it’s non-interactive,
and that helps as well. So you never have to report
your failed attempts, right? So you can have a thousand
different computers all trying one nonce with
different messages, or one chip trying
a thousand times, and you don’t need any
communication between them. So the only communication
between in the network is when a block
is actually found. So there’s no real setup needed. So it’s a very simple message
protocol where you say hey, here’s a block. Everyone just broadcasts. That’s really cool, too. So these are all really
useful properties for our network and
our consensus system. Oh, also. It uses real world resources. So when you want to go
back and rewrite history, even if a majority of
participants want to do that, there’s still
going to be a cost. So that’s pretty unique
compared to many different says consensus systems. In many systems, say, OK, well,
we have unanimous agreement. All participants in the system
are going to rewrite history. We’re going to go back,
pretend that never happened, and branch off and
create a new history. Even if everyone in
Bitcoin, every participant, tries to do that,
they’re still going to have to spend that
energy and that work. And so that really
discourages reorging and trying to rewrite history,
even when everyone wants to. So that’s cool in
that you’re tied down not just by the other
participants in the system, but by physics itself and
the way the world works. We are going to have to
do work to rewrite this. So that’s– and also, it
shows that people are sort of invested, and
they’ve done work. So that’s cool, too. OK. So any questions
about all these pros? Or if you want to say
some of these pros are actually cons before
I get to the cons? OK. We can go to cons. And this– it’s always more
fun to complain about stuff. So we can go into cons,
and I’m sure people can jump in with other things
that, oh, yeah, this is bad. So one problem is
that it’s inefficient. Almost every attempt fails. So that’s no fun, right? So the proof of work
from a few hours ago, this is 10 to
the 22 attempts. And all– you know, there’s
10 to 22 failed attempts that were required, that happened,
in order to get that one. So that’s extremely
inefficient, you know? I don’t know how to express
that as a percentage, but the actual things
moving the system are some incredibly
small percentage of the actual things happening. It’s also a problem
because you’re not going to be able to get
a valid block, right? If you have to 2
to the 72 attempts, you’re just not going to do it. Like, ever. You can run your laptop
for your entire life and you will not be able to
do two to the 72 work, which is kind of depressing. Even if you buy
specialized hardware, yeah, you’re not going to– you’re not going
to find a block. It consolidates into–
you need a factory. You need a warehouse full
of equipment, basically, in order to do this now. So that’s kind of
annoying, right? It’s not as fun. Like, the small players have
been pushed out of the game because you need to do
so much work in order to have– you can’t
get, hey, I came close. Can I get partial credit? Can I– you know, I
did 2 to the 50 work. Can I get anything for that? The system doesn’t
recognize partial work. OK. Other cons. It uses watts and chips,
uses lots of electricity. You could use that
electricity to charge your car or do something cool. It uses fabs to make microchips,
which could make more CPUs or make cool phones
or something. Once it gets big
enough, it actually starts affecting markets. So I don’t know if– I just know in Micro Center,
down there, many times– because I live near there. And you go around, and
there’s the GPU section, and everyone complains
about Bitcoin in Micro Center near the GPUs. It’s a Bitcoin. It’s usually Ethereum and other
coins that use GPUs for mining, but that has had a really big
effect on the market for GPUs. A lot of people– because
you can make money with them. So people are like,
yeah, I’ll buy one of these things
for $500, because I’ll make back my $500 in a year. And then I’ll
still have the GPU, and maybe I can sell it
used, and get a couple hundred dollars back,
and then I profited. So these things affect– it’s big enough that
it affects markets. Initially it didn’t,
because it was just a couple of nerds
running Bitcoin, and so like, who cares? You know, a couple of
people buying GPUs. But now it’s big enough. These are like billion
dollar markets, and it’s getting to be the
same sort of scale as the gamer market– or gamer, or whatever– CUDA, or whatever
people use GPUs for. But you know, mining
is significant, and so it affects the market. Who knows? Someday you could start to
affect electricity prices if you get big enough, where
a significant portion of all the electrical usage in
the world or the country is going into doing this sha256. And so that makes
electricity prices go up. And then everyone
starts complaining like, man, electricity
is twice as much as it used to be because all
these people mining Bitcoins. And it’s possible if it gets big
enough, instead of just people complaining about GPUs. So that’s sort of a con, right? That’s– it starts affecting
the real world in big ways. The corollary of it being
a memory-less process is that it’s irregular. It’s a Poisson
process, which means sometimes you get
in a few seconds, and sometimes it takes an hour. And people don’t
like that, right? I can see how you’d rather have
something come out regularly. A lot of people think,
yeah, blocks come out every 10 minutes. Well, on average, every 10
minutes, but it can be hours. It can be seconds. And so that’s hard. In some cases, you
can’t really use it. Like, hey, I want
a regular clock, or I want messages that
come out in some kind of– I want some assurance, right? If I make a
transaction, I want it to be included in the system. I want some assurance it will
be included in the next 20 minutes. You don’t get that
assurance, right? It can be 30 minutes before
anything gets included. And in fact, we’ll
get into it later, but there’s even worse
assurance properties, in that just because
five blocks came out doesn’t mean your transaction
got into any of them. It might have been ignored. It might– there’s
all sorts of reasons. So you can deal with
this, but it is annoying, and it precludes some use cases. And other consensus systems
do not have this problem. Other consensus systems can
have much more regular clocks. So this is kind of
annoying as well. Any questions about the
irregularity aspects? OK. OK, big con. It’s like 51% attacks. OK. Part of the problem
with anonymity is you have no idea who’s
doing this stuff, right? Even if they say who–
even if they claim– so one of the interesting
parts of anonymity, despite this being designed as
a really cool hacker-y, cyber punk, anonymous system, one
of the first things people did was put their
name in it, right? So if you mine a
block, you’ve got space where you can put 32 bytes
or so that are undefined, and people would start putting
the names of their mining pools or the names of their
cat or whatever. They just put their names in it. So it’s kind of like they’re
showing who they are, and you can look at
distribution of who are the different miners,
and stuff like that, even though it’s
supposed to be anonymous. So they claim– but
they can claim a name, and they can claim this
block was mined by F2Pool, or this block was
mined by BTC.com, you’re not 100% sure, right? It’s all– I could
also mine a block and claim that it’s from F2Pool. And it’s hard to disprove. So you don’t really
know who’s mining, and an attacker with 51%
of the total network power can write a chain faster
than everyone else combined. So that means they can
rewrite history, right? So like in the example
before, where hey, I made this three blocks longer
than these two blocks, I had to either get lucky or
everyone else stopped mining for a second, but that’s
not really possible, long term, if I have a minority
of the hash power, right? Because everyone’s
just going to start– you know, if the majority
is honest and playing by the right rules,
they’re just going to see what the
most, the longest worked– the most
worked, the longest chain is, and start throwing
blocks on top of that. And if I go back and
try to make a branch, the main branch will grow
faster than my sub branch, and so I’ll never
overtake the main branch, and so I’ll never be able
to reorg out a transaction. However, if I am faster than
everyone else put together, it’s assured that
I will eventually catch up and overtake
the rest of the network, and then everyone will have
to reorg out onto mine. So here’s the main chain,
and then I branch off here, and I’m faster, so I overtake
them and then, that’s sort of– everyone’s stuck, right? Even if they want
to keep mining, I can just reorg them out
every time, because I’m bigger. This is called a 51% attack. It’s pretty bad. An attacker can rewrite
history, can undo transactions. They can’t forge
transactions, right? So they can’t necessarily
reorg out a message and replace it with a
message of their choosing. All they can do is,
you know, if they– but they can do that
with their own messages. So you need to have this
as part of an attack where they reorg their
own messages out. By default, when a
reorg occurs, so like– I can– go here. So by default, when
a reorg occurs, like say, these two blocks of
messages have been invalidated, software will attempt to
include all the transactions in these blocks into
the next blocks, right? It’s not– just because
this got reorged out, doesn’t mean it was invalid. It just means it didn’t
get into a block. And so we can try to include
this message later, as long as nothing in
here conflicts with it. So just doing a 51%
attack to reorg on its own doesn’t actually do
very much damage. However, it’s not too hard to
combine that with other attacks where whoever’s
doing this mining says, oh, I’ll pay someone
here, and then pay myself here. And then undo the payment
that they made to someone. So that’s a big, big con. 51% attacks. Not only is it very
disruptive to the system, it’s very hard to predict
when it will happen, since it’s anonymous. It could be the case that all
the people mining Bitcoin now are friends and
they’re a 51% group, and they could just get
together and say, hey, let’s reorg out these things. That said, there
is a cost to do so. Yeah? AUDIENCE: There seems to be
some requirement of momentum of messages to not able
to trick the system. So if you’re setting
up a new currency, it must be much, much
easier to work the chain. TADGE DRYJA: Yeah. I mean, if there’s very little
work being done in the system, it’s probably pretty cheap
to get a bunch of hardware and be 51% of that system. True. So like– and in
the case of Bitcoin, if you have to 2 the 72
work, well, every 10 minutes, that means if I want to be 51%,
I have to do 2 to the 71 work every 10 minutes, which– that’s a lot of work. And so you’re going to need
enormous amounts of resources to become a 51% attacker. There’s two ways this
attack can happen. Either some attacker
comes out of nowhere and says, OK, I’m
just going to build up an enormous amount
of attack power, or the existing
actors in the system go bad, which seems more
likely, where they’re like, OK, we’re already– you know, I’m 5%. He’s 10%. And she’s 20%. And they all get together
and try to do an attack. So both of those different
ways are possible. Yes? AUDIENCE: But [INAUDIBLE]
mining downsides? Like, we join some other pool? TADGE DRYJA: Wait. Wait. Sorry. Who does? AUDIENCE: Like, small players. TADGE DRYJA: Yes. AUDIENCE: So like,
[INAUDIBLE] of [INAUDIBLE].. If the miner pool
rollback– like for example, I’m in a miner [INAUDIBLE],,
and the software is malicious, so one of the players can
roll back simultaneously? TADGE DRYJA: Yeah. So pools, we haven’t mentioned
pools, but the idea– part of the con of you’re never
going to find a valid proof of work, is the way
they mitigate that, is people get together in pools
and they will prove partial work to each other, and there’s
one entity that’s then– controls a lot of
different miners and gives out partial rewards. So OK, there’s a thousand
different people mining, and one of them found the block,
but I’ll distribute that reward to all the thousand people
for all the work they’ve done. And so that does
concentrate power in that mining pool,
whoever’s running it. So that can also
be a big problem. Yeah. Because if you’re
doing it solo now. So solo mining is saying,
I’m just mining on my own. I’m going to try to find
a valid proof of work. That’s very difficult, because
of the amount of work needed. So many people pool together. So yeah, that’s another issue. Yeah? AUDIENCE: So [INAUDIBLE]. TADGE DRYJA: Yeah. There’s also protocols,
one called P2Pool, where you can have another
layer of block chain-y kind of messages, which allows you
to pool together resources without having a single
entity responsible for getting the rewards and
distributing them back up. I mean, I haven’t really
talked about the rewards. The Bitcoin-specific stuff
will be in next week, probably. But yeah. There’s all sorts of– this gets really
complicated and crazy. And like, pools, there’s
so many attacks on pools, and it’s a mess. OK. Last con. People hate it. And this is not a
quantitative, objective reason, but it is a problem. And people don’t
like proof of work. Some people are fine
with it, but a lot of– especially in academia. I’ve talked to a lot of people. They’re just like, ah,
this this is horrible. The whole point of sha256 is
you can’t find collisions, and you’ve designed an entire
system where all we’re doing is trying to find collisions in
this non-collidable system, and you’ve got giant
warehouses full– uses so much
electricity, and you’ve got giant warehouses full
of chips that are just doing this pointless thing. And it’s– you know, it offends
the sensibilities of many people. And it probably
is getting worse, because it keeps getting
bigger, and so a lot of people don’t like it. And I can understand that. When I first read
about this stuff, I was like, that’s kind of cool. That’s kind of stupid. And then I was like, oh, man
what if this really takes off? There’s just going to be so much
power usage and so many chips dedicated to kind of
a pointless thing. I would say that I acknowledge
this as a big problem, and I think the best analogy is
something like gold or silver, precious metal mining
where you could make very similar arguments,
that all these you know Spanish or Portuguese
people sailed over to South America 500
years ago, and it was sort of– it was horrible
and all these people were working in these
mines, and it’s a mess, just to get silver
or gold or whatever. And it’s like, why? Why are you doing this, right? Just to get some gold? So similarly, the bitcoin and
the proof of work in general has a lot of people
who don’t like it. And so that’s why there’s
a lot of research in, OK, can we have the same kind of
system, but without the work? Or alternatively, can we have
some kind of proof of work that’s also useful
for other things? So can we have some
kind of proof of work that cures cancer? And it’s like, well, I mean–
there’s actually, right, papers about protein
folding proof of work. And I haven’t seen
a ton– there’s one where you like find
sequences of prime numbers, and it sort of worked. It sort of has most of
the properties you want. And it’s like, OK,
but it’s like, well. You found five prime
numbers in a row. Like, eh. Yeah? AUDIENCE: The fundamental
problem with those [INAUDIBLE] that’s different from
this is generally the same amount of time to
verify as they do to generate, whereas the advantage of this
is it takes ages to generate, but it’s really quick to verify. TADGE DRYJA: Yeah. So that’s another– yeah. People want useful proof work. A lot of times with
useful proofs of work, it’s hard to tell that
it’s a valid proof, or there’s not as much of a gap. Like, the gap in Bitcoin
is enormous, right? O of n takes O of 1 to
verify, which is perfect. Yeah, you can’t get
better than that. So yeah, it’s hard to verify. There’s also– that also
applies to many different proofs of work. So one of the things
with 51% attacks is if, like you
were saying, if you want to build your own coin, if
you use the same proof of work algorithm as Bitcoin, you are
in a very risky situation, because you’ve started
your own new coin that– your own new message network
that very few people are using, and there’s very little work
being done in this network. And then there’s this
huge Bitcoin network. And as soon as they
see your network, they could easily
overpower it, right? One actor, one
person who’s mining, could become more than
51% of your network, just with the flip of a– pressing of a button. And so it’s very
dangerous to be running a very small network that
shares a proof of work with the larger network. And so most of the different
coins, when people say, hey, I’m going to make my own
derivative of Bitcoin or my own new coin, I’m going to
have a different proof of work. And so there’s all
sorts of different hash. Maybe I’ll use sha3
instead of sha256. OK. Or I’ll use some other hash
function, or some other usually iterative hash function,
like for password hashing, where you actually end up
hashing several million times. And the disadvantage
there, as well, is it can take quite a while
to verify the work. Not too much, but
noticeable, where if you’re running different
clients like Lightcoin, for example, it
uses a proof of work which takes thousands of
times longer to verify. Still fast enough, but some
of them are pretty heavy. So those are all the different–
you know, it gets pretty messy, and I’m– ask– probably James
and some other people are much more familiar with
all the horrible intricacies of proof of work. AUDIENCE: [INAUDIBLE]
if you back to the part about
[INAUDIBLE],, like back when Bitcoin was first made, it
just spawned the longest chain, by absolute number or blocks. TADGE DRYJA: Oh, yeah. Well, yeah. AUDIENCE: [INAUDIBLE] TADGE DRYJA: Yeah. So there’s one– wait. So I said the longest– so if you say the longest
chain is the valid one, I think I mostly said
most work, right? They’re not necessarily
the same, right? In this case, where we have
a fixed target, a fixed amount of work per
block, they are the same. But in the case of Bitcoin
and most of these networks, the target and the amount
of work required for a block can change with
that 2016 period. And so there are attacks
where you can say, well, I’m going to
make something that’s longer, but actually
has less work, because I’ve forged all these– You know, I go back in time. I pretend it took
me a long time, and I changed the
timestamps so it looks like it took a long time
and the difficulty decreased, but I actually have more
blocks, but less total work. And then I can have
some weird attacks where I reorg out things. So in the case of
Bitcoin, I think– yeah. Pretty early. AUDIENCE: Like,
version one point– TADGE DRYJA: Version one point– Version 0.1, it
actually just looked at number of blocks,
because it’s so much easier in the code to just
do number of blocks. Otherwise, you have to treat
all the hashes as big ints and figure out how
much work was done on each one, and
this annoying stuff. But that attack was thought of. I don’t think the
attack ever happened, but whoever designed
it was like, oh, wait. Yeah. Longest is not quite right. Has to be most work. And so they changed the code. OK. So proof of work. People hate it. Yeah, but the thing
is, it does work. It’s been working
for nine years. The blocks keep on coming. Not regularly, but over
the course of a day, about 144 will come out. In practice, it’s infeasible
to write old messages, right? There are all these
known attacks, but they’re very
costly, and either you have to do an enormous
amount of work and get all these
resources, or you have to have a lot of collusion
between the different actors. One nice part is that
in these systems, people are very adversarial, and
so they don’t want to collude, and they always are attacking
each other and hate each other. So that keeps the
system working. In practice, with Bitcoin,
there are very few block reorgs. This happens– I don’t know. When’s the last time an
actual reorg happened, instead of just two? Like, years. This just never happens. Most, one or two blocks. So you can have a one block
where two blocks come out at the same time and
point to the same parent, but that’s not a reorg, right? Because then your
software sees it, and it’s like, well, which
is going to be right? And then one of
them pulls ahead. So that happens
every couple days. It used to be more frequently,
but now it’s fairly infrequent. And like, two blocks
reorg sometimes. It has happened, but
it’s very rare now. So you can build
on these things. OK I’m almost done. We’ll do one last fun
fact, and then questions. OK, so fun facts. How to estimate the total
work done throughout history of the network. Well, you just look
at the lowest hash. This is kind of
counter-intuitive, like whoa, kind of thing. You can prove all
the work ever done in the history of the system
with just one hash, the lowest. Because probabilistically,
well, I’ve been doing work the whole time. Probabilistically,
I guess the way this works is that
whether we were all trying for the same
block or whether we’re trying for all these
different blocks, it doesn’t matter, right? We’re still doing attempts. And the best attempts will have
the most zeros in front of it. And that holds true for
whatever configuration, graph configuration,
whether there’s forks, whether there’s a single
chain, whether we all just work on the same thing and
never make any progress and just admit the best hash. So that’s kind of cool. You can just look
at a single hash and see all the work that’s
ever been done in the system. Kind of cool. With pretty crummy
accuracy, of course, but actually not too bad. And so there’s a paper
that’s pretty interesting. If you’re interested in it this
and want to look into the math, there’s a paper
called HyperLogLog that uses this fact for
something completely different, to count set
cardinalities and stuff, and it’s kind of
a cool math paper. But I think the Bitcoin
software does do that, and it’ll say best hash. And it’s in there, and
you can say, like, well, this is how much work
we all have done. There’s also some
papers in Bitcoin where you can try
to use these facts, like the lucky
blocks that happen to have much more
work than they needed, and you can look
back through history and give an abridged
version of history that still took as much– that
would still take about as much work to rewrite,
without providing all of the different
blocks and stuff. You can also prove close calls. So with pools and mining,
one way you can do it is you can prove that you were trying
but didn’t quite make it. So if the requirement is you
need 2 to the 40 leading zeros, and you get 2 to the
39, you can show. Like, hey. I got 2 to the 39 and I didn’t
quite make it, but I tried. And then people can
verify that work as well, and credit you for it. So the way a mining
pool works will be you give what’s
called shares, which is like close calls that
were not sufficient to meet the proof of work, but you keep
giving them every few seconds, or every few minutes. And then the central
pool operator says, OK, well, this person
did this many shares. This person did
this many shares. I have– the central operator
has a very good estimation of how much work different
people are doing, and so credits them. And said, OK, well, he’s
doing this much work. She’s doing this much work. And then when someone
actually finds the block, distributes the rewards from
the block proportionately to how much work
everyone’s been doing. So that’s trusted,
and not great. And there’s also a
bunch of attacks. The sort of sneakiest of
which is keep submitting shares, submitting close calls. But when you actually do
find a valid proof work, immediately forget about it. Drop it, and never tell anyone. The reason that’s a good attack
is fairly counter-intuitive, but it’s a good attack, even
though it seems like, well, you just found the block. Tell everyone. You get this reward. You get– It’s like no. No, I found a block. Throw it away. But oh, I got a close call. OK, keep telling the
central operator. What that does is
that really screws over the central operator,
who now thinks you’re doing a lot of work, but you
never find an actual block. And eventually, the central
operator will be like, this person is
really unlucky, huh? He’s found so many
close calls, but never seems to actually
get over the line and find a valid proof work. And so maybe they can
kick you off, eventually, but it’s not something
you can prove. You’re like, well,
I got unlucky. So there’s all sorts of things. There’s all sorts
of fun things you can do with the proof of work
and just these hash functions.

3 thoughts on “2. Proof of Work and Mining”

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