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#### 256位加密有多安全？

How secure is 256 bit security?

In the main video on cryptocurrencies,

I made two references to situations where, in

order to break a given piece of security,

you would have to guess a specific string of

256 bits. One of these was in the

context of digital signatures and the other in the

context of a cryptographic hash function.

For example, if you want to find a message whose

SHA-256 hash is some specific string of 256 bits,

you have no better method than to just guess and check

random messages, and this would require, on average, 2^256 guesses.

Now

this is a number so far removed from

anything that we ever deal with that it

can be hard to appreciate its size.

But let’s give it a try.
2^256也就是2
2^256 is the same as 2^32,
^32和自己相乘8次
multiplied by itself 8 times.

Now what’s nice about that split is that 2^32 is 4 billion.

Which is at least a number we can think about, right?

It’s the kind of thing you might see in a headline.

So what we need to do is appreciate what multiplying
40亿连续相乘8次是怎样的概念
4 billion times itself 8 successive times really feels like.

As many of you know the GPU on

your computer can let you run a whole

bunch of computations in parallel incredibly quickly.

So if you were to specially program a

GPU to run a cryptographic hash function over and over, a

really good one might be able to do a little less

than a billion hashes per second.

Let’s say that you just take a bunch

of those and cram your computer full of extra GPUs so that your computer

can run 4 billion hashes per second.

So the first 4 billion here is going

to represent the number of hashes per second per computer. Now,

picture four billion of these GPU-packed computers.

For comparison, even though Google does not

at all make their number of servers public,

estimates have it somewhere in the single-digit millions.

In reality, most

of those servers are going to be much less powerful than our imagined GPU-packed machine.

But let’s say Google replaced all of its millions

of servers with a machine like this.

Then four billion machines would mean about a thousand copies of this souped-up Google.

Let’s call that one KiloGoogle worth of computing power.

billion people on Earth,

so next imagine giving a little over half of every individual on Earth their own

imagine four billion copies of this Earth.

For comparison, the Milky Way has somewhere between 100 and 400 billion stars.

We don’t really know,

but the estimates tend to be in that range.

So this would be akin to a full

1% of every star in the galaxy,

having a copy of Earth,

where half the people on that Earth have their own personal KiloGoogle. Next,

try to imagine 4 billion copies of the Milky Way.

And we’re going to call this your GigaGalactic Super Computer,

running about 2^160 guesses every second.
40亿秒
Now four billion seconds?

Four billion of those?

Well,

That’s 507 billion years,

which is about 37 times the age of the universe.

per person multiplanetary GigaGalactic computer guessing numbers for

37 times the age of the universe,

it would still only have a 1 in 4 billion chance

of finding the correct guess.

By the way,

the state of Bitcoin hashing these days is that all of the miners put together

guess-and-check at a rate of about five billion billion hashes per second.

That corresponds to one-third of what I just described as a KiloGoogle.

This is not because there are actually billions

of GPU-packed machines out there, but because miners actually use something

that’s about a thousand times better than a GPU –

Application Specific Integrated Circuits. These are pieces of hardware

specifically designed for Bitcoin mining,

for running a bunch of SHA-256 hashes and nothing else.

Turns out, there’s a lot of

efficiency gains to be had when you throw

out the need for general computation, and

on the topic of large powers of two

that I personally find it hard to get my mind around,

this channel recently surpassed 2^18 subscribers, and

to engage a little more with some sub-portion

of those 2^18 people,

I’m going to do a Q&A session.

I’ve left a link in the description to

a Reddit thread where you can post questions and

upload the ones you want to hear

answers to, and probably in the next video or

on Twitter or something like that,

I’ll announce the format in which I’d like to give answers.

See you then.