256位元加密到底有多安全？：英語精讀講義

In the main video on cryptocurrencies,

在關於加密貨幣的主影片中，

I made two references to situations

我兩次提到了某些情況：

where, in order to break a given piece of security, 文法

為了破解某項安全機制，

you would have to guess a specific string of 256 bits. 文法

你必須猜出一串特定的 256 位元字串。

One of these was in the context of digital signatures 片語搭配

其中一次是在數位簽章的背景下提到的，

and the other in the context of a cryptographic hash function.

另一次則是在密碼學雜湊函數的背景下。

For example, if you want to find a message 文法

舉個例子，如果你想找一則訊息，

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

它的 SHA-256 雜湊值是某串特定的 256 位元字串，

you have no better method than to just guess and check random messages. 文法

除了隨機盲猜並驗證訊息之外，你沒有更好的方法。

And this would require, on average, 片語搭配

這平均需要進行

2 to the 256 guesses.

2 的 256 次方次猜測。

Now, this is a number so far removed from anything 文法

那麼，這個數字與我們

that we ever deal with that it can be hard to appreciate its size.

平時接觸的任何事物都相差甚遠，以至於很難體會它有多大。

But let's give it a try. 片語搭配

但我們不妨試一試。

2 to the 256 is the same as 2 to the 32

2 的 256 次方等於 2 的 32 次方

multiplied by itself eight times.

連續自乘八次。

Now, what's nice about that split is that 2 to the 32 is 4 billion, 文法

這種拆分的好處在於，2 的 32 次方大約是 40 億，

which is at least a number we can think about,

這至少是一個我們能想像出的數字，

right? It's the kind of thing you might see in a headline.

對吧？這是你可能會在新聞標題裡看到的那種數字。

So, all we need to do is appreciate what 文法

所以，我們只需要去體會

multiplying 4 billion times itself

將 40 億與自身相乘

eight successive times really feels like.

連續乘八次到底是什麼感覺。

As many of you know,

你們之中的許多人都知道，

the GPU on your computer can let you run a whole bunch of computations 用詞

你電腦裡的 GPU 可以讓你

in parallel, incredibly quickly.

以極快的速度平行執行大量的運算。

So, if you were to specially program a GPU to run a cryptographic hash function over and over, 講解

因此，如果你專門為 GPU 寫程式，讓它不斷執行某個密碼學雜湊函數，

a really good one might be able to do a little less than a billion hashes per second.

一塊非常好的 GPU 每秒大概能進行略少於 10 億次的雜湊運算。

And let's say that you just take a bunch of those and 表達脈絡

假設你弄來一大堆這樣的 GPU，然後

cram your computer full of extra GPUs 片語搭配

把你的電腦塞滿額外的 GPU，

so that your computer can run 4 billion hashes per second.

讓你的電腦每秒能執行 40 億次雜湊運算。

So, the first 4 billion here is going to represent

那麼，這裡的第一個 40 億代表著

the number of hashes per second per computer.

每台電腦每秒鐘進行雜湊運算的次數。

Now, picture 4 billion of these GPU-packed computers.

現在，想像有 40 億台這種裝滿 GPU 的電腦。

For comparison, 表達脈絡

作為對比，

even though Google does not at all make their number of servers public,

儘管 Google 完全沒有公開他們的伺服器數量，

estimates have it somewhere in the single-digit millions. 文法

但據估計大約在幾百萬台左右。

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

實際上，大部分伺服器的效能遠不及我們想像中裝滿 GPU 的機器。

But let's say that Google replaced all of its millions of servers with a machine like this, 片語搭配

但假設 Google 把其數以百萬計的伺服器全換成這樣的機器，

then 4 billion machines would mean about a thousand copies of this souped-up Google. 用詞

那麼 40 億台機器就相當於大約 1000 個這樣升級版 Google 的規模。

Let's call that 1 kilo-Google worth of computing power. 講解

讓我們把這種算力稱為 1 kilo-Google（千個谷歌）。

There's about 7.3 billion people on Earth.

地球上大約有 73 億人口。

So, next, imagine giving a little over half of every individual on Earth

接下來，想像一下，把這種算力分給地球上一半多一點的人，

their own personal kilo-Google.

讓他們每個人都擁有自己的個人 kilo-Google。

Now, imagine 4 billion copies of this Earth.

現在，再想像有 40 億個這樣的地球。

For comparison,

作為對比，

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

銀河系大約有 1000 億到 4000 億顆恆星。

We don't really know,

我們其實並不確定，

but the estimates tend to be in that range. 片語搭配

但估計值往往都在這個範圍內。

So, this would be akin to a full 1% of every star in the galaxy 用詞

所以，這就類似於銀河系中整整 1% 的恆星

having a copy of Earth

都擁有一個地球的複製品，

where half the people on that Earth

而在那個地球上，有一半的人

have their own personal kilo-Google.

都擁有自己的個人 kilo-Google。

Next, try to imagine 4 billion copies of the Milky Way.

接下來，試著想像有 40 億個銀河系。

And we're going to call this

我們把這稱為

your giga-galactic supercomputer running about 2 to the 160 guesses every second.

你的十億星系級超級電腦，它每秒大約能進行 2 的 160 次方次猜測。

Now, 4 billion seconds,

接下來，是 40 億秒，

that's about 126.8 years.

那大約是 126.8 年。

4 billion of those,

再乘上 40 億個 126.8 年，

well, that's 507 billion years,

嗯，那是 5070 億年，

which is about 37 times the age of the universe.

這大約是宇宙年齡的 37 倍。

So, even if you were to have your GPU-packed kilo Google per person 文法

所以，即使你擁有這種「每人一個 kilo-Google 的滿載 GPU、

multi-planetary giga-galactic computer guessing numbers for 37 times the age of the universe,

跨越無數行星的十億星系級電腦」，讓它去猜數字，猜上宇宙年齡 37 倍的時間，

it would still only have a 1 in 4 billion chance 片語搭配

它仍然只有 40 億分之一的機會

of finding the correct guess.

能得出正確的猜測。

By the way,

順帶一提，

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

如今比特幣雜湊運算的現狀是，所有礦工加在一起，

guess and check at a rate of about 5 billion billion hashes per second. 片語搭配

其盲猜驗證的速率大約是每秒 500 億億（5 billion billion）次雜湊運算。

That corresponds to 1/3 of what I just described as a kilo-Google. 片語搭配

這相當於我剛才描述的一個 kilo-Google 算力的三分之一。

This is not because there are actually billions of GPU-packed machines out there, 文法

這並不是因為外面真的有幾十億台裝滿 GPU 的機器，

but because miners actually use something that's about a thousand times better than a GPU.

而是因為礦工們實際上使用的一種設備，比 GPU 要強上一千倍左右。

Application-specific integrated circuits. 文化背景

特殊應用積體電路（ASIC）。

These are pieces of hardware specifically designed for Bitcoin mining,

這些是專門為挖掘比特幣而設計的硬體，

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

除了執行大量 SHA-256 雜湊運算外什麼也做不了。

Turns out, there's a lot of efficiency gains to be had 講解

事實證明，這能帶來極大的效率提升——

when you throw out the need for general computation 片語動詞

當你拋開通用運算的需求，

and design your integrated circuits for one and only one task.

將你的積體電路設計成只專注於唯一一項任務時。

Also, on the topic of large powers of 2 表達脈絡

另外，關於這種大到

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

我個人都覺得難以理解的 2 的大次方問題，

this channel recently surpassed 2 to the 18th subscribers.

這個頻道最近訂閱數突破了 2 的 18 次方。

And to engage a little more with some sub-portion of those 2 to the 18 people,

為了能和這 2 的 18 次方人中的一部分有更多互動，

I'm going to do a Q&A session.

我打算辦一場 Q&A 問答環節。

I've left a link in the description to a Reddit thread

我在描述區裡留了一個 Reddit 貼文的連結，

where you can post questions and upvote the ones that you want to hear answers to. 文化背景

你可以在那裡發布問題，並為你想要聽到回答的問題按讚。

And probably in the next video or on Twitter or something like that, 語氣意圖

大概在下一個影片裡，或者在 Twitter 等平台上，

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

我會宣布我希望以何種形式來回答這些問題。

See you then.

到時候見。