In the war for information, will quantum computers defeat cryptographers? | Craig Costello

156,938 views ・ 2019-12-06

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00:00
Translator: Joseph Geni Reviewer: Camille Martínez
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譯者: Lilian Chiu 審譯者: Helen Chang
00:12
I'm in the business of safeguarding secrets,
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我的工作是保護秘密,
00:16
and this includes your secrets.
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包括你們的秘密。
00:19
Cryptographers are the first line of defense
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在一場已經激烈進行了 數世紀的戰爭中,
00:21
in an ongoing war that's been raging for centuries:
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密碼專家是第一道防線:
00:24
a war between code makers
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加密者和解密者之間的戰爭。
00:27
and code breakers.
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00:29
And this is a war on information.
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這是一場資訊戰。
00:32
The modern battlefield for information is digital.
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現代,資訊的戰場是數位的。
00:35
And it wages across your phones,
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戰場橫跨你的手機、
00:37
your computers
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你的電腦,和網路。
00:39
and the internet.
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00:41
Our job is to create systems that scramble your emails and credit card numbers,
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我們的工作是要設計系統來將 你的電子郵件和信用卡卡號、
你的電話及文字訊息變成亂碼——
00:46
your phone calls and text messages --
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00:48
and that includes those saucy selfies --
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也包括那些限制級的自拍——
00:50
(Laughter)
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(笑聲)
00:52
so that all of this information can only be descrambled
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我們要讓這些加密資訊
00:54
by the recipient that it's intended for.
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只能夠被指定的接收者解開。
00:58
Now, until very recently,
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一直到最近之前,
01:00
we thought we'd won this war for good.
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我們以為已經永久打贏了這場仗。
01:03
Right now, each of your smartphones is using encryption
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目前,各位的智慧手機 所用的加密技術
01:06
that we thought was unbreakable and that was going to remain that way.
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是我們認為無法破解, 且會一直無法破解的加密技術。
01:11
We were wrong,
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我們錯了,
01:13
because quantum computers are coming,
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因為量子電腦要出現了,
01:16
and they're going to change the game completely.
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它們會讓局勢完全改觀。
01:20
Throughout history, cryptography and code-breaking
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在整個歷史上,密碼學和破解密碼 一直在玩貓捉老鼠的遊戲。
01:22
has always been this game of cat and mouse.
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01:25
Back in the 1500s,
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十六世紀時,
01:27
Queen Mary of the Scots thought she was sending encrypted letters
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蘇格蘭的瑪莉一世女王認為 她所發出的加密信件
01:30
that only her soldiers could decipher.
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只有她的士兵能夠解開。
01:33
But Queen Elizabeth of England,
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但英格蘭的伊麗莎白 女王的解密者完全勝出。
01:35
she had code breakers that were all over it.
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01:38
They decrypted Mary's letters,
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他們破解了瑪莉的信件,
01:40
saw that she was attempting to assassinate Elizabeth
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發現她打算要刺殺伊麗莎白,
01:43
and, subsequently, they chopped Mary's head off.
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後來,他們便砍下了瑪莉一世的頭。
01:47
A few centuries later, in World War II,
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幾世紀後,在二次大戰期間,
01:50
the Nazis communicated using the Engima code,
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納粹使用恩尼格瑪密碼來溝通,
01:53
a much more complicated encryption scheme that they thought was unbreakable.
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他們認為這種更複雜的 加密方式是無法破解的。
01:58
But then good old Alan Turing,
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但,接著,好樣的艾倫圖靈,
02:00
the same guy who invented what we now call the modern computer,
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也就是發明了現代 電腦的那個傢伙,
02:03
he built a machine and used it to break Enigma.
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他打造了一台機器 來破解恩尼格瑪密碼。
02:06
He deciphered the German messages
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他破解了德國人的訊息,協助 阻止了希特勒和他的納粹德國。
02:08
and helped to bring Hitler and his Third Reich to a halt.
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02:11
And so the story has gone throughout the centuries.
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所以,這個故事 已經進行了數個世紀。
02:14
Cryptographers improve their encryption,
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密碼學家改進他們的加密方式,
02:17
and then code breakers fight back and they find a way to break it.
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接著,破解密碼的人又反擊, 找出方式來破解。
02:20
This war's gone back and forth, and it's been pretty neck and neck.
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這場戰爭你來我往,競爭激烈。
02:25
That was until the 1970s,
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直到七○年代,
02:28
when some cryptographers made a huge breakthrough.
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一些密碼學家有了重大的突破。
02:31
They discovered an extremely powerful way to do encryption
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他們發現了一種 極強大的加密方式,
02:35
called "public-key cryptography."
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叫做「公開金鑰密碼學」。
02:37
Unlike all of the prior methods used throughout history, it doesn't require
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和過去使用過的所有方法不同,
打算交換機密資訊的雙方 不用事前交換秘密金鑰。
02:42
that the two parties that want to send each other confidential information
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02:45
have exchanged the secret key beforehand.
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02:48
The magic of public-key cryptography is that it allows us to connect securely
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公開金鑰密碼學的美好之處就在於
它讓我們能夠和世界上 任何一個人進行安全的連結,
02:52
with anyone in the world,
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02:55
whether we've exchanged data before or not,
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不論我們以前是否交換過資料,
02:58
and to do it so fast that you and I don't even realize it's happening.
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且它的速度超快,快到你我 都還沒意識到之前就已經完工。
03:03
Whether you're texting your mate to catch up for a beer,
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不論是你傳訊息約好友出來喝酒,
03:06
or you're a bank that's transferring billions of dollars to another bank,
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或者你是一間銀行, 要轉數十億美金給另一家銀行,
03:10
modern encryption enables us to send data that can be secured
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現代加密方式讓我們能夠
在幾毫秒的時間內 就完成安全的資料傳輸。
03:13
in a matter of milliseconds.
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03:17
The brilliant idea that makes this magic possible,
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讓這種魔法成為可能的聰明想法
03:20
it relies on hard mathematical problems.
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要仰賴困難的數學問題。
03:23
Cryptographers are deeply interested in things that calculators can't do.
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密碼學家對於計算機 做不到的事都深感興趣。
03:29
For example, calculators can multiply any two numbers you like,
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比如,計算機可以 把任何兩個數字相乘,
03:32
no matter how big the size.
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不論數字多大。
03:35
But going back the other way --
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但換個方向——
03:37
starting with the product and then asking,
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先從乘積開始,接著問:
03:39
"Which two numbers multiply to give this one?" --
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「哪兩個數字相乘會得到 這個乘積?」——
03:41
that's actually a really hard problem.
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那就是困難的問題。
03:45
If I asked you to find which two-digit numbers multiply to give 851,
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若我請你找出哪兩個數字
相乘會得到 851,
即使有計算機,
03:51
even with a calculator,
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03:52
most people in this room would have a hard time finding the answer
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這裡大部分的人也很難 在這場演說結束前解出答案。
03:55
by the time I'm finished with this talk.
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03:57
And if I make the numbers a little larger,
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如果我用大一點的數字,
04:00
then there's no calculator on earth that can do this.
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地球上就沒有一台 計算機能找出答案來。
04:03
In fact, even the world's fastest supercomputer
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事實上,就連世界上 最快的超級電腦,
04:06
would take longer than the life age of the universe
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也要花上比宇宙生命更長的時間
04:09
to find the two numbers that multiply to give this one.
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才找得出是哪兩個數字 相乘得到這個乘積。
04:13
And this problem, called "integer factorization,"
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這個問題叫做 「整數的因數分解」,
04:16
is exactly what each of your smartphones and laptops is using right now
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各位現在的智慧手機和筆電
就是使用這個方法 來確保資料的安全性。
04:20
to keep your data secure.
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04:22
This is the basis of modern encryption.
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它是現代加密技術的基礎。
04:26
And the fact that all the computing power on the planet combined can't solve it,
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既然地球上所有的計算能力 結合起來都無法破解它,
04:30
that's the reason we cryptographers thought we'd found a way
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因此我們密碼學家便認為 我們已經找到方法
04:33
to stay ahead of the code breakers for good.
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可以永遠領先破解密碼者了。
04:37
Perhaps we got a little cocky
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也許我們太驕傲了,
04:39
because just when we thought the war was won,
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因為就在我們自以為 已經打了勝仗時,
04:42
a bunch of 20th-century physicists came to the party,
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一群二十世紀的 物理學家加入戰局,
04:45
and they revealed that the laws of the universe,
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他們點出,宇宙的定律,
04:47
the same laws that modern cryptography was built upon,
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也就是做為現代密碼學 基礎的那些定律,
04:51
they aren't as we thought they were.
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它們並非我們所想的那樣。
04:54
We thought that one object couldn't be in two places at the same time.
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我們認為一個物體不可能 同時出現在兩個地方。
04:58
It's not the case.
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並非如此。
04:59
We thought nothing can possibly spin clockwise and anticlockwise
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我們以為沒有任何東西能夠
同時順時鐘又逆時鐘轉動。
05:03
simultaneously.
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05:05
But that's incorrect.
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但那並不正確。
05:07
And we thought that two objects on opposite sides of the universe,
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我們以為在宇宙 相對兩邊的兩個物體,
05:10
light years away from each other,
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相距數光年之遠,
05:13
they can't possibly influence one another instantaneously.
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它們就不可能即時影響彼此。
05:17
We were wrong again.
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我們又錯了。
05:20
And isn't that always the way life seems to go?
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人生似乎總是這樣,不是嗎?
05:22
Just when you think you've got everything covered, your ducks in a row,
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就在你以為你什麼 都考慮了也準備好了,
卻出現一票物理學家, 點出宇宙的基本定律
05:26
a bunch of physicists come along
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05:27
and reveal that the fundamental laws of the universe are completely different
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和你所想的完全不一樣?
這把一切都搞砸了。
05:31
to what you thought?
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05:32
(Laughter)
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(笑聲)
05:33
And it screws everything up.
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05:34
See, in the teeny tiny subatomic realm,
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在非常微小的次原子領域中,
05:39
at the level of electrons and protons,
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在電子和光子的層級上,
05:42
the classical laws of physics,
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我們知道且喜愛的物理標準定律,
05:44
the ones that we all know and love,
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05:46
they go out the window.
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都可以丟掉了。
05:48
And it's here that the laws of quantum mechanics kick in.
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這就要談到量子力學的定律了。
05:51
In quantum mechanics,
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在量子力學中,
05:52
an electron can be spinning clockwise and anticlockwise at the same time,
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電子可以同時順時鐘 和逆時鐘轉動,
05:57
and a proton can be in two places at once.
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光子可以同時位在兩個地方。
06:01
It sounds like science fiction,
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聽起來很科幻,
06:04
but that's only because the crazy quantum nature of our universe,
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但那只是因為我們的宇宙 有著很瘋狂的量子特性,
06:08
it hides itself from us.
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這特性隱藏著沒被我們發現。
06:10
And it stayed hidden from us until the 20th century.
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一直藏到二十世紀才被我們發現。
06:15
But now that we've seen it, the whole world is in an arms race
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但現在我們知道了, 全世界都加入軍備競賽,
06:19
to try to build a quantum computer --
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比賽建造量子電腦——
06:22
a computer that can harness the power of this weird and wacky quantum behavior.
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量子電腦可以利用 這種怪異量子行為的力量。
06:28
These things are so revolutionary
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這種電腦非常具有革命性
06:30
and so powerful
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且非常強大,
06:32
that they'll make today's fastest supercomputer
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厲害到會讓現今最快的超級電腦
06:35
look useless in comparison.
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相較之下都變得很沒用。
06:37
In fact, for certain problems that are of great interest to us,
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事實上,針對我們 很感興趣的某些問題,
06:41
today's fastest supercomputer is closer to an abacus
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現今最快的超級電腦還比較 接近算盤,而非量子電腦。
06:44
than to a quantum computer.
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06:45
That's right, I'm talking about those little wooden things with the beads.
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是的,算盤就是那些 有珠子在上頭的木製品。
06:50
Quantum computers can simulate chemical and biological processes
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量子電腦能模擬化學和生物過程,
06:54
that are far beyond the reach of our classical computers.
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遠超過我們的標準電腦 能做到的程度。
06:58
And as such, they promise to help us solve some of our planet's biggest problems.
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因此,量子電腦保證 能協助我們解決
地球上一些最大的問題。
07:05
They're going to help us combat global hunger;
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它們可以協助我們對抗全球飢荒,
07:09
to tackle climate change;
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處理氣候變遷,
07:11
to find cures for diseases and pandemics for which we've so far been unsuccessful;
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針對我們目前沒輒的 疾病和流行病找出解藥,
07:16
to create superhuman artificial intelligence;
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創造出超人類的人工智慧,
07:20
and perhaps even more important than all of those things,
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還有,可能比上述這些都更重要的是
07:22
they're going to help us understand the very nature of our universe.
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能協助我們了解宇宙的本質。
07:28
But with this incredible potential
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但,這麼驚人的潛能
07:31
comes an incredible risk.
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也伴隨著極大的風險。
07:34
Remember those big numbers I talked about earlier?
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還記得我先前談到的那些大數字嗎?
07:38
I'm not talking about 851.
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我指的不是 851。
07:40
In fact, if anyone in here has been distracted
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事實上,如果在座有人分心 去試著找出那些因數,
07:42
trying to find those factors,
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07:43
I'm going to put you out of your misery and tell you that it's 23 times 37.
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我來幫你從痛苦中解脫, 答案是 23 乘以 37。
07:47
(Laughter)
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(笑聲)
07:48
I'm talking about the much bigger number that followed it.
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我指的是在 857 之後 更大更大的那個數字。
07:52
While today's fastest supercomputer couldn't find those factors
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雖然現今最快的超級電腦 花上宇宙一生的時間
07:55
in the life age of the universe,
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也無法找出那些因數,
07:58
a quantum computer could easily factorize numbers
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但量子電腦能夠將 比那個數字更大許多的數字
08:01
way, way bigger than that one.
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輕易拆解成因數。
08:03
Quantum computers will break all of the encryption currently used
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量子電腦能破解目前用來保護你我
08:07
to protect you and I from hackers.
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抵禦駭客的所有加密技術。
08:09
And they'll do it easily.
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且輕輕鬆鬆就能辦到。
08:12
Let me put it this way:
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讓我這麼說:
08:13
if quantum computing was a spear,
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如果量子計算是一支長矛,
08:16
then modern encryption,
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那現代的加密系統,
08:18
the same unbreakable system that's protected us for decades,
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也就是數十年都沒被破解, 一直在保護我們的系統,
08:21
it would be like a shield made of tissue paper.
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它就像是用衛生紙做的盾牌。
08:25
Anyone with access to a quantum computer will have the master key
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任何人只要能夠使用量子電腦, 就等於拿到一把萬能鑰匙,
08:29
to unlock anything they like in our digital world.
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在數位世界,他們想要 解鎖什麼就能解鎖什麼。
08:33
They could steal money from banks
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他們能從銀行偷錢,
08:35
and control economies.
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控制經濟,
08:37
They could power off hospitals or launch nukes.
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能讓醫院斷電或者發射核彈,
08:40
Or they could just sit back and watch all of us on our webcams
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還可以只是坐著,透過網路攝影機
08:43
without any of us knowing that this is happening.
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監視我們,不會被我們知道。
08:49
Now, the fundamental unit of information on all of the computers we're used to,
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在我們現在所使用的電腦上,
像這台電腦上,資訊的基礎單位
08:53
like this one,
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08:54
it's called a "bit."
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叫做「位元」。
08:56
A single bit can be one of two states:
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單一個位元可能有兩種狀態:
08:58
it can be a zero or it can be a one.
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它可能是零或一。
09:02
When I FaceTime my mum from the other side of the world --
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我媽在世界的另一端, 當我和她視訊通話時,
09:05
and she's going to kill me for having this slide --
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她看到這張投影片一定會殺了我——
09:08
(Laughter)
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(笑聲)
09:09
we're actually just sending each other long sequences of zeroes and ones
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我們其實只是發送一串 又一串的零和一給彼此,
09:13
that bounce from computer to computer, from satellite to satellite,
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它們會在電腦及衛星間彈來彈去,
09:16
transmitting our data at a rapid pace.
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快速傳輸我們的資料。
09:18
Bits are certainly very useful.
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位元非常有用,無庸置疑。
09:20
In fact, anything we currently do with technology
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事實上,我們目前 用科技所做的任何事,
09:23
is indebted to the usefulness of bits.
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都受惠於這些好用的位元。
09:26
But we're starting to realize
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但,我們開始了解到位元很不擅長
09:28
that bits are really poor at simulating complex molecules and particles.
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模擬複雜的分子和粒子。
09:33
And this is because, in some sense,
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原因是因為,在某種意義上,
09:35
subatomic processes can be doing two or more opposing things
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次原子過程可以同時進行 兩件以上相反的事情,
09:38
at the same time
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09:39
as they follow these bizarre rules of quantum mechanics.
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因為它們遵循的是 這些怪異的量子力學規則。
09:43
So, late last century,
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所以,上個世紀末,
09:44
some really brainy physicists had this ingenious idea:
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一些非常聰明的物理學家 想出了一個天才點子:
09:48
to instead build computers that are founded
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改用量子力學的原則來建造電腦。
09:50
on the principles of quantum mechanics.
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09:54
Now, the fundamental unit of information of a quantum computer,
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在量子電腦上,資訊的基礎單位
09:57
it's called a "qubit."
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叫做「量子位」。
09:59
It stands for "quantum bit."
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是「量子位元」的簡稱。
10:02
Instead of having just two states, like zero or one,
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量子位不只有零和一兩個狀態,
10:06
a qubit can be an infinite number of states.
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它可以有無限多個狀態。
10:09
And this corresponds to it being some combination of both zero and one
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因為它可以同時是零和一的組合,
10:13
at the same time,
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10:15
a phenomenon that we call "superposition."
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這種現象被我們稱為「疊加」。
10:18
And when we have two qubits in superposition,
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當有兩個量子位疊加時,
10:21
we're actually working across all four combinations
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我們其實是在處理全部四種組合:
10:23
of zero-zero, zero-one, one-zero and one-one.
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零和零、零和一、 一和零、一和一。
10:26
With three qubits,
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有三個量子位時,
10:28
we're working in superposition across eight combinations,
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我們就有八種組合的疊加,
10:31
and so on.
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以此類推。
10:33
Each time we add a single qubit, we double the number of combinations
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每當我們增加一個量子位,
我們同時能用的
10:37
that we can work with in superposition
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疊加組合數目就會加倍。
10:40
at the same time.
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10:43
And so when we scale up to work with many qubits,
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所以,當我們擴大規模, 使用許多量子位時,
10:45
we can work with an exponential number of combinations
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我們同時能夠用的組合數目
會是指數增加。
10:49
at the same time.
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10:51
And this just hints at where the power of quantum computing is coming from.
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從這點就可以略知 量子電腦的能力從何而來。
10:56
Now, in modern encryption,
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在現代的加密技術中,
10:59
our secret keys, like the two factors of that larger number,
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我們的秘密金鑰,比如 那個大數字的兩個因數,
11:03
they're just long sequences of zeroes and ones.
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它們都是長串的零和一。
11:06
To find them,
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要找出它們,標準的電腦
11:07
a classical computer must go through every single combination,
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必須把所有可能組合 一組一組試過,
11:12
one after the other,
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11:13
until it finds the one that works and breaks our encryption.
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直到找到行得通的組合, 就破解了我們的加密。
11:18
But on a quantum computer,
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但在量子電腦上,
11:20
with enough qubits in superposition,
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只要有足夠的疊加量子位,
11:25
information can be extracted from all combinations at the same time.
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就可以同時從 所有組合來擷取資訊。
11:30
In very few steps,
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只要少數幾個步驟,
11:32
a quantum computer can brush aside all of the incorrect combinations,
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量子電腦就能把所有 不正確的組合排除,
11:36
home in on the correct one
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鎖定正確的組合,
11:37
and then unlock our treasured secrets.
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接著揭露我們寶貴的秘密。
11:44
Now, at the crazy quantum level,
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在瘋狂的量子層級上,
11:47
something truly incredible is happening here.
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發生的現象非常不可思議。
11:52
The conventional wisdom held by many leading physicists --
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許多頂尖物理學家 所擁有的傳統知識是——
11:56
and you've got to stay with me on this one --
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你們要專心聽我說,別分神——
11:58
is that each combination is actually examined by its very own quantum computer
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每種組合其實是 在它自己的平行宇宙中,
由它自己的量子電腦來檢查。
12:03
inside its very own parallel universe.
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12:07
Each of these combinations, they add up like waves in a pool of water.
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每個組合加在一起, 就像一池水中的水波。
12:12
The combinations that are wrong,
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錯誤的組合
12:14
they cancel each other out.
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會彼此抵消。
12:16
And the combinations that are right,
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正確的組合
12:17
they reinforce and amplify each other.
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會強化、放大彼此。
12:20
So at the end of the quantum computing program,
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所以,在量子計算程式結束時,
12:22
all that's left is the correct answer,
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留下來的就只有正確答案,
12:25
that we can then observe here in this universe.
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我們在這個宇宙中 就可以觀察到這個答案。
12:29
Now, if that doesn't make complete sense to you, don't stress.
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如果你覺得還無法 完全理解,別擔心。
12:32
(Laughter)
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(笑聲)
12:33
You're in good company.
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你不孤單。
12:36
Niels Bohr, one of the pioneers of this field,
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尼爾斯 · 波耳是 這個領域的先鋒之一,
12:39
he once said that anyone who could contemplate quantum mechanics
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他曾經說過,如果有人 在深入思考量子力學時
12:42
without being profoundly shocked,
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沒被深深驚嚇到,
12:44
they haven't understood it.
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那他就還沒搞懂量子力學。
12:46
(Laughter)
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(笑聲)
12:47
But you get an idea of what we're up against,
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2155
但你們多少了解了我們在對抗什麼,
12:49
and why it's now up to us cryptographers
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及為什麼現在要靠 我們密碼學家來加把勁了。
12:52
to really step it up.
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12:54
And we have to do it fast,
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且我們的動作要快,
12:56
because quantum computers,
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因為量子電腦
12:58
they already exist in labs all over the world.
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已經存在於世界各地的實驗室中。
13:03
Fortunately, at this minute,
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幸運的是,此刻,
13:05
they only exist at a relatively small scale,
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它們相對還算小規模的電腦,
13:07
still too small to break our much larger cryptographic keys.
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還太小到無法破解 我們更大的密碼學金鑰。
13:12
But we might not be safe for long.
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但安全的日子可能不長了。
13:14
Some folks believe that secret government agencies
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有些人相信,政府有些秘密機構 已經建立出了夠大的量子電腦,
13:17
have already built a big enough one,
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13:19
and they just haven't told anyone yet.
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只是還沒有告訴任何人。
13:21
Some pundits say they're more like 10 years off.
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有些行家說大概還有十年的距離。
13:24
Some people say it's more like 30.
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有些人說比較可能是三十年。
你們可能想,倘若 量子電腦十年後才會出現,
13:27
You might think that if quantum computers are 10 years away,
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我們密碼學家當然有足夠的時間 想辦法及時保護網路的安全。
13:30
surely that's enough time for us cryptographers to figure it out
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13:33
and to secure the internet in time.
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13:34
But unfortunately, it's not that easy.
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但,不幸的是,沒那麼簡單。
13:37
Even if we ignore the many years that it takes
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即使我們忽略 還要花許多年的時間
13:39
to standardize and deploy and then roll out new encryption technology,
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才能將一項新的加密技術 標準化、部署、再推出,
13:43
in some ways we may already be too late.
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在某些層面上我們已經太遲了。
13:47
Smart digital criminals and government agencies
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聰明的數位罪犯和政府機構
13:50
may already be storing our most sensitive encrypted data
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可能因為預期將來會是量子的未來,
13:54
in anticipation for the quantum future ahead.
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而已經在儲存我們 最敏感的加密資料。
13:59
The messages of foreign leaders,
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來自外國領袖、
14:02
of war generals
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戰爭指揮官
14:04
or of individuals who question power,
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2162
或執疑當權者的人的訊息
14:07
they're encrypted for now.
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目前有加密。
14:10
But as soon as the day comes
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1601
但隨時間過去,
14:12
that someone gets their hands on a quantum computer,
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有人取得了量子電腦,
14:14
they can retroactively break anything from the past.
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就能追溯回去,破解 過去的任何加密資訊。
14:19
In certain government and financial sectors
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在某些政府和財務部門 或在軍事組織中,
14:21
or in military organizations,
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14:22
sensitive data has got to remain classified for 25 years.
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敏感的資料被列為 二十五年之久的機密。
14:26
So if a quantum computer really will exist in 10 years,
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3180
如果十年後真的會出現量子電腦,
14:29
then these guys are already 15 years too late
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那麼,這些人也遲了十五年 才開始想把加密做到能對付量子,
14:31
to quantum-proof their encryption.
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14:34
So while many scientists around the world
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雖然全世界許多科學家
14:36
are racing to try to build a quantum computer,
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在比賽誰先建造出量子電腦,
14:39
us cryptographers are urgently looking to reinvent encryption
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我們密碼學家則是急著 想辦法重新發明加密技術,
14:43
to protect us long before that day comes.
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在那天到來之前就先保護好我們。
14:46
We're looking for new, hard mathematical problems.
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我們在尋找新的、困難的數學問題。
14:50
We're looking for problems that, just like factorization,
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我們在尋找類似 因數拆解這樣的問題,
14:53
can be used on our smartphones and on our laptops today.
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可以用在我們現今的 智慧手機和筆電上。
14:57
But unlike factorization, we need these problems to be so hard
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但,我們需要的問題 遠比因數拆解更困難,
15:01
that they're even unbreakable with a quantum computer.
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難到用量子電腦也無法破解。
15:06
In recent years, we've been digging around a much wider realm of mathematics
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這幾年,我們在 更廣泛的數學領域中
15:09
to look for such problems.
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試圖找到這樣的問題。
15:12
We've been looking at numbers and objects
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我們在研究的那些數字和物體 奇特、抽象的程度遠超過
15:14
that are far more exotic and far more abstract
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2168
你我習慣的那些, 比如我們計算機上的那些。
15:16
than the ones that you and I are used to,
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1956
15:18
like the ones on our calculators.
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1597
15:19
And we believe we've found some geometric problems
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我們相信,我們已經找到了 一些可能可以用的幾何問題。
15:22
that just might do the trick.
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1399
15:24
Now, unlike those two- and three-dimensional geometric problems
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不像我們在高中時用筆和座標紙
15:27
that we used to have to try to solve with pen and graph paper in high school,
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就能解開的二維、三維幾何問題,
15:31
most of these problems are defined in well over 500 dimensions.
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我們找的問題大部分都定義在 至少五百維的空間上。
15:36
So not only are they a little hard to depict and solve on graph paper,
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因此不僅難以畫座標紙 來解出這些問題,
15:40
but we believe they're even out of the reach of a quantum computer.
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我們相信連量子電腦也拿它們沒輒。
15:45
So though it's early days,
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所以,雖然現在還在初期, 我們把希望放在這裡,
15:47
it's here that we are putting our hope as we try to secure our digital world
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在我們的數位世界邁向量子未來 之際,努力讓它還能保有安全性。
15:51
moving into its quantum future.
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15:55
Just like all of the other scientists,
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和所有其他科學家一樣,
15:57
we cryptographers are tremendously excited
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2163
我們密碼學家對於 有可能見到量子電腦
15:59
at the potential of living in a world alongside quantum computers.
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出現在我們的世界上, 感到非常興奮。
16:04
They could be such a force for good.
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它們可能成為強大的正義力量。
16:09
But no matter what technological future we live in,
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但,不論我們的科技未來 是什麼樣子的,
16:16
our secrets will always be a part of our humanity.
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我們的秘密將永遠是人類的一部分。
16:22
And that is worth protecting.
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那是值得去保護的。
16:25
Thanks.
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謝謝。
16:26
(Applause)
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(掌聲)
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