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The math problem that could break the internet

The math problem that could break the internet

Released Wednesday, 24th January 2024
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The math problem that could break the internet

The math problem that could break the internet

The math problem that could break the internet

The math problem that could break the internet

Wednesday, 24th January 2024
Good episode? Give it some love!
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0:00

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for the marathon at everywomensmarathon.com.

1:10

2024 is shaping up to be a huge

1:12

year for the internet, especially because

1:14

NIST, the National Institute of

1:17

Standards and Technology, recently

1:19

announced that new algorithms they've been working

1:21

on to keep the internet secure are

1:24

going to be ready later this year. There's

1:26

no telling just how successful these algorithms are

1:28

going to be, but NIST hopes

1:30

that they'll be able to protect the internet

1:32

for the future. So we wanted

1:34

to share an episode from our reporters, Meredith

1:36

Hadnaught and Brian Resnick, about

1:38

why the internet is so vulnerable to

1:41

breaking in the first place and

1:43

why it's so hard to keep it together.

1:46

Here's Meredith and Brian. Hey,

1:48

Brian. Hey, Meredith. I want you

1:50

to imagine something with me, if you will. Okay.

1:53

All right. So imagine one day you

1:56

wake up. Okay. And the

1:58

internet is broken. Oh,

2:02

so hackers are getting into your bank

2:04

accounts your to your Twitter accounts your

2:06

work emails Instead of

2:08

loading banner ads your

2:10

computer would just like start loading viruses.

2:13

Okay, great So

2:15

they have all of my money my identity.

2:17

Yep. All that

2:19

my secret exactly Is

2:22

this the day I just put down the

2:24

phone and then walk away? Just

2:26

walk away. I'm just gonna walk away.

2:28

Finally fulfill your destiny as a mountain man.

2:31

This is not working life on the internet

2:34

What you just described sounds so

2:36

broken I wouldn't I

2:38

don't know if there's a tech support that

2:41

could fix it, right? So this

2:43

doomsday scenario, this is the

2:45

internet without encryption What

2:48

is encryption? Yes largely

2:51

math. Okay Encryption

2:53

is this cloak that wraps

2:55

your private information And

2:58

so that anybody that's seeing that

3:00

information it just looks like random static.

3:02

It just looks like gibberish And

3:05

so encryption is the thing that's really Protecting

3:08

your private information as it travels

3:10

through the web So

3:13

you don't see my social security

3:15

number you see this cloak of

3:17

gibberish, right? If somebody intercepted that and

3:19

tried to read that information all they

3:21

would see was randomness. So it sounds

3:24

like I Use

3:26

encryption all the time all the time Our

3:31

everyday lives on the internet

3:33

they're built on an elaborate

3:35

and largely invisible system of

3:37

encryption Google says that 95%

3:40

of the traffic that comes through their site is encrypted

3:42

in some way Because there's this

3:45

whole system of certificates and digital

3:47

signatures that are all based on

3:49

encryption that Tell

3:51

you that when you go to

3:54

Amazon that that's actually Amazon.

3:56

Hmm So

3:58

Encryption is just a thought. The heart

4:00

of building trust on the internet.

4:02

So I know the website. I'm

4:04

going to have not been intercepted

4:06

by somebody's life and I can

4:09

send my private information to be

4:11

ball just knowing. It's for their

4:13

eyes only. Exactly exactly So I

4:15

like all this and group Sam

4:17

as you described it to me

4:19

it sounds nice right? I get

4:21

to do a lot of cool

4:23

stuff with that is it is

4:25

it in danger. So that's

4:28

what I would love to tell you about

4:30

until they sell. Okay, How the

4:32

internet was built on encryption and

4:34

how am I come tumbling down.

4:52

When. I started work in cryptography. Almost all

4:54

my colleagues told me I was crazy and

4:57

they were what they were, right? Mighty.

4:59

How Men is A professor at

5:01

Stanford University Have been for got

5:03

over fifty years. Fifty. Years

5:05

ago, computers are these massive

5:08

plastic boxes with these etti

5:10

bitty little screams. And. They

5:12

were getting more and more intertwined for

5:14

their money. A

5:17

Pm were cutting edge technology and

5:19

Nineteen Sixty Nine and Nasdaq, the

5:21

world's first electronic stock market opened

5:23

in Nineteen Seventy One. I remember

5:26

saying I could foresee the day

5:28

when you might buy a loaf

5:30

of bread with an electronic funds

5:32

transfer. A good as a debit cards as we

5:34

didn't have them. It was a

5:37

new age with a new relationship to

5:39

what money was and what it represented.

5:42

Nixon, South America off the gold

5:44

standard in this time to Nineteen

5:46

Seventy One. So many was getting

5:48

more abstract, more electronic. Safe

5:51

set protected physical bills. And

5:54

gold bars where the security of the

5:56

past. We needed a safe

5:58

to protect the information. The money

6:00

That electronic communications that were quickly

6:02

becoming more and more relevant and

6:04

I said what happens if someone?

6:06

maybe they can steal billions of

6:08

dollars, but they just crashed the

6:10

system so nobody knows how. Much when

6:12

he they've gotten their bank account. What are the

6:15

what happens that. And. So I

6:17

saw the need for encryption. Marty. Was

6:19

on a quest to bring digital

6:21

encryption to the masses. Encryption

6:23

that could be used by the public.

6:26

Used commercially to protect electronic

6:28

messages starting to send money

6:30

back. In theory that Marty

6:32

had a problem says at

6:35

this point encryption was dominated

6:37

by the government. Almost

6:39

no one outside the military and really

6:42

knew how it works. Any

6:44

research into the underlying principles

6:46

of encryption. Was automatically

6:49

classified. And considered. A

6:51

potential threat said National Security.

6:54

Agencies like the An Essay

6:56

had top secret inception departments.

6:58

Hoovering up all the best mathematicians in

7:01

the country, But. If he

7:03

wanted to study encryption. Out in the

7:05

open it was a lonely place to be.

7:08

The field was almost nonexistent. Most

7:10

of it was in the classified

7:12

literature. I got information theory conferences

7:14

and still it often be people

7:16

with name tags that said am.

7:19

At. See what was that? Department

7:21

of Defense was an essay and everyone who

7:23

said U.S. government was with the CIA so

7:26

wasn't hard to figure out who was. Might

7:28

his They all warned him off the

7:31

told on the he had no chance

7:33

going up against a juggernaut like the

7:35

an essay friends told. Me: How can

7:37

you have to discover anything that enter say

7:40

doesn't already know They have a decades head

7:42

start and said i don't care what they

7:44

know is not available for commercial use if

7:46

I developed that it is. In.

7:48

Order to bring encryption to the public. Marty.

7:51

Needed to reinvent it basically in

7:53

the light of day. And.

7:55

He needed a team. With if

7:57

he showed up on their doorstep in the fall.

8:00

Nineteen Seventy Four and day he

8:02

was an itinerant. Cryptography is the

8:04

way describes himself. As a tiny

8:06

showed up at Marty Stuart step. This. Guy

8:08

went to see. He. Had

8:10

forged his own pass in Academia.

8:13

And. Not have a good student

8:15

with. Had spent years going

8:18

to universities and libraries and

8:20

Cunningham's laboratories trying to piece

8:22

together any unclassified information that

8:24

he could find on cryptography.

8:27

And he kept hitting the same dead ends

8:29

that Marty was having. Until

8:31

and Nineteen Seventy Four, the head of

8:34

the cryptography lab at a Bm. Told.

8:36

Where is that? I can't tell you

8:38

much. Rudra Secrecy order here, but you

8:40

won't have a look at my friend

8:43

Marty Helmand when you back at Stanford.

8:45

He subsequently we wish he hadn't said

8:47

that because Marty and I became a

8:50

big pain. The sample tourists. Witten.

8:52

Marty hit it off right away. Our.

8:55

Interaction in many ways ran the

8:57

opposite of a normal. Of.

9:00

Students. Graduate student professor relationship

9:02

I'll I describe as your I think

9:04

possibly I'm more imaginative than he has.

9:06

Certainly he's smarter than I am. I

9:09

really liked working with him, but he

9:11

didn't like anyone telling them what to

9:13

do. Mighty, in which

9:15

were totally seduced by cryptography.

9:18

I sometimes joke that there's i'm used to

9:20

sectors abuse of poetry. there's some use of

9:22

cryptography and she whispered meyer she whispered with

9:25

year She probably western lot of other people's

9:27

ears who just wrote it off as a

9:29

crazy dream. And they got

9:31

to works so it haphazardly putting together

9:34

other. Bits and pieces they had gathered from

9:36

them, he says. With

9:40

had been obsessing. For years about

9:42

how to use cryptography to

9:44

communicate remotely in a digital

9:46

world. We. Were moving into a

9:48

world where people would have intimate friendships

9:50

with people they never met in person.

9:54

And that cryptography was the only thing that

9:56

would give you any sort of privacy. Into

9:58

with this person. To clear

10:01

problems. I. Had these two problems

10:03

in the back of my mind. Your

10:06

one for ten years and one for five. Have

10:09

a hot back burner. So.

10:11

Imagine that you and I on it's

10:14

prize at least share information without ever

10:16

meeting in person and. We.

10:18

Said set up a safe for us to

10:20

that letters and and no one else could

10:22

read them. Those letters they would be private.

10:25

But. We both need sees to open

10:28

the safe door and we couldn't

10:30

share those keys without exchanging them

10:32

in person. This. Was

10:34

Whips first problem. How do you

10:36

share a secret? See? Remotely.

10:40

And if were just enough, send

10:42

him he's around. Had you make

10:44

sure that you're sending them to

10:46

the right person without ever meeting

10:48

them in person. Verifying.

10:51

Identities remotely. This. Was

10:53

with second problem. And. I

10:55

was trying to combine those two problems.

10:58

And. At some point. I

11:01

realized. That. That must be

11:03

possible. One

11:06

afternoon, and nineteen seventy six

11:08

witless noodling on these problems.

11:10

And he had a breakthrough. I. Understood

11:12

I had discovered something important. And

11:16

I went downstairs get myself with

11:18

Coca Cola and almost forgot it.

11:20

And on walking down the stairs I

11:23

fortunately remembers it again. and then a

11:25

walk down hill. To. Marti's house

11:27

to explain it to him. So.

11:30

Clinton, Back to that problem of you and I.

11:32

Train a share messages without ever

11:34

meeting in person. Lives idea was

11:36

something like. What? Has to face

11:39

had a mere thought and at. That

11:41

way you did some by any time

11:43

and drop off your letters in the

11:45

second set. you wouldn't need seas and

11:48

then I to come. By later open

11:50

the safe had my. Keys and read

11:52

your letters so encrypting putting

11:54

them information in the safe

11:57

is a different steps and

11:59

decrypting. taking the information out. Which

12:02

idea was to split the encryption

12:04

and the decryption? This

12:08

also solves the second problem of

12:10

identity because you know that that's

12:12

my safe and my mail slot.

12:15

I'm the only one with the keys to the safe and

12:18

so I'm the only one that can open

12:20

the door and take the information out. Having

12:23

the keys is a way of proving

12:25

my identity. Of

12:28

course you'd need your own safe and your

12:30

own mail slot where I could come by

12:32

anytime and drop off letters for you. But

12:35

then we would have a secure way

12:37

to exchange information. The

12:40

bottom line is if we both have safes

12:42

and we both have our own protected

12:45

personal keys we can trust

12:47

that we're talking to each other and

12:49

trust that we're talking privately without

12:52

ever having to meet in person. It

12:58

was a stunningly elegant idea. Something

13:01

they called public key cryptography.

13:03

Whit had come up with the idea of

13:06

public key cryptography but no way to do

13:08

it. Now Marty and Whit had

13:10

to figure out how to build these safes.

13:13

The trick was of course they couldn't build them

13:16

out of iron and steel they needed to build

13:18

them out of math. In

13:20

cryptography the safe isn't a physical

13:22

object. It's like a mathematical

13:25

cloak covering up

13:27

private information with random static.

13:30

Transforming understandable

13:32

and usable information into

13:36

incomprehensible useless

13:39

garbage. But it isn't just

13:41

about locking up information under

13:43

random static. You also

13:45

have to be able to easily unlock

13:47

that randomness with the key and

13:50

turn it back into readable

13:52

usable information. Marty

13:55

and Whit wanted to find the simplest

13:57

system that could fit that pattern and

14:00

They looked into a type of math

14:02

problem called One Way. Functions. One.

14:07

Way functions are math problems that.

14:10

Are designed to be easy to solve but take

14:12

a lot. Of time and energy

14:14

to reverse like. A

14:16

seven. Times. Thirteen I

14:18

could do seventy Two Hundred Ninety

14:20

Six Ninety One. I. Could do that my head

14:22

in a few seconds. But as you gave

14:25

me ninety one and asked me to

14:27

factored into to primes it takes longer

14:29

so multiplying as easy and that during

14:31

is hard. But if you

14:33

have one of the factors already, Than

14:35

you can easily get the other one so

14:38

that's the secret key, but not every one

14:40

way function can be made into a cryptographic

14:42

systems. Nano one way functions

14:44

are good at meeting encryption is,

14:46

but all inscriptions have a one

14:48

way function at their heart. And

14:51

for this also works these one. Way

14:54

functions need to be super hard to

14:56

solve without a key. So

14:58

tough that it's it's not even worth a

15:00

hacker's time to turn a. One.

15:06

Night it was probably one am. Mighty

15:08

was at his desk. For. The

15:10

pencil and paper wracking his brain, trying to

15:12

figure out a way. To bring with idea

15:14

of public key cryptography the life. I

15:17

was playing and I tried or new permutation

15:19

on what secret what's public was private and

15:21

all the sudden it came out. After

15:23

a few months of work, Marty and

15:26

with published their findings. They.

15:28

Put together everything that they had been thinking

15:30

about, The safe, the public

15:32

key cryptography, the one way

15:34

functions. Who. The first

15:37

line of they wrote. We. Stand today

15:39

on the brink of a revolution

15:41

in cryptography. And. Was

15:43

probably with. That's. That sounds more

15:45

like within me. The. With will with

15:47

is not. Above. Grandstanding.

15:50

And he's often right. I've

15:52

got that was right. For.

15:55

The first time in history there was

15:57

research that could make encryption available on

15:59

a. Marshall scale. And.

16:02

The Open Research. Community was thrilled.

16:04

For. enter say had a whole

16:06

nother reaction. The. An essay Was

16:09

not happy that they had lost their

16:11

monopoly on cryptography. There was actually a

16:13

fight and as a loosely speaking maybe

16:15

more than lucy speaking wanted to throw

16:17

me in jail. Marty and Widths

16:19

work threatened the whole way that the

16:21

an Essay did business. Of

16:23

all this cryptography research without my

16:26

open. Than. More foreign

16:28

governments can encrypt their information.

16:30

And. That made the and essays job

16:33

much harder or was telling. Foreign.

16:35

Entities How to protect their secrets are trying to

16:37

tell American Entities how to protect their is that

16:40

there's no way to do one without the other.

16:42

In. An essay Employee. Wrote a letter

16:44

to the journal that publish their work.

16:47

And accuse them of breaking the law. Specifically.

16:50

The international traffic and I'm

16:52

circulations. It's against the

16:55

law, obviously to export a jet fighter

16:57

plane, right? without it export license. It's

16:59

also. Against the law to exports the plants

17:01

that are makes a fighter. Because.

17:04

That can be used to make

17:06

it and the I tar the

17:08

international traffic an orange regulations to

17:10

find anything cryptographic as an employment

17:12

of war. And so by

17:15

publishing in international. Journals. How

17:17

to design good cryptographic systems. We

17:19

were right. We were exporting technical

17:21

specification odds on Implements of War

17:23

without an export license. Marty.

17:26

Immediately brought this accusation to the

17:28

General Counsel. At Stanford University.

17:31

Is. Unconstitutional because it was be violation

17:33

of freedom of the press and freedom

17:35

of speech. That was his legal opinions.

17:37

But he also warned me and I'll

17:40

never forget this. If I was prosecuted,

17:42

Sanford would defend me. but if I

17:44

was. Found. Guilty and all appeals were

17:46

exhausted. They couldn't go to jail for me. We're

17:49

in. Marty continues. There's bite

17:51

from robust, accessible encryption. And.

17:54

Mighty came to see himself as

17:56

a security officer for the public.

17:58

No one was representing. the public and

18:00

the public needed protecting and the group that you'd

18:02

expect to protect them, the part of the government

18:05

that should be doing that, wasn't doing it. So

18:07

I realized that's the role I

18:09

had assumed. The reaction from the

18:12

NSA sparked a nationwide debate about

18:14

the government threat to open publication

18:16

and who had the right to access

18:18

tools of privacy. Articles

18:20

came out in Science and the New York

18:22

Times. The media was all on our

18:25

side. I mean, the Times, for example, because this is freedom

18:27

of the press. And remember, it was right after Watergate. My

18:30

wife was really happy when this became big

18:32

news because she said up to that point,

18:34

if something happened to me, nobody would

18:36

really know what had happened. Whereas now, if

18:39

you're a public figure and suddenly you have

18:41

an accident, there would be questions, hopefully. Remember,

18:44

I'm also pissing off not just NSA,

18:46

but their foreign equivalents. And

18:48

I had other friends worked in the community who told

18:51

me that, yes, my life was in danger. So who

18:53

knows? People told me to watch

18:55

my ass. I never worried about

18:57

it. Various people have told me

19:00

NSA threatened them and things like that. It

19:02

was never more than rude to me. Eventually,

19:05

the NSA backed off. They

19:07

never pressed charges against Marty and Witt.

19:10

And over the years, the NSA

19:13

stopped trying to classify all cryptographic

19:15

research. They came to agree

19:17

with Marty and Witt and saw

19:19

that everyone could benefit from encryption. And

19:23

secrets of great commercial importance, they

19:26

also have national security importance. Instead

19:28

of classifying all cryptography research from

19:30

the start, Witt told

19:32

me that the NSA began to

19:35

scout talent from early drafts of

19:37

scientific journals. So they

19:39

were very good at observing

19:41

papers and approaching people

19:43

informally and saying some

19:46

combination of, would you

19:48

please not publish this? And maybe you'd like to

19:50

get a clearance and come to some of our

19:52

meetings. We work on interesting problems. And

19:55

today, nearly 50 years

19:57

later, public key encryption is

19:59

a... Fundamental building blocks of

20:01

the Internet. And of our

20:03

daily lives. The. How many of

20:06

you have. Surf. The Internet? Haven't

20:08

have you bought something with a credit card

20:10

on the Internet? How many of you do

20:12

are trying to baggins you using photography. Used

20:14

to realize it's because is integrated, automatic and

20:16

transparent which is wage should be. So they

20:18

were well over the brink. Where we don't

20:21

We know of the said on the brink

20:23

of revolution Cryptography It's happened. When.

20:27

And Marty They saw a vision

20:29

of a future. That they helped

20:31

create. And all

20:34

that an that we use

20:36

every day. It depends on

20:38

those one way functions, those

20:40

mathematical lox. The.

20:42

Problem is math is always.

20:44

Changing and evolving. Today,

20:47

multiplying large prime numbers may be

20:50

a good. One way function. It's

20:52

easy to solve that takes lots of. Time

20:54

and effort to reverse without. But

20:58

tomorrow tomorrow somebody might big

21:01

route. Of. A new way to

21:03

factor numbers. A new way

21:05

that much much more efficient.

21:07

and then the asymmetry. It

21:09

disappears and is easy to

21:11

get into without the. After

21:15

the break is it possible

21:17

said future proof encryption. And

21:20

how answering that question might break

21:22

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marathon at everywomensmarathon.com. What

24:23

encryption does Tesla use? You're

24:25

Meredith, I'm Brian. Because

24:45

of encryption, I know you are

24:47

you because we're on an encrypted

24:50

channel. And

24:53

there's not just some, you know,

24:55

kind of deep fake man

24:57

in the middle giving me fake Meredith.

25:00

This has all been an elaborate ruse. So

25:03

we've like built up this pretty secure

25:05

internet. Like, I feel pretty good on

25:07

the internet. I don't think about it.

25:10

I see like the little lock icon in

25:12

my web browser and I know this is

25:15

encrypted. So

25:17

is this the internet we might have

25:19

forever? Are we

25:21

cool? So the one

25:24

way functions at the heart of the internet

25:26

security today like are hard to break.

25:30

But that's really subject to changing

25:32

technology. Oh, so these so

25:34

the simple question here is these

25:36

one way functions kind of math problems,

25:39

easy to do hard to reverse. These

25:42

are our locks on the internet. These locks

25:44

can be picked. Is that what you're saying?

25:47

Oh, definitely. One example that

25:49

comes to mind is there's a really

25:51

common one way function based on multiplication

25:53

and factoring and the

25:56

invention of quantum computers, which

25:58

are on the horizon. eyes

26:00

and a twinkle in a lot of researchers'

26:02

eyes, the way that

26:04

those computers are built would actually make

26:07

factoring as a one-way function

26:09

totally obsolete. And

26:12

so there's a lot of work and

26:14

research in cryptography right now looking

26:16

into these one-way functions and making

26:18

them, quote unquote, quantum safe. It's

26:21

a little bit like an upgrade to your

26:23

security system on your operating system on the

26:25

computer. Like, people are seeing

26:28

new technologies, new types of computing

26:30

power on the horizon and

26:32

trying to add patches or

26:34

figure out what we would need to

26:36

change in order to keep that safe. Yeah.

26:40

There's a bit of a cat and mouse thing here.

26:42

You see new tech coming. You try to beef

26:45

up the locks, but then, you know, I'm

26:47

sure new, even new new tech can come

26:50

and then beef up and then we'll need even new

26:52

locks. Yeah. That's an example

26:54

of a threat that people can see coming.

26:58

But what if there's a threat that you can't?

27:00

Okay. So can all locks be

27:03

broken? Is it possible to not

27:05

do this cat and mouse game of seeing

27:07

new tech and building a new lock? Yeah.

27:11

So that's the main question that's been

27:13

motivating the cryptographer Rafael Pass. My

27:15

name is Rafael Pass. I'm a

27:17

professor of computer science. He

27:20

basically believes that, like,

27:22

cryptography is math magic.

27:24

There's a bunch of just beautiful

27:27

and such contradictory concepts

27:29

in cryptography. Things that

27:31

just seem impossible at first and then using

27:35

cryptography, the

27:37

impossible becomes possible. It's like finding

27:39

magic in mathematics, but it's real.

27:41

It's actually true. So

27:44

this math wizard, the

27:47

sorcerer of math, what

27:49

is this question when it comes to these math locks?

27:52

Is there a perfect

27:54

lock? That would be nice.

27:57

So this is very theoretical. This is like

27:59

the perfect. fixed lock as

28:01

a concept. Yeah, before we build it, we

28:03

have to like know if this concept can

28:05

even exist. Exactly, exactly. So the

28:08

way that Raphael puts this is

28:10

like, does a true one way

28:12

function cannot exist. So

28:15

right now we've been like talking about one

28:17

way functions is like easy to solve, but

28:19

hard to reverse. But that

28:21

hard is a moving target. It's subjective to

28:24

the technology and the knowledge that we have.

28:27

But what if there was a true

28:29

one way function that was easy

28:31

to solve, but impossible to reverse. And

28:34

then I can buy things on the

28:36

internet forever and that's it.

28:39

That's what I want. Yeah. No

28:41

matter what fancy quantum computers are

28:43

coming down the road, this would

28:46

be mathematically impossible to reverse. So

28:49

how does he figure out if

28:51

this type of lock even can

28:53

exist? Like how does he even

28:55

figure out if it's even

28:57

possible? Right. So he's looking

28:59

for a unifying theory

29:03

across all one way functions. So

29:05

we try to see whether it exists some

29:08

kind of like mother problem

29:10

or master problem that can

29:12

tell us whether one way functions actually do exist

29:14

or not. Tell me, has

29:16

he, has he figured this out? So a

29:18

few years ago in 2020, I don't

29:20

know. You're

29:22

going to like tell me a whole story. Yeah,

29:25

basically, yes. He found, he found

29:28

maybe not exactly the answer, but

29:30

he found a very,

29:32

very promising lead. So

29:36

a few years ago, Raphael and

29:38

his grad student, Yani, they were

29:40

digging into this unsolved

29:42

problem of computer science. So

29:44

like totally different field than

29:47

cryptography. And they were looking

29:49

at this problem. It's called Comogorov

29:51

complexity. Comogorov

29:54

complexity. Yeah.

29:57

And so this is like a

29:59

famous. unsolved

30:01

problem in computer

30:03

science. A problem that's been studied at

30:07

least since the 1960s. And

30:09

it has to do with the nature of randomness.

30:13

Randomness is so critical in cryptography.

30:15

That's the walls of the safe that

30:17

you're locking the information behind.

30:19

You're transforming usable

30:22

information into gibberish to

30:24

do that. Gibberish is randomness, right? Yeah,

30:26

because we don't have like a physical

30:28

space here. Like our information on the

30:31

internet is cloaked in randomness.

30:34

Instead of seeing my credit card number passing

30:37

through the cyberspace, you

30:39

see some things that just

30:41

look like gibberish. And

30:44

randomness, that gibberish is

30:48

at the heart of this

30:50

complexity problem. Yeah. And

30:52

so basically the problem to solve

30:54

is like, can you write a

30:56

computer program that

30:58

can analyze randomness?

31:02

I think this is a deeply philosophical question. I

31:04

guess we're looking at something in nature and we're

31:06

trying to see, was this just random or is

31:08

there something interesting going on? So

31:11

the solution to this

31:14

complexity problem, it's

31:16

not just like some math problem

31:18

on a chalkboard somewhere where all

31:20

you have to do is like

31:22

beautiful-minded. Oh, x equals 3

31:24

is the answer. Right, exactly. There's not

31:27

like a solution like that. The solution

31:29

to this problem would actually be a

31:31

computer program that could analyze

31:34

the randomness of any given

31:36

information. And that itself is

31:39

a tool. Like if you had the

31:41

tool to really see through randomness and

31:43

see if something was truly random or

31:45

if there was like a signal, some

31:47

information buried in it, like this

31:49

computer program could

31:51

basically see through the safe

31:54

walls of any encryption scheme. Yeah,

31:58

because if our information is protected... by

32:00

randomness and if you can see

32:02

through randomness you can probably fetch out

32:04

that information. Exactly. If

32:07

you solve the complexity problem, what happens? If

32:09

you solve the complexity problem, then

32:14

one-way functions, true one-way functions

32:16

cannot exist. And not

32:19

only that, everything that we've

32:21

built on potential one-way

32:23

functions is instantly

32:25

broken. You've broken all

32:27

candidate one-way functions, all encryption

32:29

schemes, all digital signatures, everything

32:31

can be broken. So

32:38

solving this problem could give

32:40

you the power to break the internet.

32:43

Yeah. It would...

32:46

The way that it's been described to me is

32:49

that it would instantly break all

32:51

encryption. But

32:54

there may not be an

32:56

answer to this complexity problem. It

32:59

might just not be solvable at

33:02

all. We don't know if there's an

33:04

answer. What happens if we

33:06

just can't solve it? So

33:09

if this complexity problem

33:11

is difficult to solve, then

33:13

Raphael claims that he has a

33:16

very clear blueprint of how to

33:18

build the perfect lock, something that's

33:20

provably secure. Okay, so just to

33:22

acknowledge something here. You've

33:24

taken us on a journey, and

33:27

each step of the journey has an

33:29

unanswered question. We

33:31

proceed further into darkness here in

33:34

the story, because it gets a

33:36

little heady here. So first off,

33:38

you have this idea of one-way

33:40

function. We don't know

33:42

if there's a perfect lock out there. The

33:45

answer to the question, is there a perfect

33:48

lock out there, hinges on

33:50

the answer to

33:52

another unanswered question, this

33:54

complexity problem. So

33:56

there's two great big questions here, one leading

33:58

to the other. Exactly. Well,

34:01

Raphael has told us there's a road

34:03

to the answer. Right. And

34:05

if we work really hard on this math problem,

34:08

we might get an answer to the question

34:10

of, is

34:12

there a perfect lock out there? Yeah.

34:17

But this is kind of high stakes, because either

34:19

we might get perfect locks out of this or

34:22

we might realize that all locks will fail. Yes.

34:27

That would mean that communication on the Internet

34:29

would never be able to be secure. That

34:33

would be pretty bad. Do

34:35

you think that's going to happen? I

34:37

don't think so. I hope not. Is

34:40

that worth it? Is that worth pursuing

34:42

this path for that dream of perfection?

34:45

We might find ruin. And

34:47

is that worth it here? I would

34:49

maybe stay away from this complexity problem,

34:52

because I don't want to break the

34:54

Internet. Yeah.

34:57

I mean, I feel like to

34:59

me, this feels very similar to

35:02

nuclear physics. And

35:04

the study of that through the 30s

35:06

and the 40s opened the

35:08

door to weapons of tremendous power, the

35:10

atomic bomb. So that would be the

35:13

path that would lead us to breaking

35:15

all encryption on the Internet. But

35:18

it also gave us really fundamental

35:20

answers about the nature of

35:23

matter in our universe. And

35:26

then led to tremendous tools

35:29

in medicine and agriculture and

35:31

carbon free energy. The

35:34

pursuit of knowledge and the

35:36

pursuit particularly of these very

35:38

fundamental truths, they have powerful

35:40

and dramatic consequences. Yes,

35:43

there could be this world

35:45

of the atomic bomb for

35:48

encryption, but it could also

35:50

lead us to

35:52

a whole new era of

35:55

encryption and lead us to tools

35:57

that we don't even know what they are yet.

36:00

One-way functions are great, they're awesome,

36:02

but they're not everything we want

36:05

from cryptography. We have much lost

36:07

your goals, so it would

36:09

be awesome to also achieve these more

36:11

advanced cryptographic tools using

36:16

some problem like this. But also

36:18

strikes me there's a counterpoint here in

36:20

that, yes, I'm usually extremely optimistic about

36:22

an unanswered question. But here I'm

36:25

realizing that sometimes looking

36:27

into an unanswered question could

36:30

lead you to dangerous things too. Yeah,

36:32

I mean I think when you

36:35

look for fundamental truth, the

36:37

consequences of that are just inherently

36:40

bigger. If you're looking for something

36:42

that connects all locks,

36:45

then if you find a flaw, that's a flaw

36:47

in all locks. It's just

36:49

like a nature of the question. It's

36:51

a little scary. It's a little scary

36:53

for sure. On the other hand, is

36:56

it less scary to live in a world where you

37:00

have reasonable

37:02

security in the locks that

37:04

you have and like reasonable faith that

37:06

they haven't already been broken? Yeah. All

37:09

of these things, all that the cryptography

37:11

that we've been talking about, they're, they're

37:14

tools. They're ways for us

37:16

to share information. They're, are

37:18

ways for us to build

37:20

our lives and our relationships

37:22

on the internet remotely.

37:26

Like we're having this conversation remotely. If

37:29

like the development of the encryption that we

37:31

have today allowed us to do this, then

37:35

what could we use the tools

37:37

of tomorrow to build in the

37:39

future? Like there's also an inherently

37:42

optimistic view. There's still even like for

37:44

now, right? You can still run

37:47

into some shady stuff on the internet.

37:49

People can still steal things. Yeah.

37:52

Yeah. I mean, like crucially, encryption

37:54

is really about that protecting

37:56

information as it travels

37:58

through the internet. But like, there's still

38:00

data breaches all the time. Like once it

38:02

gets to a destination, like who knows how

38:05

your information is getting stored on some like

38:07

company server. Yeah, and it strikes

38:09

me that even if you have a

38:11

perfect lock and perfect encryption, you could

38:13

still give away the password or the

38:15

keys to that, potentially. Yeah, you click

38:18

on some suspicious link and it's like

38:20

10 new bread recipes. And

38:22

they ask for my Apple password. I'm like, sure,

38:25

why not? This

38:31

episode was reported and

38:34

produced by Meredith Hodnot

38:36

with help from Bird Pinkerton. It

38:38

was edited by Catherine Wells and

38:40

Brian Resnick with help from Noam

38:42

Hassenfeld and Gillian Weinberger. Scoring by

38:44

Meredith and Noam. Eh,

38:47

Epheme did a little something something too,

38:49

but you know, mainly Meredith and Noam.

38:51

Mixing and sound design by me, Epheme

38:53

Shapiro, and fabulous music by

38:55

myself, and of course, the guy

38:57

who created the song, me, Epheme

38:59

Shapiro, and fact checking by Zoe

39:01

Mullick. Mandy Nguyen is off to

39:03

adventure in the great north. Christian

39:06

Ayala found his way home. Special

39:09

thanks to Russell Brandom and Erica

39:11

Klarreich. If you want

39:13

to learn more about one-way

39:15

functions and complexity, check out

39:18

Erica's article, Researchers Identify Master

39:20

Problem Underlying All Cryptography in

39:22

Quanta Magazine. If you have

39:24

thoughts about this episode or ideas for the

39:26

show, please email us. We're

39:28

unexplainable at vox.com. We'd

39:31

also love it if you wrote us a review

39:34

or a rating. Unexplainable is part of the Vox

39:36

Media Podcast Network, and we'll be back

39:39

next week. A

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