I'm in the business
of safeguarding secrets,

and this includes your secrets.

Cryptographers are
the first line of defense

in an ongoing war that's been
raging for centuries:

a war between code makers

and code breakers.

And this is a war on information.

The modern battlefield
for information is digital.

And it wages across your phones,

your computers

and the internet.

Our job is to create systems that scramble
your emails and credit card numbers,

your phone calls and text messages --

and that includes those saucy selfies --

(Laughter)

so that all of this information
can only be descrambled

by the recipient that it's intended for.

Now, until very recently,

we thought we'd won this war for good.

Right now, each of your smartphones
is using encryption

that we thought was unbreakable
and that was going to remain that way.

We were wrong,

because quantum computers are coming,

and they're going to change
the game completely.

Throughout history,
cryptography and code-breaking

has always been this game
of cat and mouse.

Back in the 1500s,

Queen Mary of the Scots thought
she was sending encrypted letters

that only her soldiers could decipher.

But Queen Elizabeth of England,

she had code breakers
that were all over it.

They decrypted Mary's letters,

saw that she was attempting
to assassinate Elizabeth

and, subsequently,
they chopped Mary's head off.

A few centuries later, in World War II,

the Nazis communicated
using the Engima code,

a much more complicated encryption scheme
that they thought was unbreakable.

But then good old Alan Turing,

the same guy who invented
what we now call the modern computer,

he built a machine and used it
to break Enigma.

He deciphered the German messages

and helped to bring Hitler
and his Third Reich to a halt.

And so the story has gone
throughout the centuries.

Cryptographers improve their encryption,

and then code breakers fight back
and they find a way to break it.

This war's gone back and forth,
and it's been pretty neck and neck.

That was until the 1970s,

when some cryptographers
made a huge breakthrough.

They discovered an extremely
powerful way to do encryption

called "public-key cryptography."

Unlike all of the prior methods used
throughout history, it doesn't require

that the two parties that want to send
each other confidential information

have exchanged the secret key beforehand.

The magic of public-key cryptography
is that it allows us to connect securely

with anyone in the world,

whether we've exchanged
data before or not,

and to do it so fast that you and I
don't even realize it's happening.

Whether you're texting your mate
to catch up for a beer,

or you're a bank that's transferring
billions of dollars to another bank,

modern encryption enables us
to send data that can be secured

in a matter of milliseconds.

The brilliant idea that makes
this magic possible,

it relies on hard mathematical problems.

Cryptographers are deeply interested
in things that calculators can't do.

For example, calculators can multiply
any two numbers you like,

no matter how big the size.

But going back the other way --

starting with the product and then asking,

"Which two numbers multiply
to give this one?" --

that's actually a really hard problem.

If I asked you to find which two-digit
numbers multiply to give 851,

even with a calculator,

most people in this room would have
a hard time finding the answer

by the time I'm finished with this talk.

And if I make the numbers a little larger,

then there's no calculator on earth
that can do this.

In fact, even the world's
fastest supercomputer

would take longer
than the life age of the universe

to find the two numbers
that multiply to give this one.

And this problem,
called "integer factorization,"

is exactly what each of your smartphones
and laptops is using right now

to keep your data secure.

This is the basis of modern encryption.

And the fact that all the computing power
on the planet combined can't solve it,

that's the reason we cryptographers
thought we'd found a way

to stay ahead of the code
breakers for good.

Perhaps we got a little cocky

because just when we thought
the war was won,

a bunch of 20th-century physicists
came to the party,

and they revealed
that the laws of the universe,

the same laws that modern
cryptography was built upon,

they aren't as we thought they were.

We thought that one object couldn't be
in two places at the same time.

It's not the case.

We thought nothing can possibly spin
clockwise and anticlockwise

simultaneously.

But that's incorrect.

And we thought that two objects
on opposite sides of the universe,

light years away from each other,

they can't possibly influence
one another instantaneously.

We were wrong again.

And isn't that always the way
life seems to go?

Just when you think you've got
everything covered, your ducks in a row,

a bunch of physicists come along

and reveal that the fundamental laws
of the universe are completely different

to what you thought?

(Laughter)

And it screws everything up.

See, in the teeny tiny subatomic realm,

at the level of electrons and protons,

the classical laws of physics,

the ones that we all know and love,

they go out the window.

And it's here that the laws
of quantum mechanics kick in.

In quantum mechanics,

an electron can be spinning clockwise
and anticlockwise at the same time,

and a proton can be in two places at once.

It sounds like science fiction,

but that's only because
the crazy quantum nature of our universe,

it hides itself from us.

And it stayed hidden from us
until the 20th century.

But now that we've seen it,
the whole world is in an arms race

to try to build a quantum computer --

a computer that can harness the power
of this weird and wacky quantum behavior.

These things are so revolutionary

and so powerful

that they'll make today's
fastest supercomputer

look useless in comparison.

In fact, for certain problems
that are of great interest to us,

today's fastest supercomputer
is closer to an abacus

than to a quantum computer.

That's right, I'm talking about
those little wooden things with the beads.

Quantum computers can simulate
chemical and biological processes

that are far beyond the reach
of our classical computers.

And as such, they promise to help us solve
some of our planet's biggest problems.

They're going to help us
combat global hunger;

to tackle climate change;

to find cures for diseases and pandemics
for which we've so far been unsuccessful;

to create superhuman
artificial intelligence;

and perhaps even more important
than all of those things,

they're going to help us understand
the very nature of our universe.

But with this incredible potential

comes an incredible risk.

Remember those big numbers
I talked about earlier?

I'm not talking about 851.

In fact, if anyone in here
has been distracted

trying to find those factors,

I'm going to put you out of your misery
and tell you that it's 23 times 37.

(Laughter)

I'm talking about the much
bigger number that followed it.

While today's fastest supercomputer
couldn't find those factors

in the life age of the universe,

a quantum computer
could easily factorize numbers

way, way bigger than that one.

Quantum computers will break
all of the encryption currently used

to protect you and I from hackers.

And they'll do it easily.

Let me put it this way:

if quantum computing was a spear,

then modern encryption,

the same unbreakable system
that's protected us for decades,

it would be like a shield
made of tissue paper.

Anyone with access to a quantum computer
will have the master key

to unlock anything they like
in our digital world.

They could steal money from banks

and control economies.

They could power off hospitals
or launch nukes.

Or they could just sit back
and watch all of us on our webcams

without any of us knowing
that this is happening.

Now, the fundamental unit of information
on all of the computers we're used to,

like this one,

it's called a "bit."

A single bit can be one of two states:

it can be a zero or it can be a one.

When I FaceTime my mum
from the other side of the world --

and she's going to kill
me for having this slide --

(Laughter)

we're actually just sending each other
long sequences of zeroes and ones

that bounce from computer to computer,
from satellite to satellite,

transmitting our data at a rapid pace.

Bits are certainly very useful.

In fact, anything
we currently do with technology

is indebted to the usefulness of bits.

But we're starting to realize

that bits are really poor at simulating
complex molecules and particles.

And this is because, in some sense,

subatomic processes can be doing
two or more opposing things

at the same time

as they follow these bizarre rules
of quantum mechanics.

So, late last century,

some really brainy physicists
had this ingenious idea:

to instead build computers
that are founded

on the principles of quantum mechanics.

Now, the fundamental unit of information
of a quantum computer,

it's called a "qubit."

It stands for "quantum bit."

Instead of having just two states,
like zero or one,

a qubit can be an infinite
number of states.

And this corresponds to it being
some combination of both zero and one

at the same time,

a phenomenon that we call "superposition."

And when we have two qubits
in superposition,

we're actually working across
all four combinations

of zero-zero, zero-one,
one-zero and one-one.

With three qubits,

we're working in superposition
across eight combinations,

and so on.

Each time we add a single qubit,
we double the number of combinations

that we can work with in superposition

at the same time.

And so when we scale up
to work with many qubits,

we can work with an exponential
number of combinations

at the same time.

And this just hints at where the power
of quantum computing is coming from.

Now, in modern encryption,

our secret keys, like the two factors
of that larger number,

they're just long sequences
of zeroes and ones.

To find them,

a classical computer must go through
every single combination,

one after the other,

until it finds the one that works
and breaks our encryption.

But on a quantum computer,

with enough qubits in superposition,

information can be extracted
from all combinations at the same time.

In very few steps,

a quantum computer can brush aside
all of the incorrect combinations,

home in on the correct one

and then unlock our treasured secrets.

Now, at the crazy quantum level,

something truly incredible
is happening here.

The conventional wisdom
held by many leading physicists --

and you've got to stay
with me on this one --

is that each combination is actually
examined by its very own quantum computer

inside its very own parallel universe.

Each of these combinations,
they add up like waves in a pool of water.

The combinations that are wrong,

they cancel each other out.

And the combinations that are right,

they reinforce and amplify each other.

So at the end of the quantum
computing program,

all that's left is the correct answer,

that we can then observe
here in this universe.

Now, if that doesn't make
complete sense to you, don't stress.

(Laughter)

You're in good company.

Niels Bohr, one of
the pioneers of this field,

he once said that anyone
who could contemplate quantum mechanics

without being profoundly shocked,

they haven't understood it.

(Laughter)

But you get an idea
of what we're up against,

and why it's now up to us cryptographers

to really step it up.

And we have to do it fast,

because quantum computers,

they already exist in labs
all over the world.

Fortunately, at this minute,

they only exist
at a relatively small scale,

still too small to break
our much larger cryptographic keys.

But we might not be safe for long.

Some folks believe that secret
government agencies

have already built a big enough one,

and they just haven't told anyone yet.

Some pundits say
they're more like 10 years off.

Some people say it's more like 30.

You might think that
if quantum computers are 10 years away,

surely that's enough time
for us cryptographers to figure it out

and to secure the internet in time.

But unfortunately, it's not that easy.

Even if we ignore
the many years that it takes

to standardize and deploy and then
roll out new encryption technology,

in some ways we may already be too late.

Smart digital criminals
and government agencies

may already be storing
our most sensitive encrypted data

in anticipation for
the quantum future ahead.

The messages of foreign leaders,

of war generals

or of individuals who question power,

they're encrypted for now.

But as soon as the day comes

that someone gets their hands
on a quantum computer,

they can retroactively break
anything from the past.

In certain government
and financial sectors

or in military organizations,

sensitive data has got to remain
classified for 25 years.

So if a quantum computer
really will exist in 10 years,

then these guys are already
15 years too late

to quantum-proof their encryption.

So while many scientists around the world

are racing to try to build
a quantum computer,

us cryptographers are urgently
looking to reinvent encryption

to protect us long before that day comes.

We're looking for new,
hard mathematical problems.

We're looking for problems that,
just like factorization,

can be used on our smartphones
and on our laptops today.

But unlike factorization,
we need these problems to be so hard

that they're even unbreakable
with a quantum computer.

In recent years, we've been digging around
a much wider realm of mathematics

to look for such problems.

We've been looking at numbers and objects

that are far more exotic
and far more abstract

than the ones that you and I are used to,

like the ones on our calculators.

And we believe we've found
some geometric problems

that just might do the trick.

Now, unlike those two-
and three-dimensional geometric problems

that we used to have to try to solve
with pen and graph paper in high school,

most of these problems are defined
in well over 500 dimensions.

So not only are they a little hard
to depict and solve on graph paper,

but we believe they're even
out of the reach of a quantum computer.

So though it's early days,

it's here that we are putting our hope
as we try to secure our digital world

moving into its quantum future.

Just like all of the other scientists,

we cryptographers are tremendously excited

at the potential of living in a world
alongside quantum computers.

They could be such a force for good.

But no matter what
technological future we live in,

our secrets will always be
a part of our humanity.

And that is worth protecting.

Thanks.

(Applause)