The goal of encryption is to garble data is

such a way so that no one who has the data can read it unless they’re the intended

recipient. And the encryption of pretty much all private

information sent over the internet relies immensely on one numerical phenomenon – as

far as we can tell, it’s really really hard to take a really big number and find its factors

using a normal, non-quantum computer. Unlike multiplication, which is very fast

(just multiply the digits together and add them up ), finding the prime numbers that

multiply together to give you an arbitrary, big, non-prime number appears to be slow – at

least, the best approach we currently have that runs on a normal computer – even a very

powerful one – is very slow. Like, to find the factors of this number , it

took 2000 years of computer processor time! Now, it’s not yet proven that we won’t

eventually find a fast way to break encryption just with normal computers, but it’s certain

that anybody with a large working quantum computer today would pose an immediate privacy

and security threat to the whole internet. And that’s due to something called “Shor’s

Algorithm.” Well actually it’s due to quantum superposition

and interference; they’re just taken advantage of by an algorithm developed by Peter Shor,

which I’m now going to attempt to explain. The kind of encryption we’re talking about

garbles or “locks” messages using a large number in such a way that decrypting or “unlocking”

the data requires knowing the factors of that number . If somebody doesn’t have the factors,

either they can’t decrypt the data, or they have to spend a really really long time or

a huge amount of investment in computing resources finding the factors. Our current best methods essentially just

guess a number that might be a factor, and check if it is . And if it isn’t, you try

again. And again. And again. It’s slow. There are so many numbers to check that even

the fast clever ways to make really good guesses are slow. For example, my computer took almost 9 minutes

to find the prime factors of this number. So if you used this number to encrypt your

data, it would only be safe from me for 9 minutes. If, on the other hand, you used a number like

the one that took 2000 years of computer processor time to factor , your data would definitely

be safe from me and my laptop, but not from somebody with access to a server farm .

This is similar to how putting a lock on your door and bars on your windows doesn’t guarantee

you won’t have stuff stolen from your house, but does make it take more time and more work. Encrypting data isn’t a guarantee of protection

– it’s a way of making it harder to access; hopefully enough harder that no one thinks

it’s worth trying. But quantum computation has the potential

to make it super super easy to access encrypted data – like having a lightsaber you can use

to cut through any lock or barrier, no matter how strong. Shor’s algorithm is that lightsaber. Roughly speaking, to factor a given number

Shor’s algorithm starts with a random crappy guess that might share a factor with your

target number, (but which probably doesn’t), and then the algorithm transforms it into

a much better guess that probably DOES share a factor! There’s nothing intrinsically quantum mechanical

about this – you can, in fact, run a version of Shor’s algorithm on a regular computer

to factor big numbers, but perhaps unsurprisingly the “turning your bad guess into a better

guess” part of the process takes a very very long time on a normal computer. On the other hand, this key step happens to

be ridiculously fast on quantum computers. So, our task is to explain how Shor’s algorithm

turns a crappy guess into a better guess (which is purely mathematics), and why quantum computers

make that fast (which is where the physics comes in). It all starts with a big number, N, that you’ll

need to find the factors of to break into some encrypted data. If you don’t know what the factors are (which

you don’t), you can make a guess; just pick some number g that’s less than N . We actually

don’t need the guess to be a pure factor of N – it could also be a number that shares

some factors with N, like how 4 isn’t a factor of 6, but shares a factor with it. Numbers that share factors are ok because

there’s a two-thousand-year-old method to check for and find common factors – it’s

called Euclid’s algorithm and it’s pretty darn efficient. All this is to say that to find a factor of

N, we don’t have to guess a factor of N – guessing numbers that share factors with N works, too,

thanks to Euclid. And if Euclid’s algorithm found any shared

factors with N, then we’d be done! You could just divide N by that factor to

get the other factor and break the encryption. But for the big numbers used in encryption,

it’s astronomically unlikely that any single guess will actually share a factor with N. Instead, we’ll use a trick to help transform

your crappy guess into a pair of guesses that are way more likely to share factors with

N. The trick is based on a simple mathematical fact: for any pair of whole numbers that don’t

share a factor, if you multiply one of them by itself enough times, you’ll eventually

arrive at some whole number multiple of the other number, plus 1 . That is, if a and b

are integers that don’t share factors, then eventually a^p will be equal to m times b

+ 1, for some power p and some multiple m . We don’t have the time to get into why this

is true, but hopefully a few illustrations can at least give you a feeling for it. For example, 7 and 15. While seven squared isn’t one more than

a multiple of 15, and neither is seven cubed, seven to the fourth is. Or take 42 and 13 – 42 squared isn’t one

more than a multiple of 13 , but 42 cubed is. This same kind of thing works for any pair

of numbers that don’t share factors, though the power p might be ridiculously large. So, for the big number, N, and your crappy

guess, g, we’re guaranteed that some power of g is equal to some multiple of N, plus

1 . And here’s the clever part – if we rearrange this equation by subtracting the 1 from both

sides, we can rewrite g^p-1 as (g^p/2 + 1)(g^p/2 – 1) . You can multiply that back together

to convince yourself that it works. And now we have an equation that almost looks

like “something” times “something” is equal to N, which is exactly what we’re

trying to find – factors of N! These two terms are precisely the new and

improved guesses that Shor’s algorithm prescribes: take the initial crappy guess, multiply it

by itself p/2 times, and either add or subtract one! Of course, since we’re dealing with a multiple

of N rather than N itself, the terms on the left hand side might be multiples of factors

of N, rather than the factors themselves. Like how 7^4/2+1=50, and 7^4/2-1=48, neither

of which is a factor of 15. But we can find shared factors by using Euclid’s

algorithm again, and once we do, we’ll have broken the encryption! So is this all Shor’s algorithm is? Where’s the quantum mechanics? Why can’t we use this to break encryption

right now? Well, indeed, there are three problems with

these new and improved guesses. First, one of the new guesses might itself

be a multiple of N, in which case the other would be a factor of m and neither would be

useful to us in any way. And second, the power “p” might be an

odd number , in which case p/2 isn’t a whole number and so our guess taken to the power

of p/2 probably isn’t a whole number either, which is no good. However, for a random starting guess, it turns

out that at least 3/8ths of the time neither of these problems happens and p does generate

guesses that share factors with N and break the encryption! This is worth repeating – for ANY initial

guess that we make, at least 37.5% of the time g^p/2 ±1 will lead to a factor of N,

decrypting the garbled message. Which means we’re 99% likely to break the

encryption with fewer than 10 guesses. However, problem number three is the big one. Remember, to turn a crappy guess into a good

guess we need to know how many times you have to multiply our guess by itself before we

get a multiple of N, plus 1. And for a normal computer, the act of finding

that power p takes a ton of work and time. It’s not hard for small numbers like 42

and 13, but if our big number is a thousand digits long, and our crappy guess is 500 digits

long, then trying to figure out how many times you have to multiply our guess by itself before

you get some multiple of the big number, plus one, takes a ridiculous amount of trial and

error on a normal computer – more effort than it would have taken to just factor N by brute

force in the first place! So finally, this is where quantum mechanics

comes in and speeds things up an INSANE amount. Unlike a normal computation which gives only

one answer for a given input, a quantum computation can simultaneously calculate a bunch of possible

answers for a single input by using a quantum superposition – but you only get one of the

answers out at the end, randomly, with different probabilities for each one. The key behind fast quantum computations is

to set up a quantum superposition that calculates all possible answers at once while being cleverly

arranged so that all of the wrong answers destructively interfere with each other. That way when you actually measure the output

of the calculation, the result of your measurement is most likely the right answer. In general it can be really hard to figure

out how to put any particular problem into a quantum form where all the wrong answers

destructively interfere, but that’s what Shor’s algorithm does for the problem of

factoring large numbers – well, actually, it does it for the problem of finding the

power “p”. Remember, at this point we’ve made a crappy

guess g, and we’re trying to find the power p so that g to the p is one more than a multiple

of N. A p that does that also means that g^p/2 ±1 is very likely to share factors with N. So to begin the quantum computation, we need

to set up a quantum mechanical computer that takes a number x as input, and raises our

guess to the power of x. For reasons we’ll see later, we need to keep

track of both the number x, and our guess to that power. The computer then needs to take that result

and calculate how much bigger than a multiple of N it is. We’ll call that the “remainder”, and we’ll

write it as plus “something” for whatever something the remainder is (remember, we want

a remainder of 1). So far, no different from a normal computer. But since it’s a quantum computer, we can

send in a superposition of numbers and the computation will be done simultaneously on

all of them, first resulting in a superposition for each p of all possible powers our guess

could be raised to , and then a superposition for each p of how much bigger each of those

powers are than a multiple of N. We can’t just measure this superposition

to get the answer – if we did, we’d get a single random element of the superposition

as output, like “our guess squared is 5 more than a multiple of N” . Which is no

better than just randomly guessing powers, which we can do with a normal computer. No, we need to do something clever to get

all the non-p answers to destructively interfere and cancel out, leaving us with only one possible

answer: p. Which it turns out we can do, based on another

mathematical observation. This mathematical observation isn’t particularly

complicated, but it is a tad subtle and it may not be immediately clear why we care. However, it’s the key idea that allows us

to turn the problem of finding p into one that works well on a quantum computer, and

so in some ways it’s the crux of Shor’s algorithm – which is to say, it’s worth

the effort! Ok, so remember that IF we knew what p was,

we could raise our guess to that power and get one more than a multiple of N. On the

other hand, if we take our guess to a random power , it’s probably going to be some other

number more than a multiple of N – say, 3 more . But check this out – if we raise our

guess to that random power plus p, it’s again 3 more than a multiple of N . If we

raise our guess to that random power plus 2 p, it’s again 3 more than a multiple of

N. And so on. It’s pretty straightforward to show why

this works by multiplying out “something times N plus 1” with “something else times

N plus 3”; you get “a different something times N, again plus 3” . And this works

for any power x – if g^x is r more than a multiple of N, then g^(x+p) will also be r

more than a multiple of N (though a different multiple). So the power p that we’re looking for – the

one that allows us to improve our crappy guess and find factors of N and break encryption

– it has a repeating property where if we take another power and add (or subtract) p

to it, the amount more than a multiple of N stays the same. This repeating property isn’t something

you could figure out from taking our guess to just one power – it’s a structural relationship

between different powers, and we can take advantage of it since quantum computations

can be performed on superpositions of different possible powers. Specifically, if we take the superposition

of all possible powers and JUST measure the “amount more than a multiple of N“ part,

then we’ll randomly get one of the possible “amounts more than a multiple of N” as

the output – say, 3. The specific number doesn’t matter to us,

but what does matter is that this means we must be left with a superposition of purely

the powers that could have resulted in a remainder of 3. This is one of the special properties of quantum

computation – if you put in a superposition and get an answer that could have come from

more than one element of the superposition, then you’ll be left with a superposition of

just those elements! And in our case, because of the repeating

property, those powers are all numbers that are “p” apart from each other. To recap, we’re trying to find p because

it will allow us to turn our crappy guess into a good guess for a number that shares

factors with N, which will allow us to break the encryption. And we now have a quantum superposition of

numbers that repeat periodically with a period of p, or equivalently, they repeat with a

frequency of 1/p . If we can find the frequency, we can find p and break the encryption! And the best tool to find the frequencies

of things is called a Fourier transform. Fourier transforms are what allow you to input

an audio signal as a wave and convert it into a graph showing the different frequencies

that the wave is made up of. And there’s a quantum version of the Fourier

transform, which we can apply to our superposition that repeats with a frequency of 1/p to cause

all the different possible wrong frequencies to destructively interfere, leaving us with

a single quantum state: the number 1/p. So how does the quantum Fourier transform

perform this magic? Well, if you input a single number into the

quantum Fourier transform, it will give you a superposition of all other numbers – but

not any old superposition. A superposition where the other numbers are

all weighted by different amounts, and those weights look roughly like a sine wave with

the frequency of the single number we put in. If you put in a higher number, you get a sine

wave-style superposition of all other numbers, but with a higher frequency. And the magic is that when you put IN a superposition

of numbers, you get out a superposition of superpositions and the sine waves add together

– or subtract and cancel out. And it happens that if you put in a superposition

of numbers that are all separated by an amount p, all those sine waves interfere so that

what you get out (and I’m oversimplifying a touch), is the single quantum state representing

1/p. Which we can finally measure to get the output

of the computation: 1/p! Which we invert to find p, and as long as

p is even we can now finally raise our guess to the power p over two and add or subtract

one, and as long as we don’t get an exact multiple of N, we are guaranteed to have a

number that shares factors with N. And therefore we can use Euclid’s algorithm to quickly

find those factors, and thus we can finally take the encrypted data and decrypt it. And thus we will have broken the encryption. And that is Shor’s algorithm – the lightsaber

that can be used to cut through locks on the internet. As complicated as this clearly is in practice…

(and we’ve glossed over a ton of details), it’s surprising to me how simple the core

structure of Shor’s algorithm actually is: for any crappy guess at a number that shares

factors with N, that guess to the power p/2 plus or minus one is a much much better guess,

if we can find p. And we CAN find p almost immediately with

a single (if complex) quantum computation. A normal computer would have to go one by

one through all possible powers, which would take an incredible amount of time for any

really really big number like the ones used in encryption, since p could be almost any

number up to N. The quantum version is ridiculously ridiculously faster, and if a big enough quantum

computer is ever built, then Shor’s algorithm would allow the user to very easily decrypt

any data encrypted with a large-number factoring based system – which would pretty much ruin

the entire internet. At this point, however, the biggest actual

quantum implementations of Shor’s algorithm don’t have enough memory to hold more than

a few bits, which only allows factoring of numbers like 15, 21, and 35 . Now, there are

other methods of factoring using quantum computations that are a bit more advanced, and have factored

numbers as big as a few hundred thousand using just a few quantum bits of memory . But they

would still need 2000 times more quantum memory to factor even some of the smaller of the

really big numbers used in modern encryption . So, no need to worry about quantum computers

just yet. If all this talk of breaking encryption makes

you a bit nervous and worried about your online safety, well, there’s something you can

do to improve your internet security right now – I’ve been a long time user of the

password manager Dashlane who are sponsoring this video, and if you’ve never used a password

manager before, Dashlane is amazing. It generates and remembers a long, unique

password for each site or service that I use so that I don’t have to worry about remembering

passwords; and of course all of my data and passwords are stored encrypted with very very

large numbers. And Dashlane is more than just a password

manager – it lets you know when your passwords are old or weak or when a site or app you

use has been hacked so you can change your passwords, it encrypts and lets you securely

share passwords with family and coworkers, it can be used to securely store or share

your address, credit card info, and banking info, with just the people and sites you want

to, it can be used as a VPN, and more. Oh, and Dashlane uses 2048 bit numbers for

its encryption – numbers that big are estimated to take a trillion times more effort to factor

than any that have so far been factored by brute force. And of course Dashlane is free for up to 50

passwords for as long as you like, so you have nothing to lose checking it out. But, if you want the very useful features

of unlimited passwords, encrypted syncing of passwords, VPN, remote account access,

and more, the first 200 people get 10% off Dashlane premium by going to dashlane.com/minutephysics

and using promo code minutephysics. Again, that’s dashlane.com/minutephysics

with promo code minutephysics to simplify and encrypt your online life. Dashlane has legitimately improved my online

security and changed my password habits for the better. What could it do for you?

## Rodolfo Reyes S. says:

So 1 dosen't work rigth? Hahaha

## Rodolfo Reyes S. says:

Do the factors of N have to be prime numbers? If there were more than 2 factors (not 4 factors because 1 and N don't work so they don't count) there would be more possible solutions and I don't know what it would imply

## 김주만 says:

Thank you for a great explanation on how to factorize large numbers with Shore's algorithm quantum mechanically. However, when we compute QFT, how can we leave a peak for remainder 1 with destructive interference where QFT just reads weights for p's of random remainder?

## Khajiit Hadwares says:

tl;dr secure digital currency is an illusion. (even without any leaks or backdoors present)

## Fabrizio Giordano says:

Finally long videos😍

## Julian Leung says:

You put a whole semester worth of info in the 20 minutes.

## The following is wrong: says:

Oh my God that was so easy!

## TheNinthGeneration says:

Why don’t you add complexity by making N a prime itself, and the key being N + X

## Rontez valentine says:

How to understand your girlfriend. Then again if you watched the entire 17.5 minutes you probably don't have one.

## ordinary Oddball says:

Oh my god, YouTubers, STOP telling your whole audience which specific password manager you use! That's a great way to get targetted by someone looking to get into your master password!

## Tumpal Leonardo h Sinurat says:

Wait, this video was 17 minutes?

That was fast

## Ben Quinney says:

Brute force

## Ben Quinney says:

Rigorous proof

## Walter Burton says:

Good enough for gubment work.

## jankat özden says:

Jesus christ what

## Warsin says:

Eculid is my dude im abbout to hack the shiit out of them passwords

## matt pflanz says:

So pretty much this is like brute forcing every possible password outcome? They already have programs like that… you insert a password file and run a “death by captcha” so you can constantly keep trying passwords without the website limiting your attempts. I have a password .txt file that has over 3 million different password combinations and I just slowly add different ones to it. If you do as many as you possibly can and then go in and delete the duplicates you can pretty much crack anything

## Meowsenberg says:

yeah I don't get it

## Pranjal Sharma says:

what

## El Guapo says:

5:00 … And I'm lost.

## Nishkal Kashyap says:

*I don't understand what you just said bit it sounds smart so I'm going to give you a like anyway*## Alex 99 says:

Thing is, even if you find the two prime numbers that form the modulo of the encryption protocol, you still need to find the private key, and that's not fast. RSA uses the fact that factorising a huge number into two primes is hard, but it isn't the only thing that protects your message

## Meep Changeling says:

Cute, but my 5 dollar wrench already makes any and all encryption void. "Give me the password or I break your other kneecap."

## S S says:

17-minute physics

## Jyotiraditya Deka says:

I had to slow down the video to understand

## Silica says:

this acturally lets you get the RSA private key^ which means it can also be used to sign things. so on the plus side~ this will also allow us to run custom software on all the (current) major consoles, ps4, psvita, xbox, switch. without any modifications to the firmware 😀

## Indy Visualist says:

So if P has to be even for it to work, is it possible to protect data by making certain that P is not even?

I guess I am missing something!

## Tim Schulz says:

14:30 Why does it share factors with N? I thought it shared factors with m*N.

## Irreales Disrupt Real Estate with VR says:

Don't worry if an intel agency can break all encryption using a QC they will tell us before so we can know, because they are the good guys

## Irreales Disrupt Real Estate with VR says:

1998 : Quantum algorithms can break all modern encryption

2019 : don't worry quantum computers don't exist nothing to worry about, carry on with your normal life

2025 : Euh computers, math, algebra? What is that bro?

See the pattern?

## Edukate95 says:

5:19 "… and here's the clever part."

I'm obviously not very clever if things didn't get tricky until now.

## Sebastian Nielsen says:

it would be interested to have a similiar video about how "quantium-computer safe encryption algoritms" like elliptic curve, why these cannot be calculated by quantium computers?

## MR. Macaroni says:

I may have a theory that could serve as a safe guard for quantum computers here goes

So normal encryption just takes one really big number like the one that took 2000 years to finish but what if the computer just kept on making extremely large numbers up. It would probably quadriple the amount of decryption required to complete. So the one that took 2000 years on a normal computer would take an estimated 8000 years for a normal computer and might make it harder for a quantum computer because the number is ever-Changing.

Please tell me if you think this would work and if not please explain why thank you for reading.

## Scott Cress says:

If I understood all this does that mean I should get a degree in cryptography?

## Emily Rose Lacy-Nichols says:

Great video! Really clear explanation, and your illustrations are always super cute!

Now excuse me while I mop my brain up off the floor cuz it asplode…

## Jarrod Yuki says:

we need to protect privacy or otherwise the texture of society and what it means to be human will collapse and there will be no more humanity.

## Dash Quinnten says:

Halfway through the video I noticed his mouth making wet noises (when your tongue makes a sticky when it peels off the roof of your mouth, etc.) and I couldn't stop focusing on that

## Henrique Vieira dos Santos Guerra says:

What's the name of the theorem that says m*b+1=a^p ?

## Austin B says:

Wouldn’t there be quantum encryptions too then?

## Cherilyn Kuan says:

My brain cells died

## John Price says:

Took me 16 minutes to realize this is a commercial…

## Deltexterity says:

Channel name: minute physics

Video length: 17:30

wait. that’s illegal.## sunath khadikar says:

This video is GOLD !! I thank you for every second of it.

## Ian Moline says:

So if this is true then how come the FBI made a big deal about how they weren't able to crack the apple 4 digit passcode and even Apple themselves said they couldn't crack their own 4 digit passcode? (Asking honestly.)

## ΝΤΕΝΤΑ Νικολιν says:

I didn't understand nothing

## Sohun Patel says:

Quantum computer currently only have 50 qubits. We need around 6000 qubits to actually run Shor's algorithm. Furthermore, modern quantum computer are not failure tolerant. So, good luck trying to run Shor's algorithm successfully.

## DarkThomy says:

The fact the bass stops playing one minute in scares me somehow..

## Kj16V says:

Minute Physics:

17 minute long video## Marcus Åkerman says:

But Shor’s only breaks some encryption, but there are already lot of encryption that doesn’t depend on this.

## Fact Sheet says:

What I don't get is about the frequencies.

Like couldn't you just take one minus the other and get the difference which is the frequency?

Why do you need to apply a Quantum Fourier Transform on them? 🤔

## Behfar Bastani says:

Such a great explanation! Would love to see you do sketches of famous complexity theory proofs or constructions, like pseudorandom generators, expanders, randomized algors, etc. Awesome video!

## John England says:

I wonder, how would quantum computers handle one time pads? One time pads that have generated random character sets to begin with. One time pads that have cloak values that create a new character set and one time pad for each iteration of the cloak value and are encrypted into pictures using multiple fonts and glyphs. Pictures with multiple layers that can be scrambled into a disordered set. Then, using steganography with password, embed the encrypted picture/s into the original picture. Should be interesting seeing them decode a picture. Interesting.

## Lone Ghost _/__/_ says:

Takes em around 4 hours to crack aes-256 we need to upgrade encryption

## Funny Memes says:

I need a upgrade so I can keep up with this video…

## Funny Memes says:

Are quantum computers actually created yet?

## Seba says:

What a fucking cool video

## George Andrews says:

I wrote an encryption method for messages that quantum computers can’t break.

It doesn’t use keys and doesn’t allow you to know exactly when a encoded message stops or starts in the output.

## Cajun Gangster says:

Okay now I understand I just have to learn alphabet as numbers ¿?????¿ Duh

## BookWorm84 says:

Oh! I totally get it!

QFT means Quantum Freakin Tmagic also known by its superposition PFM which is an expression expressed expressly by singing waves and lots of numbers that mean things.

Joking aside… Seriously, this is insanely good. I understood everything you explained… somehow. Despite having a background that failed algebra 2. Your teaching method is amazing. Thank you.

## brad vankoughnett says:

Ohhh interesting. I always thought that quantum computers just allowed 3state data instead of binary. Never knew that it could superimpose computations

## Alapan Das says:

That comes from the formula- there exist x,y such that ax+by=1(modulo b) for gcd(a,b)=1.

## Vic W says:

never hit the "rewind 5 sec" button so many times before – this took 60min to watch 17min

## Menya Savut says:

one time pad – choke on this, quantum computer.

## Menya Savut says:

still doesn't explain how quantum computers break encryption, because it doesn't explain how QFT works. it's only presented as a black-box.

## Rath says:

So… Why am I watching this if I have little to no idea what he's saying? I'm not actually good at math

… keeps watching anyway## FinicalBillyYT says:

I’m losing my ability to concentrate 5 minutes in

## אשל שחמון says:

OK, but since when encryption works like this, and why do you need to find the factors of a number to break encryption? Don’t you need to find the password? And, what do you do with the factors, after you find them?

(Please someone answer this)

## David Soto says:

I watch this when I’m feeling too smart

To remind myself that I’m not really smart

## Dries Analog says:

i wonder if quantum computing means the end of bitcoin and other cryptocurrencies.

## A Person Eating Bread says:

What

## Aaron says:

Quantum encryption then 👀

## jull1234 says:

Dashlane ain't gonna save you from the quantum revolution.

## Wesley L says:

I need a quantum computer to decipher this video.

## Jordan Crawford says:

I was so focused until the baseline came in and said, “just give it up, dude.”

## Saschahi says:

Got to 12:50 before I gave up even listening and just started reading comments

## MrDontuknowme says:

Lost me 🤷🏾♂️

## Jordan Hicks says:

all i learned is how we encrypt stuff

was gonna say how but i cant explain it 😛

## Satwik Mudgal says:

Nine:-i…i……am not crappy

Nine has left the conversation## faox says:

I was thinking about this when I heard the news about Google’s “breakthrough”. They read my mind

## PlasmaRuler says:

It’s not that bad but if you don’t have 2 factor authentication yeah your screwed

## Tes Tos says:

Anyone has Aspiring? Bottom line is nothing is secure and now less than ever. Keep your money under the mattress and an AR next to your bed. Better yet put a sign by the front door telling everyone where is your cash and just let them in and take it, if you shoot a thieve most likely you will need that cash to get you out of jail either way your going to loose everything thanks to your government.

## Nick Ergodos says:

So the quantum computers with quantum supremacy is here now

## Spencer Shackleton says:

what

## seasong says:

can you talk about quantum ray tracing?

## zelzmiy says:

Yes, i understand this

## therealquade says:

So uhhhhh about Google's quantum computer….

## Insert your feelings [here] says:

Video wasn’t a minute dislike for misleading channel name

## The Legend of Tobi says:

Great explanation! Thank you 🙂

## Kyle Chin says:

Watch as I destroy the world's economy by turning a 1 into a 0.

## Kyle Chin says:

But remember people no need to panic because this only works for numerical encryption.

## Aidenne Campbell says:

I'm lost…

## shad sluiter says:

Perfect. Shor's algorithm should be mentioned with all of the news stories that are currently covering Google's claim to have created a working quantum computer.

## the1gip says:

4:47 So in the case of recurring decimals, this would be true of say A=10, B=7, P=6, m=142857 then?

## Pat John says:

Except you’ll have quantum encryption too so they will cancel each other oth

## William M. says:

is this what they call the archetype of verbal diarrhea?

## Shaunak Marathe says:

That's the Fermat's Little theorem @ 5:19

## ngocbach phan says:

Why can't we just take a perfect number for g? That way, even if p is odd, g^p/2+1 or g^p/2-1 will still be a natural number.

## warmCabin says:

Dashlane's cool and all, but it doesn't sound like it's Shor-proof.

## Zenax says:

Who else didn’t understand and felt lost but watched cause it was interesting?

## Snubagaff says:

Head hurty