# How Quantum Computers Break Encryption | Shor's Algorithm Explained

How Quantum Computers Break Encryption | Shor's Algorithm Explained

Go to http://www.dashlane.com/minutephysics to download Dashlane for free, and use offer code minutephysics for 10% off Dashlane Premium!

Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics

This video explains Shor’s Algorithm, a way to efficiently factor large pseudoprime integers into their prime factors using a quantum computer. The quantum computation relies on the number-theoretic analysis of the factoring problem via modular arithmetic mod N (where N is the number to be factored), and finding the order or period of a random coprime number mod N. The exponential speedup comes in part from the use of the quantum fast fourier transform which achieves interference among frequencies that are not related to the period (period-finding is the goal of the QFT FFT).

REFERENCES

RSA Numbers (sample large numbers to try factoring)

https://en.wikipedia.org/wiki/RSA_numbers

IBM on RSA

https://www.ibm.com/support/knowledgecenter/en/SSB23S1.1.0.13/gtps7/s7pkey.html

Modulo Multiplication Group Tables

http://mathworld.wolfram.com/ModuloMultiplicationGroup.html

Difference of squares factorization

https://en.wikipedia.org/wiki/Difference_of_two_squares

Euclid’s Algorithm

https://en.wikipedia.org/wiki/Euclideanalgorithm

Rational sieve for factoring

https://en.wikipedia.org/wiki/Rational_sieve

General Number field Sieve

https://en.wikipedia.org/wiki/Generalnumberfieldsieve

Scott Aaronson blog post about Shor’s Algorithm

Experimental implementation of Shor’s Algorithm (factoring 15, 21, and 35)

https://arxiv.org/pdf/1903.00768.pdf

Adiabatic Quantum Computation factoring the number 291311

https://arxiv.org/pdf/1706.08061.pdf

Scott Aaronson course notes

https://www.scottaaronson.com/qclec/

https://www.scottaaronson.com/qclec/combined.pdf

Shor’s Algorithm on Quantiki

https://www.quantiki.org/wiki/shors-factoring-algorithm

TLS And SSL use RSA encryption

https://en.wikipedia.org/wiki/TransportLayerSecurity

Dashlane security whitepaper

https://www.dashlane.com/download/DashlaneSecurityWhitePaperOctober2018.pdf

Link to Patreon Supporters: http://www.minutephysics.com/supporters/

MinutePhysics is on twitter – @minutephysics

And facebook – http://facebook.com/minutephysics

Minute Physics provides an energetic and entertaining view of old and new problems in physics — all in a minute!

Created by Henry Reich

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

Video wasn’t a minute dislike for misleading channel name

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

top 10 facts that will have almost no difference in your life

Wow alot of math

Looked outside the window for 15 secs, got back to the video and I was lost 🙁

Hooking up time crystals with quantum computers will enable the cracking of any encryption used today. I’m pretty damned sure people are working on this…. and some of them are not very nice.

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

Head hurty

what

all i learned is how we encrypt stuff

was gonna say how but i cant explain it 😛

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

i loved the video, well done. still you got a thump down for the ad at the end + no subscription

But can quantuim computer decode girls "hints"?

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

In Quantum world, you could be a man, a woman and a ladyboy at the same time.

i understand almost everything. the only thing i don’t is how you do that smooth transition between quantum mechanics and advertising your sponsor. you are a genius.

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

And then alter the website code a bit to add a captcha

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.

So uhhhhh about Google’s quantum computer….

why dont u jsut put 1, isn’t that a factor of every whole number?

Thank you. After watching this, I feel smarter and dumber at the same time now.

13:58 ‘I’m oversimplifying a bit here’

Lol what

Why am I watching this and how did I get here

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.

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

Shor Algorithm: will break all encryption, none of your data is safe

Quantum cryptography: i am about to ruin this man day

Great explanation! Thank you 🙂

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.

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

The first quantum computer was made one week ago from when I’m writing this.

I watched the whole video and the only thing i got is: one over pee 🙁

Why im even here

Nine:-i…i……am not crappy

*Nine has left the conversation*

You’re daily dose of "So, you thought you were smart?" Also, you were over simplifying?? I’ll have to watch it a few times.

This video ignores ECC, that everyone is switching to!

can you talk about quantum ray tracing?

Hey a one time pad still works. The key just needs to be as big as the data

Lost me 🤷🏾♂️

I’m lost…

Your channel both encourages me and discourages me from studying physics in the future.

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

Yes, i understand this

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

So the quantum computers with quantum supremacy is here now

2048bit RSA encryption isn’t even that good. For RSA 4096bit is standard and RSA is obsolete anyways..

Welcome minutephysics fans. Today you just took a semesters worth of discrete mathematics for computer science.

C’mon guys I am 14 and still understand this

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

Just use a key file for two factor authentication, literally unbreakable unless you know what that key file is