How Quantum Computers Break Encryption | Shor's Algorithm Explained
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Publicado 2019-04-30
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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)
en.wikipedia.org/wiki/RSA_numbers
IBM on RSA
www.ibm.com/support/knowledgecenter/en/SSB23S1.1.0…
Modulo Multiplication Group Tables
mathworld.wolfram.com/ModuloMultiplicationGroup.ht…
Difference of squares factorization
en.wikipedia.org/wiki/Difference_of_two_squares
Euclid’s Algorithm
en.wikipedia.org/wiki/Euclideanalgorithm
Rational sieve for factoring
en.wikipedia.org/wiki/Rational_sieve
General Number field Sieve
en.wikipedia.org/wiki/Generalnumberfieldsieve
Scott Aaronson blog post about Shor’s Algorithm
www.scottaaronson.com/blog/?p=208
Experimental implementation of Shor’s Algorithm (factoring 15, 21, and 35)
arxiv.org/pdf/1903.00768.pdf
Adiabatic Quantum Computation factoring the number 291311
arxiv.org/pdf/1706.08061.pdf
Scott Aaronson course notes
www.scottaaronson.com/qclec/
www.scottaaronson.com/qclec/combined.pdf
Shor’s Algorithm on Quantiki
www.quantiki.org/wiki/shors-factoring-algorithm
TLS And SSL use RSA encryption
en.wikipedia.org/wiki/TransportLayerSecurity
Dashlane security whitepaper
www.dashlane.com/download/DashlaneSecurityWhitePap…
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Todos los comentarios (21)
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Hey, that's a lot of minutes of physics.
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My brain waves superpositioned in a way that only the neurons which did not undertand got positive interference
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Him: "...and here's the clever part." Me: "WHAT WAS THE REST OF THIS?!"
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It's amazing to see that someone can grasp such difficult concepts well enough to make this "simple" explanation. I don't have the knowledge to understand, but I still can have an idea of what it's about. And it's even more reassuring to see comments from physics students who find this video useful in addition to their study material. Thank you very much and keep the good work!
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Me at the half mark: "This couldn't get anymore complicated." minutephysics: "Fourier Transforms!"
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"I'm going to attempt to explain" me: brain explodes
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I HAVE UNDERSTOOD. NOTHING. AT. ALL.
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I love how he makes very hard concepts approachable. Now I’ll share this video with anyone who thinks quantum computers are basically magic
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I watch this when I’m feeling too smart To remind myself that I’m not really smart
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I did a project on shors algorithms problems and benefits, instead of trying to explain what it did, I just summed it up with "using math" 😂.
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The scary part of this is that breaking encryption is no longer a mathematical or scientific question, it’s an engineering question.
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As a physics student I clicked into this thinking it's just another super basic introductory video... Ends up thoroughly reviewing 2 weeks of solid materials from my quantum computing class Edit: Highly recommend a quantum computing class if you can take one! More of a math class than physics but still super interesting
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I think I follow. Smart computer makes maths go fast. Fast math is equal to no more computer security.
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Thanks for making this video. I took a class with Peter Shor and I still didnt understand his algorithm. But this video makes it so clear. Great work!
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Me looking at quantum computers: It’s so cute. Brutus: We must think of this quantum computer as a serpents egg, not dangerous now but will be later if not dealt with.
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Ooooh. Now I understand. That box full of little dots is where the maths come from.
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13:59 "...and I'm oversimplifying a touch here." ...Uh huh. 0_0
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Great vid, thanks minutephysics! Been following your channel since I was 9 or 10 and now I'm going into uni and your content is still great and useful.
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I'm gonna be honest I only understood a tiny bit of the math but the overall concept is really cool and I am really excited about the future of computing both quantum and "regular." Thanks for the video
