minutephysics | How Quantum Computers Break Encryption | Shor's Algorithm Explained @MinutePhysics | Uploaded 5 years ago | Updated 2 hours ago
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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
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
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
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
scottaaronson.com/qclec
scottaaronson.com/qclec/combined.pdf
Shor’s Algorithm on Quantiki
quantiki.org/wiki/shors-factoring-algorithm
TLS And SSL use RSA encryption
en.wikipedia.org/wiki/TransportLayerSecurity
Dashlane security whitepaper
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
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)
en.wikipedia.org/wiki/RSA_numbers
IBM on RSA
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
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
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
scottaaronson.com/qclec
scottaaronson.com/qclec/combined.pdf
Shor’s Algorithm on Quantiki
quantiki.org/wiki/shors-factoring-algorithm
TLS And SSL use RSA encryption
en.wikipedia.org/wiki/TransportLayerSecurity
Dashlane security whitepaper
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
