How Shor's Algorithm Factors 314191
4,314
by Super User, 5 years ago
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This video explains how Shor’s Algorithm factors the pseudoprime number 314191 into its 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 https://www.scottaaronson.com/blog/?p=208
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
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Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! Created by Henry Reich
Watch the main video: https://www.youtube.com/watch?v=lvTqbM5Dq4Q
Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics
This video explains how Shor’s Algorithm factors the pseudoprime number 314191 into its 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 https://www.scottaaronson.com/blog/?p=208
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
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5 years ago
