How Shor's Algorithm Factors 314191

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