Channel: minutephysics

Category: Science & Technology

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Description: Go to dashlane.com/minutephysics to download Dashlane for free, and use offer code minutephysics for 10% off Dashlane Premium! Support MinutePhysics on Patreon! 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 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: minutephysics.com/supporters MinutePhysics is on twitter - @minutephysics And facebook - 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