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How Quantum Computers Break Encryption | Shor's Algorithm Explained

minutephysics
5.85M subscribers
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3.2M views 5 years ago
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!   / 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) https://en.wikipedia.org/wiki/RSA_num... IBM on RSA https://www.ibm.com/support/knowledge... Modulo Multiplication  …...more
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How Quantum Computers Break Encryption | Shor's Algorithm Explained
97KLikes
3,213,061Views
2019Apr 30
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!   / 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) https://en.wikipedia.org/wiki/RSA_num... IBM on RSA https://www.ibm.com/support/knowledge... Modulo Multiplication Group Tables http://mathworld.wolfram.com/ModuloMu... Difference of squares factorization https://en.wikipedia.org/wiki/Differe... Euclid’s Algorithm https://en.wikipedia.org/wiki/Euclide... Rational sieve for factoring https://en.wikipedia.org/wiki/Rationa... General Number field Sieve https://en.wikipedia.org/wiki/General... Scott Aaronson blog post about Shor’s Algorithm https://www.scottaaronson.com/blog/?p... 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/c... Shor’s Algorithm on Quantiki https://www.quantiki.org/wiki/shors-f... TLS And SSL use RSA encryption https://en.wikipedia.org/wiki/Transpo... Dashlane security whitepaper https://www.dashlane.com/download/Das... Link to Patreon Supporters: http://www.minutephysics.com/supporters/ MinutePhysics is on twitter - @minutephysics And facebook -   / 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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minutephysics

5.85M subscribers