How Shor's Algorithm Factors 314191
4,314
by Super User, 5 years ago
Watch the main video: https://www.youtube.com/watch?v=lvTqbM5Dq4Q
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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 numbertheoretic 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 (periodfinding 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/shorsfactoringalgorithm
TLS And SSL use RSA encryption https://en.wikipedia.org/wiki/TransportLayerSecurity
Dashlane security whitepaper https://www.dashlane.com/download/DashlaneSecurityWhitePaperOctober2018.pdf
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5 years ago