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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
www.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
www.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
www.scottaaronson.com/qclec/
www.scottaaronson.com/qclec/combined.pdf
Shor’s Algorithm on Quantiki
www.quantiki.org/wiki/shors-factoring-algorithm
TLS And SSL use RSA encryption
en.wikipedia.org/wiki/TransportLayerSecurity
Dashlane security whitepaper
www.dashlane.com/download/DashlaneSecurityWhitePaperOctober2018.pdf
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