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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)
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
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