How Shor's Algorithm Factors 314191

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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 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)
IBM on RSA
Modulo Multiplication Group Tables
Difference of squares factorization
Euclid’s Algorithm
Rational sieve for factoring
General Number field Sieve
Scott Aaronson blog post about Shor’s Algorithm
Experimental implementation of Shor’s Algorithm (factoring 15, 21, and 35)
Adiabatic Quantum Computation factoring the number 291311
Scott Aaronson course notes
Shor’s Algorithm on Quantiki
TLS And SSL use RSA encryption
Dashlane security whitepaper
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Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! Created by Henry Reich