How Quantum Computers Break Encryption | Shor's Algorithm Explained

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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_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...


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