Integer factorization algorithms | Quantum algorithms | Post-quantum cryptography
Shor's algorithm is a quantum computer algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. On a quantum computer, to factor an integer , Shor's algorithm runs in polynomial time, meaning the time taken is polynomial in , the size of the integer given as input. Specifically, it takes quantum gates of order using fast multiplication, or even utilizing the asymptotically fastest multiplication algorithm currently known due to Harvey and Van Der Hoven, thus demonstrating that the integer factorization problem can be efficiently solved on a quantum computer and is consequently in the complexity class BQP. This is almost exponentially faster than the most efficient known classical factoring algorithm, the general number field sieve, which works in sub-exponential time: . The efficiency of Shor's algorithm is due to the efficiency of the quantum Fourier transform, and modular exponentiation by repeated squarings. If a quantum computer with a sufficient number of qubits could operate without succumbing to quantum noise and other quantum-decoherence phenomena, then Shor's algorithm could be used to break public-key cryptography schemes, such as * The RSA scheme * The Finite Field Diffie-Hellman key exchange * The Elliptic Curve Diffie-Hellman key exchange RSA is based on the assumption that factoring large integers is computationally intractable. As far as is known, this assumption is valid for classical (non-quantum) computers; no classical algorithm is known that can factor integers in polynomial time. However, Shor's algorithm shows that factoring integers is efficient on an ideal quantum computer, so it may be feasible to defeat RSA by constructing a large quantum computer. It was also a powerful motivator for the design and construction of quantum computers, and for the study of new quantum-computer algorithms. It has also facilitated research on new cryptosystems that are secure from quantum computers, collectively called post-quantum cryptography. In 2001, Shor's algorithm was demonstrated by a group at IBM, who factored into , using an NMR implementation of a quantum computer with qubits. After IBM's implementation, two independent groups implemented Shor's algorithm using photonic qubits, emphasizing that multi-qubit entanglement was observed when running the Shor's algorithm circuits. In 2012, the factorization of was performed with solid-state qubits. Later, in 2012, the factorization of was achieved. In 2019 an attempt was made to factor the number using Shor's algorithm on an IBM Q System One, but the algorithm failed because of accumulating errors. Though larger numbers have been factored by quantum computers using other algorithms, these algorithms are similar to classical brute-force checking of factors, so unlike Shor's algorithm, they are not expected to ever perform better than classical factoring algorithms. (Wikipedia).
Understanding and computing the Riemann zeta function
In this video I explain Riemann's zeta function and the Riemann hypothesis. I also implement and algorithm to compute the return values - here's the Python script:https://gist.github.com/Nikolaj-K/996dba1ff1045d767b10d4d07b1b032f
From playlist Programming
Solving a logarithm with a fraction
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
How Quantum Computers Break Encryption | Shor's Algorithm Explained
Go to http://www.dashlane.com/minutephysics to download Dashlane for free, and use offer code minutephysics for 10% off Dashlane Premium! Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics This video explains Shor’s Algorithm, a way to efficiently factor large pseudop
From playlist MinutePhysics
Hacking at Quantum Speed with Shor's Algorithm | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Classical computers struggle to crack modern encryption. But quantum computers using Shor’s Algorithm make short work of RSA cryptography. Find out how. Tweet at us! @
From playlist Cryptography 101
Find all the solutions of trig equation with cotangent
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include by factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given
From playlist Solve Trigonometric Equations
How Shor's Algorithm Factors 314191
Go to http://www.dashlane.com/minutephysics to download Dashlane for free, and use offer code minutephysics for 10% off Dashlane Premium! Watch the main video: https://www.youtube.com/watch?v=lvTqbM5Dq4Q Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics This video ex
From playlist MinutePhysics
Are Quantum Computers Really A Threat To Cryptography?
Shor's Algorithm for factoring integer numbers is the big threat to cryptography (RSA/ECC) as it reduces the complexity from exponential to polynomial, which means a Quantum Computer can reduce the time to crack RSA-2048 to a mere 10 seconds. However current noisy NISQ type quantum compute
From playlist Blockchain
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Solving a trigonometric equation with applying pythagorean identity
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
Solving a trig function with sine and cosine
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
Building an Infinite Bridge | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Using the harmonic series we can build an infinitely long bridge. It takes a very long time though. A faster method was discovered in 2009. Tweet at us! @pbsinfinite F
From playlist An Infinite Playlist
Isolating a logarithm and using the power rule to solve
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
The Map of Quantum Computing | Quantum Computers Explained
An excellent summary of the field of quantum computing. Find out more about Qiskit at https://qiskit.org and their YouTube channel https://www.youtube.com/c/qiskit And get the poster here: https://store.dftba.com/collections/domain-of-science/products/map-of-quantum-computing With this vi
From playlist Quantum Physics Videos - Domain of Science
Solving an logarithmic equation
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Stanford Seminar - How to Compute with Schrödinger's Cat: An Introduction to Quantum Computing
"How to Compute with Schrödinger's Cat: An Introduction to Quantum Computing" - Eleanor Rieffel of NASA Ames Research & Wolfgang Polak, Independent Consultant About the talk: The success of the abstract model of classical computation in terms of bits, logical operations, algorithms, and
From playlist Engineering
We compute cos(3pi/4) by hand. We don't use a calculator at all and only use trigonometry. I hope this helps someone who is learning trig. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affiliate links) ***********Math, Physics, and C
From playlist Computing Trigonometric Function Values
How to Break Cryptography | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Only 4 steps stand between you and the secrets hidden behind RSA cryptography. Find out how to crack the world’s most commonly used form of encryption. Tweet at us! @p
From playlist Cryptography 101
Quantum Computing 'Magic' - Computerphile
Quantum Computing offers a potential sea-change in computer power, but what are the issues with it, why aren't we all using quantum iphones already? Associate Professor Dr Thorsten Altenkirch. Link to more information & Quantum IO Monad Code: http://bit.ly/Computerphile_QIOMonad *From Th
From playlist Subtitled Films
Solve a Bernoulli Differential Equation (Part 2)
This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
Quantum computing with noninteracting particles - Alex Arkhipov
Alex Arkhipov Massachusetts Institute of Technology February 9, 2015 We introduce an abstract model of computation corresponding to an experiment in which identical, non-interacting bosons are sent through a non-adaptive linear circuit before being measured. We show that despite the very
From playlist Mathematics