22 lines
1.7 KiB
Markdown
22 lines
1.7 KiB
Markdown
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We have presented Shor’s algorithm as a Las Vegas algorithm, which means that the output is always correct and the expected runtime is finite. With a small modification, it can be presented as a Monte Carlo algorithm, which means that the output may be incorrect with a certain probability.
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- Shor's algorithm is a quantum computer algorithm for integer factorization. Informally, it solves the following problem: Given an integer, find its prime factors. It was invented in 1994 by the American mathematician Peter Shor. On a quantum computer, to factor an integer, Shor's algorithm runs in polynomial time. -search unordered list in square root n time rather than searching every element which leads to O(n)
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- The algorithm that quantum computers can effectively use to solve various problems that we have set up in society today. Essentially, our entire system is set up on mathematics; therefore, with this algorithm, a quantum computer can solve issues of factorization, discrete log, elliptical curve and more which means all RSA encrypted cryptosystems could easily be broken.
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Shor’s Algorithm for Discrete Logarithm
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The full paper on Shor’s algorithms was published in 1997 and has described not only an
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algorithm for integer factoring but also an exponentially faster algorithm for discrete logarithm.
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It is a remarkable and celebrated scientific contribution to quantum computing, but the algo-
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rithm for discrete logarithm has not been described in many books. Some papers apply this
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algorithm to cryptography.
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---
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## Code implementations of Shor's Algorithm
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The full description of the code can be found [here](https://qiskit.org/textbook/ch-algorithms/shor.html) in the qisket textbook.
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