How to crack the RSA encryption with Shor’s algorithm

Здраво омиљена особа,

out of pure madness I am diving into the world of quantum computing. One topic that’s been grabbing my attention is Shor’s algorithm. Okay, to be honest, there is no way around it in quantum computing. It is cited over 10k times in other papers, and can quite frankly be considered the rock star of algorithms in the realm of quantum computing.
If it works, this algorithm has the power to crack two complex mathematical problems: discrete logarithms and integer factoring, which are the foundation of modern encryption methods like RSA, used to secure our online data.

This has serious implications for cybersecurity, as it challenges the security of encryption systems we rely on today…

As the paper is quite mathematically, and hard to understand, linked you a nice YouTube explainer as well.

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A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factor: It is not clear whether this is still true when quantum mechanics is taken into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored. These two problems are generally considered hard on a classical computer and have been used as the basis of several proposed cryptosystems. (We thus give the first examples of quantum crypto analysis.)

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