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For these methods, quantum computing is not a fatal threat, because an adversary must still engage in brute-force search.
But there is a quantum shortcut, called Grover’s Algorithm, that can speed up any brute-force search substantially, allowing a space of a given size to be searched in an amount of time proportional to the square root of that size.
So the arrival of practical quantum computers would change some of the tradeoffs involved in designing algorithms, including cryptographic algorithms.
As described below, cryptography experts in government, industry, and academia have been working for years to prepare for the potential arrival of quantum computers, although much work remains to be done. As of yet, nobody has succeeded in building a quantum computer that is large enough or fast enough to offer any practical advantages over (or even parity with) classical computers.
The effect of quantum computing on the security of an encryption algorithm depends on how large of an effect quantum computing will have on the time required for nonkeyholders to find the secret key.
In this case, it is possible to compensate for the effect of quantum computing by increasing the key size, expanding the space that must be searched by brute force, so as to counteract the effect of Grover’s Algorithm.
The product of multiplying P and Q is published, but it is assumed that an adversary who knows the product of P and Q cannot derive the factors P and Q from that product except by a variant of brute-force search.