Afterwards, in the next decade, the concept has drawn an increased level of interest due to the

Shor's algorithm, which, if it had been put into practice using a quantum computing machine, it would have risked decrypting classified data due to the exponential computational speedup potential offered by quantum computing [1].

But sufficiently advanced quantum computers could crack even 4,096-bit key pairs in just a few hours using a method called

Shor's algorithm.

Quantum computer can break RSA using

Shor's algorithm.

A quantum system, once it exists, may use

Shor's algorithm to solve this problem in polynomial time [11].

The computer uses laser pulses to carry out

Shor's algorithm on each atom, to correctly factor the number 15.

The algorithm has no practical application, but Tame says the work is a step toward implementing quantum software such as

Shor's algorithm (SN Online: 4/10/14), which has implications for data encryption.

Shor's Algorithm with a quantum computer, however, uses exotic-sounding math -- Hadamard and Quantum Fourier Transformations -- to quickly discover the probabilities of various number pairs being the factors or keys.

Without them, one can reduce the [FP.sup.G.sub.g,h] problem to the DLP problems over the cyclic groups <g> and <h>, which are quantumly tractable by using

Shor's algorithm [31].

While

Shor's algorithm may be of more immediate utility, Grover's algorithm seems more interesting in a theoretical sense, as it highlights an area of fundamental superiority in quantum computation.

On the theoretical side, we have, as an outgrowth of Bell's theorem, the constantly improving classification of entangled states, and the development of measures of entropy and information content of such states; GHZ states,

Shor's algorithm, various sorting techniques, and error-correcting codes.

This idea is exploited in

Shor's algorithm, which uses a quantum Fourier transformation to obtain the period of f.

"(https://en.wikipedia.org/wiki/Shor%27s_algorithm)

Shor's algorithm can break existing cryptography with less than 2000 qubits.