Shor’s factoring algorithm and modern cryptography. An illustration of the capabilities inherent in quantum computers
Year: 2005
Type: article
Abstract: The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (conventional) computers. In 1994 Peter Shor showed that for sufficiently large N, a quantum computer could perform the factoring with much less computational effort. This paper endeavors to explain, in a fashion comprehensible to the nonexpert, the RSA encryption protocol; the various quantum computer manipulations constituting the Shor algorithm; how the Shor algorithm performs the factoring; and the precise sense in which a quantum computer employing Shor’s algorithm can be said to accomplish the factoring of very large numbers with less computational effort than a classical computer. It is made apparent that factoring N generally requires many successive runs of the algorithm. Our analysis reveals that the probability of achieving a successful factorization on a single run is about twice as large as commonly quoted in the literature.
Source: American Journal of Physics
DOI: 10.1119/1.1891170
Author: Edward Gerjuoy
Institution: University of Pittsburgh
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2117231715