Year: 2021
Type: preprint
Abstract: Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the Carmichael function for any integer $N$ with a probability as close to 1 as desired. The algorithm requires $O((\log n )^3n^3)$ quantum operations, or $O(\log\log n (\log n)^4 n^2)$ operations using fast multiplication. Verification, quantum optimizations and applications to RSA and primality tests are also discussed.
Source: arXiv (Cornell University)
Author: Garcia-Escartin, Juan Carlos
Institution: Universidad de Valladolid
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1378648301, G146946678, G5805502524
OpenAlex ID: W3209352128