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Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Open Access Research Article

A quantum algorithm for computing multiplicative order of integers modulo a prime

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pp. 573–584Vol. 26Issue 2March 2022DOI: 10.47974/JDMSC-1557 Crossmark XML
Received:
05 Jul 2021
Accepted:
05 Jan 2022
Published Online:
30 Mar 2023
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1557
Pages:
573–584

Abstract

One of the challenging problems in number theory is to compute efficiently multiplicative order of integers modulo a prime. This problem was listed under open problems in the number theoretic complexity II proposed by Leonard M. Adleman and Kevin S.McCurley in 1994. This paper offers a polynomial-time quantum algorithm for computing the order k = min {x|x∈N, ax ≡ 1(mod p)}, if p∈ Primes and gcd(a,p) = 1, where a, p∈N, and it requires O((log2p)2+O(1)) quantum operations.

Keywords

Subject Classifications

2020 - 11F0668Q1268Q30

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