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ECM Factorization with QRT Maps

Hone, Andrew N.W. (2020) ECM Factorization with QRT Maps. Transactions on Computational Science and Computational Intelligence, . ISSN 2569-7072. (In press) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:81861)

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Language: English

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Abstract

Quispel-Roberts-Thompson (QRT) maps are a family of birational maps of the plane which provide the simplest discrete analogue of an integrable Hamiltonian system, and are associated with elliptic fibrations in terms of biquadratic curves. Each generic orbit of a QRT map corresponds to a sequence of points on an elliptic curve. In this preliminary study, we explore versions of the elliptic curve method (ECM) for integer factorization based on performing scalar multiplication of a point on an elliptic curve by iterating three different QRT maps with particular initial data. Pseudorandom number generation and other possible applications are briefly discussed.

Item Type: Article
Projects: Projects 26013 not found.
Uncontrolled keywords: elliptic curve method, scalar multiplication, QRT map
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QA Mathematics (inc Computing science) > QA101 Arithmetic
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra > QA241 Number theory
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew Hone
Date Deposited: 25 Jun 2020 08:46 UTC
Last Modified: 26 Jun 2020 11:57 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/81861 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
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