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ECM Factorization with QRT Maps

Hone, Andrew N.W. (2021) ECM Factorization with QRT Maps. In: Advances in Software Engineering, Education, and e-Learning. Transactions on Computational Science and Computational Intelligence. Springer. ISBN 978-3-030-70872-6. (doi:10.1007/978-3-030-70873-3_28) (KAR id:81861)


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: Book section
DOI/Identification number: 10.1007/978-3-030-70873-3_28
Projects: Cluster algebras with periodicity and discrete dynamics over finite fields
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: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: Engineering and Physical Sciences Research Council (
Depositing User: Andrew Hone
Date Deposited: 25 Jun 2020 08:46 UTC
Last Modified: 12 Jul 2022 10:41 UTC
Resource URI: (The current URI for this page, for reference purposes)

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