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)
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Official URL: https://doi.org/10.1007/978-3-030-70873-3_28 |
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.
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