2020/01/24 by Andrew N. W. Hone, Hone, Andrew N. W.
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Cryptography and Residue Arithmetic #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #nlin.SI
paper · pdf · doi:10.48550/arxiv.2001.09076
14 pages, full version for FCS'20 proceedings
openalex publication_date 2020/01/24 · arxiv created 2020/07/15 · arxiv updated 2020/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 iterating three different QRT maps with particular initial data. Pseudorandom number generation and other possible applications are briefly discussed.