Elif Ozbay GurlerHüseyin HişilOzbay Gurler, ElifHisil, HuseyinGurler, Elif Ozbay2025-10-06202421908516, 219085082190-85082190-851610.1007/s13389-024-00351-72-s2.0-85190543677https://www.scopus.com/inward/record.uri?eid=2-s2.0-85190543677&doi=10.1007%2Fs13389-024-00351-7&partnerID=40&md5=e68dccb07efc8a63f70e919f17714350https://gcris.yasar.edu.tr/handle/123456789/8219https://doi.org/10.1007/s13389-024-00351-7This manuscript provides complete inversion-free and explicit group law formulas in Jacobian coordinates for the genus 2 hyperelliptic curves of the form y2=x5+a<inf>3</inf>x3+a<inf>2</inf>x2+a<inf>1</inf>x+a<inf>0</inf> over a field K with char(K)≠2. The formulas do not require the use of polynomial arithmetic operations such as resultant mod or gcd computations but only operations in K. © 2024 Elsevier B.V. All rights reserved.Englishinfo:eu-repo/semantics/openAccessExplicit Formulas, Genus 2, Group Law, Hyperelliptic Curves, Jacobian Coordinates, Arithmetic Operations, Explicit Formula, Genus 2, Group Law, Hyper-elliptic Curves, Jacobian Coordinate, Jacobians, Polynomial Arithmetic, GeometryArithmetic operations, Explicit formula, Genus 2, Group law, Hyper-elliptic curves, Jacobian coordinate, Jacobians, Polynomial arithmetic, GeometryGenus 2Group LawExplicit FormulasHyperelliptic CurvesJacobian CoordinatesArticle