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Division polynomials on the Hessian model of elliptic curves

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Abstract

In this paper we derive formulas for the scalar multiplication by n map, denoted [n], on the Hessian model of elliptic curve. This enables to characterize n-torsion points on this curve. The computation involves three families of polynomials \(P_n\), \(Q_n\) and \(V_n\) and we show some properties on the coefficients and degrees of these polynomials. We also show some functional equations satisfied by these polynomials. As application we provide a type of mean-value theorem for the Hessian elliptic curve.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Sciences, The University of Maroua, P.O. Box 814, Maroua, Cameroon

    Perez Broon Fouazou Lontouo

  2. Department of Mathematics, Higher Teacher Training College, The University of Bamenda, P.O. Box 37, Bambili, Cameroon

    Emmanuel Fouotsa

  3. ENSAI, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon

    Daniel Tieudjo

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  1. Perez Broon Fouazou Lontouo
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  2. Emmanuel Fouotsa
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Correspondence to Perez Broon Fouazou Lontouo.

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Fouazou Lontouo, P., Fouotsa, E. & Tieudjo, D. Division polynomials on the Hessian model of elliptic curves. AAECC 34, 1–16 (2023). https://doi.org/10.1007/s00200-020-00470-8

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  • DOI: https://doi.org/10.1007/s00200-020-00470-8

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