Elliptic curves over the ring R

  • A. Boulbot Sidi Mohamed Ben Abdellah University Polydisciplinary Faculty of Taza FPT Laboratory of Engineering Sciences LSI
  • Abdelhakim Chillali Sidi Mohamed Ben Abdellah University Polydisciplinary Faculty of Taza FPT Laboratory of Engineering Sciences LSI http://orcid.org/0000-0002-2033-0280
  • A. Mouhib Sidi Mohamed Ben Abdellah University Polydisciplinary Faculty of Taza FPT Laboratory of Engineering Sciences LSI

Resumen

Let Fq be a finite field of q elements, where q is a power of a prime number p greater than or equal to 5. In this paper, we study the elliptic curve denoted Ea,b(Fq[e]) over the ring Fq[e], where e2 = e and (a,b) ∈ (Fq[e])2. In a first time, we study the arithmetic of this ring. In addition, using the Weierstrass equation, we define the elliptic curve Ea,b(Fq[e]) and we will show that Eπ0(a),π0(b)(Fq) and Eπ1(a),π1(b)(Fq) are two elliptic curves over the field Fq, where π0 and π1 are respectively the canonical projection and the sum projection of coordinates of X ∈Fq[e]. Precisely, we give a bijection between the sets Ea,b(Fq[e]) and Eπ0(a),π0(b)(Fq)×Eπ1(a),π1(b)(Fq).

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Biografía del autor/a

Abdelhakim Chillali, Sidi Mohamed Ben Abdellah University Polydisciplinary Faculty of Taza FPT Laboratory of Engineering Sciences LSI
Department of Mathematics, Physical and Computer FP, LSI, Taza Morocco
Publicado
2019-02-18
Sección
Research Articles