CLASSIFICATION OF ELEMENTS IN ELLIPTIC CURVE OVER THE RING F
| dc.contributor.author | Bilel Selikh | |
| dc.contributor.author | Douadi Mihoubi | |
| dc.date.accessioned | 2022-07-17T09:46:10Z | |
| dc.date.available | 2022-07-17T09:46:10Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | Let Fq["] := Fq[X]/(X4 − X3) be a finite quotient ring where "4 = "3, with Fq is a finite field of order q such that q is a power of a prime number p greater than or equal to 5. In this work, we will study the elliptic curve over Fq["], "4 = "3 of characteristic p 6= 2, 3 given by homogeneous Weierstrass equation of the form Y 2Z = X3 + aXZ2 + bZ3 where a and b are parameters taken in Fq["]. Firstly, we study the arithmetic operation of this ring. In addition, we define the elliptic curve Ea,b(Fq["]) and we will show that E 0(a), 0(b)(Fq) and E 1(a), 1(b)(Fq) are two elliptic curves over the finite field Fq, such that 0 is a canonical projection and 1 is a sum projection of coordinate of element in Fq["]. Precisely, we give a classification of elements in elliptic curve over the finite ring Fq["]. | en_US |
| dc.identifier.uri | http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/30478 | |
| dc.publisher | Université de M'sila | en_US |
| dc.subject | elliptic curves, finite ring, finite field, projective space. 2010Mathematics Subject Classification: 14H52, 11T55, 20K30, 20K27 | en_US |
| dc.title | CLASSIFICATION OF ELEMENTS IN ELLIPTIC CURVE OVER THE RING F | en_US |
| dc.type | Article | en_US |