Research Communication | Open Access
Volume 2021 | Communication ID 322
Volume 2021 | Communication ID 322
| Elliptic Curves Over the Ring F_q [a] |
Zakariae Cheddour, Abdelhakim Chillali, Ali Mouhib
Received |
Accepted |
Published |
February 27, 2021 |
March 10, 2021 |
March 15, 2021 |
Abstract: Let F_q be a finite field, where q is a power of a prime number p such that p > 5. In this paper, we study the elliptic curve denoted E_(a,b) (F_q [α]) over the ring F_q [α], where α is algebraic over F_q and (a,b)∈〖(F_q [α])〗^×. More precisely we will define an internal composition law denoted by * on the set F_q [α] , and we study the arithmetic of this ring. In addition, using the Weierstrass equation, we define the elliptic curve 〖E_(a,b) (F〗_q [α]) and we will show that 〖E_(φ_k (a),φ_k (b)) (F〗_q) are elliptic curves over the field F_q, where φ_k are the sum ...