Open AccessThe binary operations calculus in H
Author(s) -
Abdelâli Grini,
Abdelhakim Chillali,
Hakima Mouanis
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.52539
Subject(s) - hessian matrix , mathematics , binary number , prime (order theory) , calculus (dental) , ring (chemistry) , discrete mathematics , pure mathematics , combinatorics , arithmetic , medicine , chemistry , dentistry , organic chemistry
Let Fq be a nite eld of q elements, where q is a power of a prime number p greater than or equal to 5, such that −3 is not a square in Fp. In this paper, we will study the twisted Hessian curve over the ring R2 = Fq[e], where the relation e^2 = 0. More precisely, we will give many various explicit formulas, which describe the binary operations calculus in H2a,d, where H2a,d is the twisted Hessian curve over R2, and we will reduce the cost of the complexity of the calculus in H2a,d.