The binary operations calculus in H

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, 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.