Cryptography over the elliptic curve Ea,b(A3)

In this work, we are going to study the elliptic curves over the ring A3=(F2d[X])/(X3), precisely we will establish the short exact sequence which is split, and we will define the group extension Ea,b(A3) of Ea0,b0(F2d) by Ker(π3) which seems to be beneficial and interesting in ECC.