601.sagews

F.<a>=GF(2^5)
E=EllipticCurve(F,[0,0,1,1,1])
P = E(a^4 + 1, a^3)
Fx.<b>=GF(2^(4*5))
Ex=EllipticCurve(Fx,[0,0,1,1,1])
phi=Hom(F,Fx)(F.gen().minpoly().roots(Fx)[0][0])
Px=Ex(phi(P.xy()[0]),phi(P.xy()[1]))
O = Ex(0)
Qx = Ex(b^19 + b^18 + b^16 + b^12 + b^10 + b^9 + b^8 + b^5 + b^3 + 1, b^18 + b^13 + b^10 + b^8 + b^5 + b^4 + b^3 + b)
Px.weil_pairing(Qx,41) == b^19 + b^15 + b^9 + b^8 + b^6 + b^4 + b^3 + b^2 + 1

True

Px.weil_pairing(17*Px,41) == Fx(1)

True

Px.weil_pairing(O,41) == Fx(1)

True

Px.weil_pairing(O,40)

Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1013, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "/ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/ell_point.py", line 1554, in weil_pairing raise ValueError("points must both be n-torsion") ValueError: points must both be n-torsion