ec endomorphism tests

script/research/ec/pairing/2.2.6-endo1.sage

@@ -0,0 +1,19 @@
+q = 19
+Fq = GF(q)
+E = EllipticCurve(Fq, [0, 5])
+assert q % 3 == 1
+
+xi3 = Fq(7)
+assert xi3^3 == 1
+
+P = E(-1, 2)
+print(f"xi(P) = {E(xi3 * -1, 2)}")
+
+Fq.<x> = GF(23)[]
+Fq2.<u> = Fq.extension(x^2 + 1)
+E = EllipticCurve(Fq2, [0, 5])
+P = E(-1, 2)
+
+xi3 = 8 * u + 11
+print(f"xi(P) = {E(-xi3, 2)}")
+