Initial Commit

Co-Authored-By: Damien Robert <Damien.Olivier.Robert+git@gmail.com>
Co-Authored-By: Frederik Vercauteren <frederik.vercauteren@gmail.com>
Co-Authored-By: Jonathan Komada Eriksen <jonathan.eriksen97@gmail.com>
Co-Authored-By: Pierrick Dartois <pierrickdartois@icloud.com>
Co-Authored-By: Riccardo Invernizzi <nidadoni@gmail.com>
Co-Authored-By: Ryan Rueger <git@rueg.re>                                                                                                                                           [0.01s]
Co-Authored-By: Benjamin Wesolowski <benjamin@pasch.umpa.ens-lyon.fr>
Co-Authored-By: Arthur Herlédan Le Merdy <ahlm@riseup.net>
Co-Authored-By: Boris Fouotsa <tako.fouotsa@epfl.ch>

1 files changed, 68 insertions, 0 deletions

diff --git a/theta_lib/theta_structures/montgomery_theta.py b/theta_lib/theta_structures/montgomery_theta.py
new file mode 100644
index 0000000..6dddb2b
--- /dev/null
+++ b/theta_lib/theta_structures/montgomery_theta.py
@@ -0,0 +1,68 @@
+from sage.all import *
+
+def torsion_to_theta_null_point(P):
+	r=P[0]
+	s=P[2]
+	return (r+s,r-s)
+
+def montgomery_point_to_theta_point(O,P):
+	if P[0]==P[2]==0:
+		return O
+	else:
+		a,b=O
+		return (a*(P[0]-P[2]),b*(P[0]+P[2]))
+
+def theta_point_to_montgomery_point(E,O,P,twist=False):
+	a,b=O
+
+	x=a*P[1]+b*P[0]
+	z=a*P[1]-b*P[0]
+
+	if twist:
+		x=-x
+
+	if z==0:
+		return E(0)
+	else:
+		x=x/z
+
+		a_inv=E.a_invariants()
+		
+		A =a_inv[1]
+		if a_inv != (0,A,0,1,0):
+			raise ValueError("The elliptic curve E is not in the Montgomery model.")
+
+		y2=x*(x**2+A*x+1)
+		if not is_square(y2):
+			raise ValueError("The Montgomery point is not on the base field.")
+		else:
+			y=y2.sqrt()
+			return E([x,y,1])
+
+def lift_kummer_montgomery_point(E,x,z=1):
+	if z==0:
+		return E(0)
+	elif z!=1:
+		x=x/z
+
+	a_inv=E.a_invariants()
+		
+	A =a_inv[1]
+	if a_inv != (0,A,0,1,0):
+		raise ValueError("The elliptic curve E is not in the Montgomery model.")
+
+	y2=x*(x**2+A*x+1)
+	if not is_square(y2):
+		raise ValueError("The Montgomery point is not on the base field.")
+	else:
+		y=y2.sqrt()
+		return E([x,y,1])
+
+def null_point_to_montgomery_coeff(a,b):
+	return -2*(a**4+b**4)/(a**4-b**4)
+
+
+
+
+
+