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, 98 insertions, 0 deletions

diff --git a/theta_lib/theta_structures/Theta_dim1.py b/theta_lib/theta_structures/Theta_dim1.py
new file mode 100644
index 0000000..e8e94dd
--- /dev/null
+++ b/theta_lib/theta_structures/Theta_dim1.py
@@ -0,0 +1,98 @@
+from sage.all import *
+from ..utilities.supersingular import compute_linearly_independent_point
+from .montgomery_theta import (
+    montgomery_point_to_theta_point,
+    theta_point_to_montgomery_point,
+    torsion_to_theta_null_point,
+)
+
+
+class ThetaStructureDim1:
+	def __init__(self,E,P=None,Q=None):
+		self.E=E
+
+		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.")
+
+		if Q==None:
+			y2=A-2
+			y=y2.sqrt()
+			Q=E([-1,y,1])
+			P=compute_linearly_independent_point(E,Q,4)
+		else:
+			if Q[0]!=-1:
+				raise ValueError("You should enter a canonical 4-torsion basis. Q[0] should be -1.")
+
+		self.P=P
+		self.Q=Q
+
+		self._base_ring=E.base_ring()
+
+		self._point=ThetaPointDim1
+		self._null_point=self._point(self,torsion_to_theta_null_point(P))
+
+	def null_point(self):
+		"""
+		"""
+		return self._null_point
+
+	def base_ring(self):
+		"""
+		"""
+		return self._base_ring
+
+	def zero(self):
+		"""
+		"""
+		return self.null_point()
+
+	def elliptic_curve(self):
+		return self.E
+
+	def torsion_basis(self):
+		return (self.P,self.Q)
+
+	def __call__(self,coords):
+		r"""
+		Input: either a tuple or list of 2 coordinates or an elliptic curve point.
+
+		Output: the corresponding theta point for the self theta structure.
+		"""
+		if isinstance(coords,tuple):
+			return self._point(self,coords)
+		elif isinstance(coords,list):
+			return self._point(self,coords)
+		else:
+			return self._point(self,montgomery_point_to_theta_point(self.null_point().coords(),coords))
+
+	def __repr__(self):
+		return f"Theta structure on {self.elliptic_curve()} with null point: {self.null_point()} induced by the 4-torsion basis {self.torsion_basis()}"
+
+	def to_montgomery_point(self,P):
+		return theta_point_to_montgomery_point(self.E,self.null_point().coords(),P.coords())
+
+
+class ThetaPointDim1:
+    def __init__(self, parent, coords):
+        """
+        """
+        if not isinstance(parent, ThetaStructureDim1):
+            raise ValueError("Entry parent should be a ThetaStructureDim1 object.")
+
+        self._parent = parent
+        self._coords = tuple(coords)
+
+
+    def coords(self):
+    	return self._coords
+
+    def __repr__(self):
+    	return f"Theta point with coordinates: {self.coords()}"
+
+
+
+
+