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Diffstat (limited to 'theta_lib/isogenies_dim2/gluing_isogeny_dim2.py')
| -rw-r--r-- | theta_lib/isogenies_dim2/gluing_isogeny_dim2.py | 292 |
1 files changed, 0 insertions, 292 deletions
diff --git a/theta_lib/isogenies_dim2/gluing_isogeny_dim2.py b/theta_lib/isogenies_dim2/gluing_isogeny_dim2.py deleted file mode 100644 index 2dac387..0000000 --- a/theta_lib/isogenies_dim2/gluing_isogeny_dim2.py +++ /dev/null @@ -1,292 +0,0 @@ -""" -This code is based on a copy of: -https://github.com/ThetaIsogenies/two-isogenies - -MIT License - -Copyright (c) 2023 Pierrick Dartois, Luciano Maino, Giacomo Pope and Damien Robert - -Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -SOFTWARE. -""" - -from sage.all import * -from ..theta_structures.Tuple_point import TuplePoint -from ..theta_structures.Theta_dim2 import ThetaStructureDim2, ThetaPointDim2 -from ..theta_structures.theta_helpers_dim2 import batch_inversion -from ..basis_change.base_change_dim2 import montgomery_to_theta_matrix_dim2, apply_base_change_theta_dim2 -from ..theta_structures.montgomery_theta import lift_kummer_montgomery_point - -class GluingThetaIsogenyDim2: - """ - Compute the gluing isogeny from E1 x E2 (Elliptic Product) -> A (Theta Model) - - Expected input: - - - (K1_8, K2_8) The 8-torsion above the kernel generating the isogeny - - M (Optional) a base change matrix, if this is not including, it can - be derived from [2](K1_8, K2_8) - """ - - def __init__(self, K1_8, K2_8, Theta12, N): - # Double points to get four-torsion, we always need one of these, used - # for the image computations but we'll need both if we wish to derived - # the base change matrix as well - K1_4 = 2*K1_8 - - # Initalise self - # This is the base change matrix for product Theta coordinates (not used, except in the dual) - self._base_change_matrix_theta = N - # Here, base change matrix directly applied to the Montgomery coordinates. null_point_bc is the - # theta null point obtained after applying the base change to the product Theta-structure. - self._base_change_matrix, null_point_bc = montgomery_to_theta_matrix_dim2(Theta12.zero().coords(),N, return_null_point = True) - self._domain_bc = ThetaStructureDim2(null_point_bc) - self.T_shift = K1_4 - self._precomputation = None - self._zero_idx = 0 - self._domain_product = Theta12 - self._domain=(K1_8[0].curve(), K1_8[1].curve()) - - # Map points from elliptic product onto the product theta structure - # using the base change matrix - T1_8 = self.base_change(K1_8) - T2_8 = self.base_change(K2_8) - - # Compute the codomain of the gluing isogeny - self._codomain = self._special_compute_codomain(T1_8, T2_8) - - def apply_base_change(self, coords): - """ - Apply the basis change by acting with matrix multiplication, treating - the coordinates as a vector - """ - N = self._base_change_matrix - x, y, z, t = coords - X = N[0, 0] * x + N[0, 1] * y + N[0, 2] * z + N[0, 3] * t - Y = N[1, 0] * x + N[1, 1] * y + N[1, 2] * z + N[1, 3] * t - Z = N[2, 0] * x + N[2, 1] * y + N[2, 2] * z + N[2, 3] * t - T = N[3, 0] * x + N[3, 1] * y + N[3, 2] * z + N[3, 3] * t - - return (X, Y, Z, T) - - def base_change(self, P): - """ - Compute the basis change on a TuplePoint to recover a ThetaPointDim2 of - compatible form - """ - if not isinstance(P, TuplePoint): - raise TypeError("Function assumes that the input is of type `TuplePoint`") - - # extract X,Z coordinates on pairs of points - P1, P2 = P.points() - X1, Z1 = P1[0], P1[2] - X2, Z2 = P2[0], P2[2] - - # Correct in the case of (0 : 0) - if X1 == 0 and Z1 == 0: - X1 = 1 - Z1 = 0 - if X2 == 0 and Z2 == 0: - X2 = 1 - Z2 = 0 - - # Apply the basis transformation on the product - coords = self.apply_base_change([X1 * X2, X1 * Z2, Z1 * X2, Z1 * Z2]) - return coords - - def _special_compute_codomain(self, T1, T2): - """ - Given twzero_matro isotropic points of 8-torsion T1 and T2, compatible with - the theta null point, compute the level two theta null point A/K_2 - """ - xAxByCyD = ThetaPointDim2.to_squared_theta(*T1) - zAtBzYtD = ThetaPointDim2.to_squared_theta(*T2) - - # Find the value of the non-zero index - zero_idx = next((i for i, x in enumerate(xAxByCyD) if x == 0), None) - self._zero_idx = zero_idx - - # Dumb check to make sure everything is OK - assert xAxByCyD[self._zero_idx] == zAtBzYtD[self._zero_idx] == 0 - - # Initialize lists - # The zero index described the permutation - ABCD = [0 for _ in range(4)] - precomp = [0 for _ in range(4)] - - # Compute non-trivial numerators (Others are either 1 or 0) - num_1 = zAtBzYtD[1 ^ self._zero_idx] - num_2 = xAxByCyD[2 ^ self._zero_idx] - num_3 = zAtBzYtD[3 ^ self._zero_idx] - num_4 = xAxByCyD[3 ^ self._zero_idx] - - # Compute and invert non-trivial denominators - den_1, den_2, den_3, den_4 = batch_inversion([num_1, num_2, num_3, num_4]) - - # Compute A, B, C, D - ABCD[0 ^ self._zero_idx] = 0 - ABCD[1 ^ self._zero_idx] = num_1 * den_3 - ABCD[2 ^ self._zero_idx] = num_2 * den_4 - ABCD[3 ^ self._zero_idx] = 1 - - # Compute precomputation for isogeny images - precomp[0 ^ self._zero_idx] = 0 - precomp[1 ^ self._zero_idx] = den_1 * num_3 - precomp[2 ^ self._zero_idx] = den_2 * num_4 - precomp[3 ^ self._zero_idx] = 1 - self._precomputation = precomp - - # Final Hadamard of the above coordinates - a, b, c, d = ThetaPointDim2.to_hadamard(*ABCD) - - return ThetaStructureDim2([a, b, c, d]) - - def special_image(self, P, translate): - """ - When the domain is a non product theta structure on a product of - elliptic curves, we will have one of A,B,C,D=0, so the image is more - difficult. We need to give the coordinates of P but also of - P+Ti, Ti one of the point of 4-torsion used in the isogeny - normalisation - """ - AxByCzDt = ThetaPointDim2.to_squared_theta(*P) - - # We are in the case where at most one of A, B, C, D is - # zero, so we need to account for this - # - # To recover values, we use the translated point to get - AyBxCtDz = ThetaPointDim2.to_squared_theta(*translate) - - # Directly compute y,z,t - y = AxByCzDt[1 ^ self._zero_idx] * self._precomputation[1 ^ self._zero_idx] - z = AxByCzDt[2 ^ self._zero_idx] * self._precomputation[2 ^ self._zero_idx] - t = AxByCzDt[3 ^ self._zero_idx] - - # We can compute x from the translation - # First we need a normalisation - if z != 0: - zb = AyBxCtDz[3 ^ self._zero_idx] - lam = z / zb - else: - tb = AyBxCtDz[2 ^ self._zero_idx] * self._precomputation[2 ^ self._zero_idx] - lam = t / tb - - # Finally we recover x - xb = AyBxCtDz[1 ^ self._zero_idx] * self._precomputation[1 ^ self._zero_idx] - x = xb * lam - - xyzt = [0 for _ in range(4)] - xyzt[0 ^ self._zero_idx] = x - xyzt[1 ^ self._zero_idx] = y - xyzt[2 ^ self._zero_idx] = z - xyzt[3 ^ self._zero_idx] = t - - image = ThetaPointDim2.to_hadamard(*xyzt) - return self._codomain(image) - - def __call__(self, P): - """ - Take into input the theta null point of A/K_2, and return the image - of the point by the isogeny - """ - if not isinstance(P, TuplePoint): - raise TypeError( - "Isogeny image for the gluing isogeny is defined to act on TuplePoints" - ) - - # Compute sum of points on elliptic curve - P_sum_T = P + self.T_shift - - # Push both the point and the translation through the - # completion - iso_P = self.base_change(P) - iso_P_sum_T = self.base_change(P_sum_T) - - return self.special_image(iso_P, iso_P_sum_T) - - def dual(self): - domain = self._codomain.hadamard() - codomain_bc = self._domain_bc.hadamard() - codomain = self._domain - - precomputation = batch_inversion(codomain_bc.null_point_dual()) - - N_split = self._base_change_matrix.inverse() - - return DualGluingThetaIsogenyDim2(domain, codomain_bc, codomain, N_split, precomputation) - - -class DualGluingThetaIsogenyDim2: - def __init__(self, domain, codomain_bc, codomain, N_split, precomputation): - self._domain = domain - self._codomain_bc = codomain_bc # Theta structure - self._codomain = codomain # Elliptic curves E1 and E2 - self._precomputation = precomputation - self._splitting_matrix = N_split - - def __call__(self,P): - # Returns a TuplePoint. - if not isinstance(P, ThetaPointDim2): - raise TypeError("Isogeny evaluation expects a ThetaPointDim2 as input") - - xx, yy, zz, tt = P.squared_theta() - - Ai, Bi, Ci, Di = self._precomputation - - xx = xx * Ai - yy = yy * Bi - zz = zz * Ci - tt = tt * Di - - image_coords = (xx, yy, zz, tt) - - X1X2, X1Z2, Z1X2, Z1Z2 = apply_base_change_theta_dim2(self._splitting_matrix, image_coords) - - E1, E2 = self._codomain - - if Z1Z2!=0: - #Z1=1, Z2=Z1Z2 - - Z2_inv=1/Z1Z2 - X2=Z1X2*Z2_inv# Normalize (X2:Z2)=(X2/Z2:1) - - X1=X1Z2*Z2_inv - - assert X1*Z1X2==X1X2 - P1 = lift_kummer_montgomery_point(E1, X1) - P2 = lift_kummer_montgomery_point(E2, X2) - return TuplePoint(P1,P2) - elif Z1X2==0 and X1Z2!=0: - # Case (X1:Z1)=0, X1!=0 and (X2:Z2)!=0 - - X2=X1X2/X1Z2 - P2 = lift_kummer_montgomery_point(E2, X2) - return TuplePoint(E1(0),P2) - elif Z1X2!=0 and X1Z2==0: - # Case (X1:Z1)!=0 and (X2:Z2)=0, X2!=0 - - X1=X1X2/Z1X2 - P1 = lift_kummer_montgomery_point(E1, X1) - return TuplePoint(P1,E2(0)) - else: - return TuplePoint(E1(0),E2(0)) - - - - - |