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authorPierrick-Dartois <pierrickdartois@icloud.com>2025-05-22 18:51:58 +0200
committerPierrick-Dartois <pierrickdartois@icloud.com>2025-05-22 18:51:58 +0200
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tree4d080ade8db9faa0da5268ab420dad2b02a4e248 /theta_lib/isogenies_dim2/isogeny_dim2.py
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Clean up PEGASIS submodule inclusion
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-"""
-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 ZZ
-from ..theta_structures.Theta_dim2 import ThetaStructureDim2, ThetaPointDim2
-from ..theta_structures.theta_helpers_dim2 import batch_inversion
-
-
-class ThetaIsogenyDim2:
- def __init__(self, domain, T1_8, T2_8, hadamard=(False, True)):
- """
- Compute a (2,2)-isogeny in the theta model. Expects as input:
-
- - domain: the ThetaStructureDim2 from which we compute the isogeny
- - (T1_8, T2_8): points of 8-torsion above the kernel generating the isogeny
-
- When the 8-torsion is not available (for example at the end of a long
- (2,2)-isogeny chain), the the helper functions in isogeny_sqrt.py
- must be used.
-
- NOTE: on the hadamard bools:
-
- The optional parameter 'hadamard' controls if we are in standard or dual
- coordinates, and if the codomain is in standard or dual coordinates. By
- default this is (False, True), meaning we use standard coordinates on
- the domain A and the codomain B.
-
- The kernel is then the kernel K_2 where the action is by sign. Other
- possibilities: - (False, False): standard coordinates on A, dual
- coordinates on B - (True, True): start in dual coordinates on A
- (alternatively: standard coordinates on A but quotient by K_1 whose
- action is by permutation), and standard coordinates on B. - (True,
- False): dual coordinates on A and B
-
- These can be composed as follows for A -> B -> C:
-
- - (False, True) -> (False, True) (False, False) -> (True, True):
- - standard coordinates on A and C,
- - standard/resp dual coordinates on B
- - (False, True) -> (False, False) (False, False) -> (True, False):
- - standard coordinates on A,
- - dual coordinates on C,
- - standard/resp dual coordinates on B
- - (True, True) -> (False, True) (True, False) -> (True, True):
- - dual coordinates on A,
- - standard coordinates on C,
- - standard/resp dual coordiantes on B
- - (True, True) -> (False, False) (True, False) -> (True, False):
- - dual coordinates on A and C
- - standard/resp dual coordinates on B
-
- On the other hand, these gives the multiplication by [2] on A:
-
- - (False, False) -> (False, True) (False, True) -> (True, True):
- - doubling in standard coordinates on A
- - going through dual/standard coordinates on B=A/K_2
- - (True, False) -> (False, False) (True, True) -> (True, False):
- - doubling in dual coordinates on A
- - going through dual/standard coordinates on B=A/K_2
- (alternatively: doubling in standard coordinates on A going
- through B'=A/K_1)
- - (False, False) -> (False, False) (False, True) -> (True, False):
- - doubling from standard to dual coordinates on A
- - (True, False) -> (False, True) (True, True) -> (True, True):
- - doubling from dual to standard coordinates on A
- """
- if not isinstance(domain, ThetaStructureDim2):
- raise ValueError
- self._domain = domain
-
- self._hadamard = hadamard
- self._precomputation = None
- self._codomain = self._compute_codomain(T1_8, T2_8)
-
- def _compute_codomain(self, T1, T2):
- """
- Given two isotropic points of 8-torsion T1 and T2, compatible with
- the theta null point, compute the level two theta null point A/K_2
- """
- if self._hadamard[0]:
- xA, xB, _, _ = ThetaPointDim2.to_squared_theta(
- *ThetaPointDim2.to_hadamard(*T1.coords())
- )
- zA, tB, zC, tD = ThetaPointDim2.to_squared_theta(
- *ThetaPointDim2.to_hadamard(*T2.coords())
- )
- else:
- xA, xB, _, _ = T1.squared_theta()
- zA, tB, zC, tD = T2.squared_theta()
-
- if not self._hadamard[0] and self._domain._precomputation:
- # Batch invert denominators
- xA_inv, zA_inv, tB_inv = batch_inversion([xA, zA, tB])
-
- # Compute A, B, C, D
- A = ZZ(1)
- B = xB * xA_inv
- C = zC * zA_inv
- D = tD * tB_inv * B
-
- _, _, _, BBinv, CCinv, DDinv = self._domain._arithmetic_precomputation()
- B_inv = BBinv * B
- C_inv = CCinv * C
- D_inv = DDinv * D
- else:
- # Batch invert denominators
- xA_inv, zA_inv, tB_inv, xB_inv, zC_inv, tD_inv = batch_inversion([xA, zA, tB, xB, zC, tD])
-
- # Compute A, B, C, D
- A = ZZ(1)
- B = xB * xA_inv
- C = zC * zA_inv
- D = tD * tB_inv * B
- B_inv = xB_inv * xA
- C_inv = zC_inv * zA
- D_inv = tD_inv * tB * B_inv
-
- # NOTE: some of the computations we did here could be reused for the
- # arithmetic precomputations of the codomain However, we are always
- # in the mode (False, True) except the very last isogeny, so we do
- # not lose much by not doing this optimisation Just in case we need
- # it later:
- # - for hadamard=(False, True): we can reuse the arithmetic
- # precomputation; we do this already above
- # - for hadamard=(False, False): we can reuse the arithmetic
- # precomputation as above, and furthermore we could reuse B_inv,
- # C_inv, D_inv for the precomputation of the codomain
- # - for hadamard=(True, False): we could reuse B_inv, C_inv, D_inv
- # for the precomputation of the codomain
- # - for hadamard=(True, True): nothing to reuse!
-
- self._precomputation = (B_inv, C_inv, D_inv)
- if self._hadamard[1]:
- a, b, c, d = ThetaPointDim2.to_hadamard(A, B, C, D)
- return ThetaStructureDim2([a, b, c, d], null_point_dual=[A, B, C, D])
- else:
- return ThetaStructureDim2([A, B, C, D])
-
- 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, ThetaPointDim2):
- raise TypeError("Isogeny evaluation expects a ThetaPointDim2 as input")
-
- if self._hadamard[0]:
- xx, yy, zz, tt = ThetaPointDim2.to_squared_theta(
- *ThetaPointDim2.to_hadamard(*P.coords())
- )
- else:
- xx, yy, zz, tt = P.squared_theta()
-
- Bi, Ci, Di = self._precomputation
-
- yy = yy * Bi
- zz = zz * Ci
- tt = tt * Di
-
- image_coords = (xx, yy, zz, tt)
- if self._hadamard[1]:
- image_coords = ThetaPointDim2.to_hadamard(*image_coords)
- return self._codomain(image_coords)
-
- def dual(self):
- # Returns the dual isogeny (domain and codomain are inverted).
- # By convention, the new domain and codomain are in standard coordinates.
- if self._hadamard[1]:
- domain=self._codomain.hadamard()
- else:
- domain=self._codomain
- if self._hadamard[0]:
- codomain=self._domain
- else:
- codomain=self._domain.hadamard()
-
- precomputation = batch_inversion(self._domain.null_point().coords())
-
- return DualThetaIsogenyDim2(domain,codomain,precomputation)
-
-class DualThetaIsogenyDim2:
- def __init__(self,domain,codomain,precomputation):
- self._domain=domain
- self._codomain=codomain
- self._precomputation=precomputation
-
- def __call__(self,P):
- 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)
- image_coords = ThetaPointDim2.to_hadamard(*image_coords)
-
- return self._codomain(image_coords)
-
-