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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
commitcb6080eaa4f326d9fce5f0a9157be46e91d55e09 (patch)
tree4d080ade8db9faa0da5268ab420dad2b02a4e248 /theta_lib/isogenies_dim2/isogeny_chain_dim2.py
parentd40de259097c5e8d8fd35539560ca7c3d47523e7 (diff)
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Clean up PEGASIS submodule inclusion
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diff --git a/theta_lib/isogenies_dim2/isogeny_chain_dim2.py b/theta_lib/isogenies_dim2/isogeny_chain_dim2.py
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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 *
-from ..theta_structures.Tuple_point import TuplePoint
-from ..theta_structures.Theta_dim2 import ThetaPointDim2
-from .gluing_isogeny_dim2 import GluingThetaIsogenyDim2
-from .isogeny_dim2 import ThetaIsogenyDim2
-from ..utilities.strategy import optimised_strategy
-
-
-class IsogenyChainDim2:
- r"""
- Given (P1, P2), (Q1, Q2) in (E1 x E2)[2^(n+2)] as the generators of a kernel
- of a (2^n, 2^n)-isogeny
-
- ker(Phi) = <(P1, P2), (Q1, Q2)>
-
- Input:
-
- - kernel = TuplePoint(P1, P2), TuplePoint(Q1, Q2):
- where points are on the elliptic curves E1, E2 of order 2^(n+2)
- - n: the length of the chain
- - strategy: the optimises strategy to compute a walk through the graph of
- images and doublings with a quasli-linear number of steps
- """
-
- def __init__(self, kernel, Theta12, M, n, strategy=None):
- self.n = n
- self.E1, self.E2 = kernel[0].parent_curves()
- assert kernel[1].parent_curves() == [self.E1, self.E2]
-
- self._domain = (self.E1, self.E2)
-
- if strategy is None:
- strategy = self.get_strategy()
- self.strategy = strategy
-
- self._phis = self.isogeny_chain(kernel, Theta12, M)
-
- self._codomain=self._phis[-1]._codomain
-
- def get_strategy(self):
- return optimised_strategy(self.n)
-
- def isogeny_chain(self, kernel, Theta12, M):
- """
- Compute the isogeny chain and store intermediate isogenies for evaluation
- """
- # Extract the CouplePoints from the Kernel
- Tp1, Tp2 = kernel
-
- # Store chain of (2,2)-isogenies
- isogeny_chain = []
-
- # Bookkeeping for optimal strategy
- strat_idx = 0
- level = [0]
- ker = (Tp1, Tp2)
- kernel_elements = [ker]
-
- for k in range(self.n):
- prev = sum(level)
- ker = kernel_elements[-1]
-
- while prev != (self.n - 1 - k):
- level.append(self.strategy[strat_idx])
-
- # Perform the doublings
- Tp1 = ker[0].double_iter(self.strategy[strat_idx])
- Tp2 = ker[1].double_iter(self.strategy[strat_idx])
-
- ker = (Tp1, Tp2)
-
- # Update kernel elements and bookkeeping variables
- kernel_elements.append(ker)
- prev += self.strategy[strat_idx]
- strat_idx += 1
-
- # Compute the codomain from the 8-torsion
- Tp1, Tp2 = ker
- if k == 0:
- phi = GluingThetaIsogenyDim2(Tp1, Tp2, Theta12, M)
- else:
- phi = ThetaIsogenyDim2(Th, Tp1, Tp2)
-
- # Update the chain of isogenies
- Th = phi._codomain
- isogeny_chain.append(phi)
-
- # Remove elements from list
- kernel_elements.pop()
- level.pop()
-
- # Push through points for the next step
- kernel_elements = [(phi(T1), phi(T2)) for T1, T2 in kernel_elements]
-
- return isogeny_chain
-
- def evaluate_isogeny(self, P):
- """
- Given a point P, of type TuplePoint on the domain E1 x E2, computes the
- ThetaPointDim2 on the codomain ThetaStructureDim2.
- """
- if not isinstance(P, TuplePoint):
- raise TypeError(
- "IsogenyChainDim2 isogeny expects as input a TuplePoint on the domain product E1 x E2"
- )
- n=len(self._phis)
- for i in range(n):
- P = self._phis[i](P)
- return P
-
- def __call__(self, P):
- """
- Evaluate a TuplePoint under the action of this isogeny.
- """
- return self.evaluate_isogeny(P)
-
- def dual(self):
- domain = self._codomain
- codomain = self._domain
- n=len(self._phis)
- isogenies=[]
- for i in range(n):
- isogenies.append(self._phis[n-1-i].dual())
- return DualIsogenyChainDim2(domain, codomain, isogenies)
-
-
-class DualIsogenyChainDim2:
- def __init__(self, domain, codomain, isogenies):
- self._domain = domain
- self._codomain = codomain
- self._phis = isogenies
-
- def evaluate_isogeny(self, P):
- """
- Given a ThetaPointDim2 point P on the codomain ThetaStructureDim2,
- computes the image TuplePoint on the codomain E1 x E2.
- """
- if not isinstance(P, ThetaPointDim2):
- raise TypeError(
- "DualIsogenyChainDim2 isogeny expects as input a ThetaPointDim2."
- )
- n=len(self._phis)
- for i in range(n):
- P = self._phis[i](P)
- return P
-
- def __call__(self, P):
- """
- Evaluate a ThetaPointDim2 under the action of this isogeny.
- """
- return self.evaluate_isogeny(P)