2 files changed, 21 insertions, 14 deletions

diff --git a/pyecsca/ec/formula/fake.py b/pyecsca/ec/formula/fake.py
index a07c5ed..9ea7934 100644
--- a/pyecsca/ec/formula/fake.py
+++ b/pyecsca/ec/formula/fake.py
@@ -2,6 +2,7 @@
 
 from abc import ABC
 from typing import Any, Tuple
+from functools import cache
 
 from public import public
 
@@ -26,7 +27,7 @@ class FakeFormula(Formula, ABC):
     No matter what the input point is, it just returns the right amount of FakePoints.
 
     Useful for computing with the scalar multipliers without having concrete formulas
-    and points (for example to get the addition chain via the :py:class:`~.MultipleContext`).
+    and points (for example, to get the addition chain via the :py:class:`~.MultipleContext`).
     """
 
     def __init__(self, coordinate_model):
@@ -36,12 +37,10 @@ class FakeFormula(Formula, ABC):
 
     def __call__(self, field: int, *points: Any, **params: Mod) -> Tuple[Any, ...]:
         with FormulaAction(self, *points, **params) as action:
-            result = []
             for i in range(self.num_outputs):
                 res = FakePoint(self.coordinate_model)
                 action.output_points.append(res)
-                result.append(res)
-            return action.exit(tuple(result))
+            return action.exit(tuple(action.output_points))
 
 
 @public
@@ -79,13 +78,20 @@ class FakeLadderFormula(FakeFormula, LadderFormula):
     name = "fake"
 
 
+@cache
+def _fake_coords(model):
+    """Return a dictionary of fake coordinates for the given model."""
+    return {key: Undefined() for key in model.variables}
+
+
 @public
 class FakePoint(Point):
     """Just a fake point."""
 
-    def __init__(self, model):
-        coords = {key: Undefined() for key in model.variables}
-        super().__init__(model, **coords)
+    def __init__(self, model):  # noqa: We initialize everything here
+        self.coords = _fake_coords(model)
+        self.coordinate_model = model
+        self.field = 0
 
     def __str__(self):
         return f"FakePoint{id(self)}"
diff --git a/pyecsca/sca/re/rpa.py b/pyecsca/sca/re/rpa.py
index dbfb844..adef84d 100644
--- a/pyecsca/sca/re/rpa.py
+++ b/pyecsca/sca/re/rpa.py
@@ -112,37 +112,38 @@ class MultipleContext(Context):
                 self.precomp.update(action.result)
         if isinstance(action, FormulaAction) and self.inside:
             action = cast(FormulaAction, action)
-            if isinstance(action.formula, DoublingFormula):
+            shortname = action.formula.shortname
+            if shortname == "dbl":
                 inp = action.input_points[0]
                 out = action.output_points[0]
                 self.points[out] = 2 * self.points[inp]
                 self.parents[out] = [inp]
                 self.formulas[out] = action.formula.shortname
-            elif isinstance(action.formula, TriplingFormula):
+            elif shortname == "tpl":
                 inp = action.input_points[0]
                 out = action.output_points[0]
                 self.points[out] = 3 * self.points[inp]
                 self.parents[out] = [inp]
                 self.formulas[out] = action.formula.shortname
-            elif isinstance(action.formula, AdditionFormula):
+            elif shortname == "add":
                 one, other = action.input_points
                 out = action.output_points[0]
                 self.points[out] = self.points[one] + self.points[other]
                 self.parents[out] = [one, other]
                 self.formulas[out] = action.formula.shortname
-            elif isinstance(action.formula, NegationFormula):
+            elif shortname == "neg":
                 inp = action.input_points[0]
                 out = action.output_points[0]
                 self.points[out] = -self.points[inp]
                 self.parents[out] = [inp]
                 self.formulas[out] = action.formula.shortname
-            elif isinstance(action.formula, DifferentialAdditionFormula):
+            elif shortname == "dadd":
                 _, one, other = action.input_points
                 out = action.output_points[0]
                 self.points[out] = self.points[one] + self.points[other]
                 self.parents[out] = [one, other]
                 self.formulas[out] = action.formula.shortname
-            elif isinstance(action.formula, LadderFormula):
+            elif shortname == "ladd":
                 _, one, other = action.input_points
                 dbl, add = action.output_points
                 self.points[add] = self.points[one] + self.points[other]
@@ -151,7 +152,7 @@ class MultipleContext(Context):
                 self.points[dbl] = 2 * self.points[one]
                 self.parents[dbl] = [one]
                 self.formulas[dbl] = action.formula.shortname
-            elif isinstance(action.formula, ScalingFormula):
+            elif shortname == "scl":
                 inp = action.input_points[0]
                 out = action.output_points[0]
                 self.points[out] = self.points[inp]