Add more curve transformations.

1 files changed, 108 insertions, 8 deletions

diff --git a/pyecsca/ec/transformations.py b/pyecsca/ec/transformations.py
index 6e3b24c..986064b 100644
--- a/pyecsca/ec/transformations.py
+++ b/pyecsca/ec/transformations.py
@@ -2,25 +2,27 @@
 This module provides functions for transforming curves to different models.
 """
 from public import public
+from sympy import FF, symbols, Poly
 
 from .coordinates import AffineCoordinateModel
 from .curve import EllipticCurve
+from .mod import Mod
 from .model import ShortWeierstrassModel, MontgomeryModel, TwistedEdwardsModel
 from .params import DomainParameters
 from .point import InfinityPoint, Point
 
 
-def __M_map(params, map_parameters, map_point, model):
-    A = params.curve.parameters["a"]
-    B = params.curve.parameters["b"]
-    parameters = map_parameters(A, B)
+def __M_map(params, param_names, map_parameters, map_point, model):
+    param_one = params.curve.parameters[param_names[0]]
+    param_other = params.curve.parameters[param_names[1]]
+    parameters = map_parameters(param_one, param_other)
     aff = AffineCoordinateModel(model)
     if isinstance(params.curve.neutral, InfinityPoint):
         neutral = InfinityPoint(aff)
     else:
-        neutral = map_point(A, B, params.curve.neutral, aff)
+        neutral = map_point(param_one, param_other, params.curve.neutral, aff)
     curve = EllipticCurve(model, aff, params.curve.prime, neutral, parameters)
-    return DomainParameters(curve, map_point(A, B, params.generator, aff), params.order,
+    return DomainParameters(curve, map_point(param_one, param_other, params.generator, aff), params.order,
                             params.cofactor)
 
 
@@ -46,7 +48,7 @@ def M2SW(params: DomainParameters) -> DomainParameters:
         v = pt.y / B
         return Point(aff, x=u, y=v)
 
-    return __M_map(params, map_parameters, map_point, ShortWeierstrassModel())
+    return __M_map(params, ("a", "b"), map_parameters, map_point, ShortWeierstrassModel())
 
 
 @public
@@ -71,4 +73,102 @@ def M2TE(params: DomainParameters) -> DomainParameters:
         v = (pt.x - 1) / (pt.x + 1)
         return Point(aff, x=u, y=v)
 
-    return __M_map(params, map_parameters, map_point, TwistedEdwardsModel())
+    return __M_map(params, ("a", "b"), map_parameters, map_point, TwistedEdwardsModel())
+
+
+@public
+def TE2M(params: DomainParameters) -> DomainParameters:
+    """
+    Convert a TwistedEdwards curve to Montgomery.
+
+    :param params: The domain parameters to convert.
+    :return: The converted domain parameters.
+    """
+    if not isinstance(params.curve.model, TwistedEdwardsModel) or not isinstance(
+            params.curve.coordinate_model, AffineCoordinateModel):
+        raise ValueError
+
+    def map_parameters(a, d):
+        A = (2 * (a + d)) / (a - d)
+        B = 4 / (a - d)
+        return {"a": A, "b": B}
+
+    def map_point(a, d, pt, aff):
+        u = (1 + pt.y) / (1 - pt.y)
+        v = (1 + pt.y) / ((1 - pt.y) * pt.x)
+        return Point(aff, x=u, y=v)
+
+    return __M_map(params, ("a", "d"), map_parameters, map_point, MontgomeryModel())
+
+
+@public
+def SW2M(params: DomainParameters) -> DomainParameters:
+    """
+    Convert a ShortWeierstrass curve to Montgomery.
+
+    :param params: The domain parameters to convert.
+    :return: The converted domain parameters.
+    """
+    if not isinstance(params.curve.model, ShortWeierstrassModel) or not isinstance(
+            params.curve.coordinate_model, AffineCoordinateModel):
+        raise ValueError
+    ax = symbols("α")
+    field = FF(params.curve.prime)
+    rhs = Poly(ax ** 3 + field(int(params.curve.parameters["a"])) * ax + field(int(params.curve.parameters["b"])), ax, domain=field)
+    roots = rhs.ground_roots()
+    if not roots:
+        raise ValueError("Curve cannot be transformed to Montgomery model (x^3 + ax + b has no root).")
+    alpha = Mod(int(next(iter(roots.keys()))), params.curve.prime)
+    beta = (3 * alpha**2 + params.curve.parameters["a"]).sqrt()
+
+    def map_parameters(a, b):
+        A = (3 * alpha) / beta
+        B = 1 / beta
+        return {"a": A, "b": B}
+
+    def map_point(a, b, pt, aff):
+        u = (pt.x - alpha) / beta
+        v = pt.y / beta
+        return Point(aff, x=u, y=v)
+
+    return __M_map(params, ("a", "b"), map_parameters, map_point, MontgomeryModel())
+
+
+@public
+def SW2TE(params: DomainParameters) -> DomainParameters:
+    """
+    Convert a ShortWeierstrass curve to TwistedEdwards.
+
+    :param params: The domain parameters to convert.
+    :return: The converted domain parameters.
+    """
+    if not isinstance(params.curve.model, ShortWeierstrassModel) or not isinstance(
+            params.curve.coordinate_model, AffineCoordinateModel):
+        raise ValueError
+    ax = symbols("α")
+    field = FF(params.curve.prime)
+    rhs = Poly(ax ** 3 + field(int(params.curve.parameters["a"])) * ax + field(int(params.curve.parameters["b"])), ax, domain=field)
+    roots = rhs.ground_roots()
+    if not roots:
+        raise ValueError("Curve cannot be transformed to Montgomery model (x^3 + ax + b has no root).")
+    alpha = Mod(int(next(iter(roots.keys()))), params.curve.prime)
+    beta = (3 * alpha**2 + params.curve.parameters["a"]).sqrt()
+
+    def map_parameters(a, b):
+        a = 3 * alpha + 2 * beta
+        d = 3 * alpha - 2 * beta
+        return {"a": a, "d": d}
+
+    def map_point(a, b, pt, aff):
+        if params.curve.is_neutral(pt):
+            u = Mod(0, params.curve.prime)
+            v = Mod(1, params.curve.prime)
+        elif pt.x == alpha and pt.y == 0:
+            u = Mod(0, params.curve.prime)
+            v = Mod(-1, params.curve.prime)
+        else:
+            u = (pt.x - alpha) / pt.y
+            v = (pt.x - alpha - beta) / (pt.x - alpha + beta)
+        return Point(aff, x=u, y=v)
+
+    return __M_map(params, ("a", "b"), map_parameters, map_point, TwistedEdwardsModel())