From c2b75500aa3dbcb0d2367439e29d33440bf77688 Mon Sep 17 00:00:00 2001
From: J08nY
Date: Mon, 16 Mar 2020 20:44:22 +0100
Subject: Add curve transformations M2SW and M2TE.

---
 Makefile                        |  2 +-
 pyecsca/ec/transformations.py   | 71 +++++++++++++++++++++++++++++++++++++++++
 test/ec/test_transformations.py | 18 +++++++++++
 3 files changed, 90 insertions(+), 1 deletion(-)
 create mode 100644 pyecsca/ec/transformations.py
 create mode 100644 test/ec/test_transformations.py

diff --git a/Makefile b/Makefile
index bd30ab1..5aeb2ed 100644
--- a/Makefile
+++ b/Makefile
@@ -1,6 +1,6 @@
 EC_TESTS = ec.test_context ec.test_configuration ec.test_curve ec.test_formula \
 ec.test_params ec.test_key_agreement ec.test_key_generation ec.test_mod ec.test_model \
-ec.test_mult ec.test_naf ec.test_op ec.test_point ec.test_signature
+ec.test_mult ec.test_naf ec.test_op ec.test_point ec.test_signature ec.test_transformations
 
 SCA_TESTS = sca.test_align sca.test_combine sca.test_edit sca.test_filter sca.test_match sca.test_process \
 sca.test_sampling sca.test_target sca.test_test sca.test_trace sca.test_traceset sca.test_plot
diff --git a/pyecsca/ec/transformations.py b/pyecsca/ec/transformations.py
new file mode 100644
index 0000000..1363483
--- /dev/null
+++ b/pyecsca/ec/transformations.py
@@ -0,0 +1,71 @@
+from public import public
+
+from .coordinates import AffineCoordinateModel
+from .curve import EllipticCurve
+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)
+    aff = AffineCoordinateModel(model)
+    if isinstance(params.curve.neutral, InfinityPoint):
+        neutral = InfinityPoint(aff)
+    else:
+        neutral = map_point(A, B, 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,
+                            params.cofactor)
+
+
+@public
+def M2SW(params: DomainParameters) -> DomainParameters:
+    """
+    Convert a Montgomery curve to ShortWeierstrass.
+
+    :param params: The domain parameters to convert.
+    :return: The converted domain parameters.
+    """
+    if not isinstance(params.curve.model, MontgomeryModel) or not isinstance(
+            params.curve.coordinate_model, AffineCoordinateModel):
+        raise ValueError
+
+    def map_parameters(A, B):
+        a = (3 - A ** 2) / (3 * B ** 2)
+        b = (2 * A ** 3 - 9 * A) / (27 * B ** 3)
+        return {"a": a, "b": b}
+
+    def map_point(A, B, pt, aff):
+        u = pt.x / B + A / (3 * B)
+        v = pt.y / B
+        return Point(aff, x=u, y=v)
+
+    return __M_map(params, map_parameters, map_point, ShortWeierstrassModel())
+
+
+@public
+def M2TE(params: DomainParameters) -> DomainParameters:
+    """
+    Convert a Montgomery curve to TwistedEdwards.
+
+    :param params: The domain parameters to convert.
+    :return: The converted domain parameters.
+    """
+    if not isinstance(params.curve.model, MontgomeryModel) or not isinstance(
+            params.curve.coordinate_model, AffineCoordinateModel):
+        raise ValueError
+
+    def map_parameters(A, B):
+        a = (A + 2) / B
+        d = (A - 2) / B
+        return {"a": a, "d": d}
+
+    def map_point(A, B, pt, aff):
+        u = pt.x / pt.y
+        v = (pt.x - 1) / (pt.x + 1)
+        return Point(aff, x=u, y=v)
+
+    return __M_map(params, map_parameters, map_point, TwistedEdwardsModel())
diff --git a/test/ec/test_transformations.py b/test/ec/test_transformations.py
new file mode 100644
index 0000000..2f2383c
--- /dev/null
+++ b/test/ec/test_transformations.py
@@ -0,0 +1,18 @@
+from unittest import TestCase
+
+from pyecsca.ec.params import get_params
+from pyecsca.ec.transformations import M2SW, M2TE
+
+
+class TransformationTests(TestCase):
+
+    def test_montgomery(self):
+        curve25519 = get_params("other", "Curve25519", "affine")
+        sw = M2SW(curve25519)
+        self.assertIsNotNone(sw)
+        self.assertTrue(sw.curve.is_on_curve(sw.generator))
+        self.assertTrue(sw.curve.is_neutral(sw.curve.neutral))
+        te = M2TE(curve25519)
+        self.assertIsNotNone(te)
+        self.assertTrue(te.curve.is_on_curve(te.generator))
+        self.assertTrue(te.curve.is_neutral(te.curve.neutral))
-- 
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