Add ellswift mapping functions

Co-authored-by: Pieter Wuille <pieter.wuille@gmail.com>

Author: stratospher

test/functional/test_framework/ellswift.py

@@ -0,0 +1,79 @@
+#!/usr/bin/env python3
+# Copyright (c) 2022 The Bitcoin Core developers
+# Distributed under the MIT software license, see the accompanying
+# file COPYING or http://www.opensource.org/licenses/mit-license.php.
+"""Test-only Elligator Swift implementation
+
+WARNING: This code is slow and uses bad randomness.
+Do not use for anything but tests."""
+
+import random
+import unittest
+
+from .key import FE, GE
+
+MINUS_3_SQRT = FE(-3).sqrt()
+
+def xswiftec(u, t):
+    """Decode field elements (u, t) to an X coordinate on the curve."""
+    if u == 0:
+        u = FE(1)
+    if t == 0:
+        t = FE(1)
+    if u**3 + t**2 + 7 == 0:
+        t = 2 * t
+    X = (u**3 - t**2 + 7) / (2 * t)
+    Y = (X + t) / (MINUS_3_SQRT * u)
+    for x in (u + 4 * Y**2, (-X / Y - u) / 2, (X / Y - u) / 2):
+        if GE.is_valid_x(x):
+            return x
+    assert False
+
+def xswiftec_inv(x, u, case):
+    """Given x and u, find t such that xswiftec(u, t) = x, or return None.
+    Case selects which of the up to 8 results to return."""
+    if case & 2 == 0:
+        if GE.is_valid_x(-x - u):
+            return None
+        v = x if case & 1 == 0 else -x - u
+        s = -(u**3 + 7) / (u**2 + u*v + v**2)
+    else:
+        s = x - u
+        if s == 0:
+            return None
+        r = (-s * (4 * (u**3 + 7) + 3 * s * u**2)).sqrt()
+        if r is None:
+            return None
+        if case & 1:
+            if r == 0:
+                return None
+            r = -r
+        v = (-u + r / s) / 2
+    w = s.sqrt()
+    if w is None:
+        return None
+    if case & 4:
+        w = -w
+    return w * (u * (MINUS_3_SQRT - 1) / 2 - v)
+
+class TestFrameworkEllSwift(unittest.TestCase):
+    def test_elligator_forward(self):
+        """Verify that xswiftec maps all inputs to the curve."""
+        for _ in range(32):
+            u = FE(random.randrange(0, FE.SIZE))
+            t = FE(random.randrange(0, FE.SIZE))
+            x = xswiftec(u, t)
+            self.assertTrue(GE.is_valid_x(x))
+
+    def test_elligator_roundtrip(self):
+        """Verify that encoding using xelligatorswift decodes back using xswiftec."""
+        for _ in range(32):
+            while True:
+                # Loop until we find a valid X coordinate on the curve.
+                x = FE(random.randrange(1, FE.SIZE))
+                if GE.is_valid_x(x):
+                    break
+            # Encoding it to (u, t), decode it back, and compare.
+            u, t = xelligatorswift(x)
+            x2 = xswiftec(u, t)
+            self.assertEqual(x2, x)

test/functional/test_runner.py

@@ -72,8 +72,9 @@
 TEST_FRAMEWORK_MODULES = [
     "address",
     "blocktools",
-    "muhash",
+    "ellswift",
     "key",
+    "muhash",
     "script",
     "segwit_addr",
     "util",