test: add python implementation of Elligator squared

test/functional/test_framework/ellswift.py

@@ -0,0 +1,163 @@
+#!/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 csv
+import os
+import random
+import unittest
+
+from test_framework.secp256k1 import FE, G, GE
+
+# Precomputed constant square root of -3 (mod p).
+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 + 7 - t**2) / (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
+        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 and r == 0:
+            return None
+        v = (-u + r / s) / 2
+    w = s.sqrt()
+    if w is None:
+        return None
+    if case & 5 == 0:
+        return -w * (u * (1 - MINUS_3_SQRT) / 2 + v)
+    if case & 5 == 1:
+        return w * (u * (1 + MINUS_3_SQRT) / 2 + v)
+    if case & 5 == 4:
+        return w * (u * (1 - MINUS_3_SQRT) / 2 + v)
+    if case & 5 == 5:
+        return -w * (u * (1 + MINUS_3_SQRT) / 2 + v)
+
+def xelligatorswift(x):
+    """Given a field element X on the curve, find (u, t) that encode them."""
+    assert GE.is_valid_x(x)
+    while True:
+        u = FE(random.randrange(1, FE.SIZE))
+        case = random.randrange(0, 8)
+        t = xswiftec_inv(x, u, case)
+        if t is not None:
+            return u, t
+
+def ellswift_create():
+    """Generate a (privkey, ellswift_pubkey) pair."""
+    priv = random.randrange(1, GE.ORDER)
+    u, t = xelligatorswift((priv * G).x)
+    return priv.to_bytes(32, 'big'), u.to_bytes() + t.to_bytes()
+
+def ellswift_ecdh_xonly(pubkey_theirs, privkey):
+    """Compute X coordinate of shared ECDH point between ellswift pubkey and privkey."""
+    u = FE(int.from_bytes(pubkey_theirs[:32], 'big'))
+    t = FE(int.from_bytes(pubkey_theirs[32:], 'big'))
+    d = int.from_bytes(privkey, 'big')
+    return (d * GE.lift_x(xswiftec(u, t))).x.to_bytes()
+
+
+class TestFrameworkEllSwift(unittest.TestCase):
+    def test_xswiftec(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))
+
+        # Check that inputs which are considered undefined in the original
+        # SwiftEC paper can also be decoded successfully (by remapping)
+        undefined_inputs = [
+            (FE(0), FE(23)),  # u = 0
+            (FE(42), FE(0)),  # t = 0
+            (FE(5), FE(-132).sqrt()),  # u^3 + t^2 + 7 = 0
+        ]
+        assert undefined_inputs[-1][0]**3 + undefined_inputs[-1][1]**2 + 7 == 0
+        for u, t in undefined_inputs:
+            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)
+
+    def test_ellswift_ecdh_xonly(self):
+        """Verify that shared secret computed by ellswift_ecdh_xonly match."""
+        for _ in range(32):
+            privkey1, encoding1 = ellswift_create()
+            privkey2, encoding2 = ellswift_create()
+            shared_secret1 = ellswift_ecdh_xonly(encoding1, privkey2)
+            shared_secret2 = ellswift_ecdh_xonly(encoding2, privkey1)
+            self.assertEqual(shared_secret1, shared_secret2)
+
+    def test_elligator_encode_testvectors(self):
+        """Implement the BIP324 test vectors for ellswift encoding (read from xswiftec_inv_test_vectors.csv)."""
+        vectors_file = os.path.join(os.path.dirname(os.path.realpath(__file__)), 'xswiftec_inv_test_vectors.csv')
+        with open(vectors_file, newline='', encoding='utf8') as csvfile:
+            reader = csv.DictReader(csvfile)
+            for row in reader:
+                u = FE.from_bytes(bytes.fromhex(row['u']))
+                x = FE.from_bytes(bytes.fromhex(row['x']))
+                for case in range(8):
+                    ret = xswiftec_inv(x, u, case)
+                    if ret is None:
+                        self.assertEqual(row[f"case{case}_t"], "")
+                    else:
+                        self.assertEqual(row[f"case{case}_t"], ret.to_bytes().hex())
+                        self.assertEqual(xswiftec(u, ret), x)
+
+    def test_elligator_decode_testvectors(self):
+        """Implement the BIP324 test vectors for ellswift decoding (read from ellswift_decode_test_vectors.csv)."""
+        vectors_file = os.path.join(os.path.dirname(os.path.realpath(__file__)), 'ellswift_decode_test_vectors.csv')
+        with open(vectors_file, newline='', encoding='utf8') as csvfile:
+            reader = csv.DictReader(csvfile)
+            for row in reader:
+                encoding = bytes.fromhex(row['ellswift'])
+                assert len(encoding) == 64
+                expected_x = FE(int(row['x'], 16))
+                u = FE(int.from_bytes(encoding[:32], 'big'))
+                t = FE(int.from_bytes(encoding[32:], 'big'))
+                x = xswiftec(u, t)
+                self.assertEqual(x, expected_x)
+                self.assertTrue(GE.is_valid_x(x))