Inside Bitcoin

1#!/usr/bin/env python3
2# Copyright (c) 2022-present The Bitcoin Core developers
3# Distributed under the MIT software license, see the accompanying
4# file COPYING or http://www.opensource.org/licenses/mit-license.php.
5"""Test-only Elligator Swift implementation
6
7WARNING: This code is slow and uses bad randomness.
8Do not use for anything but tests."""
9
10import csv
11import os
12import random
13import unittest
14
15from test_framework.crypto.secp256k1 import FE, G, GE
16from test_framework.util import assert_equal
17
18# Precomputed constant square root of -3 (mod p).
19MINUS_3_SQRT = FE(-3).sqrt()
20
21def xswiftec(u, t):
22    """Decode field elements (u, t) to an X coordinate on the curve."""
23    if u == 0:
24        u = FE(1)
25    if t == 0:
26        t = FE(1)
27    if u**3 + t**2 + 7 == 0:
28        t = 2 * t
29    X = (u**3 + 7 - t**2) / (2 * t)
30    Y = (X + t) / (MINUS_3_SQRT * u)
31    for x in (u + 4 * Y**2, (-X / Y - u) / 2, (X / Y - u) / 2):
32        if GE.is_valid_x(x):
33            return x
34    assert False
35
36def xswiftec_inv(x, u, case):
37    """Given x and u, find t such that xswiftec(u, t) = x, or return None.
38
39    Case selects which of the up to 8 results to return."""
40
41    if case & 2 == 0:
42        if GE.is_valid_x(-x - u):
43            return None
44        v = x
45        s = -(u**3 + 7) / (u**2 + u*v + v**2)
46    else:
47        s = x - u
48        if s == 0:
49            return None
50        r = (-s * (4 * (u**3 + 7) + 3 * s * u**2)).sqrt()
51        if r is None:
52            return None
53        if case & 1 and r == 0:
54            return None
55        v = (-u + r / s) / 2
56    w = s.sqrt()
57    if w is None:
58        return None
59    if case & 5 == 0:
60        return -w * (u * (1 - MINUS_3_SQRT) / 2 + v)
61    if case & 5 == 1:
62        return w * (u * (1 + MINUS_3_SQRT) / 2 + v)
63    if case & 5 == 4:
64        return w * (u * (1 - MINUS_3_SQRT) / 2 + v)
65    if case & 5 == 5:
66        return -w * (u * (1 + MINUS_3_SQRT) / 2 + v)
67
68def xelligatorswift(x):
69    """Given a field element X on the curve, find (u, t) that encode them."""
70    assert GE.is_valid_x(x)
71    while True:
72        u = FE(random.randrange(1, FE.SIZE))
73        case = random.randrange(0, 8)
74        t = xswiftec_inv(x, u, case)
75        if t is not None:
76            return u, t
77
78def ellswift_create():
79    """Generate a (privkey, ellswift_pubkey) pair."""
80    priv = random.randrange(1, GE.ORDER)
81    u, t = xelligatorswift((priv * G).x)
82    return priv.to_bytes(32, 'big'), u.to_bytes() + t.to_bytes()
83
84def ellswift_ecdh_xonly(pubkey_theirs, privkey):
85    """Compute X coordinate of shared ECDH point between ellswift pubkey and privkey."""
86    u = FE(int.from_bytes(pubkey_theirs[:32], 'big'))
87    t = FE(int.from_bytes(pubkey_theirs[32:], 'big'))
88    d = int.from_bytes(privkey, 'big')
89    return (d * GE.lift_x(xswiftec(u, t))).x.to_bytes()
90
91
92class TestFrameworkEllSwift(unittest.TestCase):
93    def test_xswiftec(self):
94        """Verify that xswiftec maps all inputs to the curve."""
95        for _ in range(32):
96            u = FE(random.randrange(0, FE.SIZE))
97            t = FE(random.randrange(0, FE.SIZE))
98            x = xswiftec(u, t)
99            self.assertTrue(GE.is_valid_x(x))
100
101        # Check that inputs which are considered undefined in the original
102        # SwiftEC paper can also be decoded successfully (by remapping)
103        undefined_inputs = [
104            (FE(0), FE(23)),  # u = 0
105            (FE(42), FE(0)),  # t = 0
106            (FE(5), FE(-132).sqrt()),  # u^3 + t^2 + 7 = 0
107        ]
108        assert_equal(undefined_inputs[-1][0]**3 + undefined_inputs[-1][1]**2 + 7, 0)
109        for u, t in undefined_inputs:
110            x = xswiftec(u, t)
111            self.assertTrue(GE.is_valid_x(x))
112
113    def test_elligator_roundtrip(self):
114        """Verify that encoding using xelligatorswift decodes back using xswiftec."""
115        for _ in range(32):
116            while True:
117                # Loop until we find a valid X coordinate on the curve.
118                x = FE(random.randrange(1, FE.SIZE))
119                if GE.is_valid_x(x):
120                    break
121            # Encoding it to (u, t), decode it back, and compare.
122            u, t = xelligatorswift(x)
123            x2 = xswiftec(u, t)
124            self.assertEqual(x2, x)
125
126    def test_ellswift_ecdh_xonly(self):
127        """Verify that shared secret computed by ellswift_ecdh_xonly match."""
128        for _ in range(32):
129            privkey1, encoding1 = ellswift_create()
130            privkey2, encoding2 = ellswift_create()
131            shared_secret1 = ellswift_ecdh_xonly(encoding1, privkey2)
132            shared_secret2 = ellswift_ecdh_xonly(encoding2, privkey1)
133            self.assertEqual(shared_secret1, shared_secret2)
134
135    def test_elligator_encode_testvectors(self):
136        """Implement the BIP324 test vectors for ellswift encoding (read from xswiftec_inv_test_vectors.csv)."""
137        vectors_file = os.path.join(os.path.dirname(os.path.realpath(__file__)), 'xswiftec_inv_test_vectors.csv')
138        with open(vectors_file, newline='') as csvfile:
139            reader = csv.DictReader(csvfile)
140            for row in reader:
141                u = FE.from_bytes(bytes.fromhex(row['u']))
142                x = FE.from_bytes(bytes.fromhex(row['x']))
143                for case in range(8):
144                    ret = xswiftec_inv(x, u, case)
145                    if ret is None:
146                        self.assertEqual(row[f"case{case}_t"], "")
147                    else:
148                        self.assertEqual(row[f"case{case}_t"], ret.to_bytes().hex())
149                        self.assertEqual(xswiftec(u, ret), x)
150
151    def test_elligator_decode_testvectors(self):
152        """Implement the BIP324 test vectors for ellswift decoding (read from ellswift_decode_test_vectors.csv)."""
153        vectors_file = os.path.join(os.path.dirname(os.path.realpath(__file__)), 'ellswift_decode_test_vectors.csv')
154        with open(vectors_file, newline='') as csvfile:
155            reader = csv.DictReader(csvfile)
156            for row in reader:
157                encoding = bytes.fromhex(row['ellswift'])
158                assert_equal(len(encoding), 64)
159                expected_x = FE(int(row['x'], 16))
160                u = FE(int.from_bytes(encoding[:32], 'big'))
161                t = FE(int.from_bytes(encoding[32:], 'big'))
162                x = xswiftec(u, t)
163                self.assertEqual(x, expected_x)
164                self.assertTrue(GE.is_valid_x(x))
165