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| 1 | +#!/usr/bin/env python3 |
| 2 | +# Copyright (c) 2022 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 | +
|
| 7 | +WARNING: This code is slow and uses bad randomness. |
| 8 | +Do not use for anything but tests.""" |
| 9 | + |
| 10 | +import csv |
| 11 | +import os |
| 12 | +import random |
| 13 | +import unittest |
| 14 | + |
| 15 | +from test_framework.secp256k1 import FE, G, GE |
| 16 | + |
| 17 | +# Precomputed constant square root of -3 (mod p). |
| 18 | +MINUS_3_SQRT = FE(-3).sqrt() |
| 19 | + |
| 20 | +def xswiftec(u, t): |
| 21 | + """Decode field elements (u, t) to an X coordinate on the curve.""" |
| 22 | + if u == 0: |
| 23 | + u = FE(1) |
| 24 | + if t == 0: |
| 25 | + t = FE(1) |
| 26 | + if u**3 + t**2 + 7 == 0: |
| 27 | + t = 2 * t |
| 28 | + X = (u**3 + 7 - t**2) / (2 * t) |
| 29 | + Y = (X + t) / (MINUS_3_SQRT * u) |
| 30 | + for x in (u + 4 * Y**2, (-X / Y - u) / 2, (X / Y - u) / 2): |
| 31 | + if GE.is_valid_x(x): |
| 32 | + return x |
| 33 | + assert False |
| 34 | + |
| 35 | +def xswiftec_inv(x, u, case): |
| 36 | + """Given x and u, find t such that xswiftec(u, t) = x, or return None. |
| 37 | +
|
| 38 | + Case selects which of the up to 8 results to return.""" |
| 39 | + |
| 40 | + if case & 2 == 0: |
| 41 | + if GE.is_valid_x(-x - u): |
| 42 | + return None |
| 43 | + v = x |
| 44 | + s = -(u**3 + 7) / (u**2 + u*v + v**2) |
| 45 | + else: |
| 46 | + s = x - u |
| 47 | + if s == 0: |
| 48 | + return None |
| 49 | + r = (-s * (4 * (u**3 + 7) + 3 * s * u**2)).sqrt() |
| 50 | + if r is None: |
| 51 | + return None |
| 52 | + if case & 1 and r == 0: |
| 53 | + return None |
| 54 | + v = (-u + r / s) / 2 |
| 55 | + w = s.sqrt() |
| 56 | + if w is None: |
| 57 | + return None |
| 58 | + if case & 5 == 0: |
| 59 | + return -w * (u * (1 - MINUS_3_SQRT) / 2 + v) |
| 60 | + if case & 5 == 1: |
| 61 | + return w * (u * (1 + MINUS_3_SQRT) / 2 + v) |
| 62 | + if case & 5 == 4: |
| 63 | + return w * (u * (1 - MINUS_3_SQRT) / 2 + v) |
| 64 | + if case & 5 == 5: |
| 65 | + return -w * (u * (1 + MINUS_3_SQRT) / 2 + v) |
| 66 | + |
| 67 | +def xelligatorswift(x): |
| 68 | + """Given a field element X on the curve, find (u, t) that encode them.""" |
| 69 | + assert GE.is_valid_x(x) |
| 70 | + while True: |
| 71 | + u = FE(random.randrange(1, FE.SIZE)) |
| 72 | + case = random.randrange(0, 8) |
| 73 | + t = xswiftec_inv(x, u, case) |
| 74 | + if t is not None: |
| 75 | + return u, t |
| 76 | + |
| 77 | +def ellswift_create(): |
| 78 | + """Generate a (privkey, ellswift_pubkey) pair.""" |
| 79 | + priv = random.randrange(1, GE.ORDER) |
| 80 | + u, t = xelligatorswift((priv * G).x) |
| 81 | + return priv.to_bytes(32, 'big'), u.to_bytes() + t.to_bytes() |
| 82 | + |
| 83 | +def ellswift_ecdh_xonly(pubkey_theirs, privkey): |
| 84 | + """Compute X coordinate of shared ECDH point between ellswift pubkey and privkey.""" |
| 85 | + u = FE(int.from_bytes(pubkey_theirs[:32], 'big')) |
| 86 | + t = FE(int.from_bytes(pubkey_theirs[32:], 'big')) |
| 87 | + d = int.from_bytes(privkey, 'big') |
| 88 | + return (d * GE.lift_x(xswiftec(u, t))).x.to_bytes() |
| 89 | + |
| 90 | + |
| 91 | +class TestFrameworkEllSwift(unittest.TestCase): |
| 92 | + def test_xswiftec(self): |
| 93 | + """Verify that xswiftec maps all inputs to the curve.""" |
| 94 | + for _ in range(32): |
| 95 | + u = FE(random.randrange(0, FE.SIZE)) |
| 96 | + t = FE(random.randrange(0, FE.SIZE)) |
| 97 | + x = xswiftec(u, t) |
| 98 | + self.assertTrue(GE.is_valid_x(x)) |
| 99 | + |
| 100 | + # Check that inputs which are considered undefined in the original |
| 101 | + # SwiftEC paper can also be decoded successfully (by remapping) |
| 102 | + undefined_inputs = [ |
| 103 | + (FE(0), FE(23)), # u = 0 |
| 104 | + (FE(42), FE(0)), # t = 0 |
| 105 | + (FE(5), FE(-132).sqrt()), # u^3 + t^2 + 7 = 0 |
| 106 | + ] |
| 107 | + assert undefined_inputs[-1][0]**3 + undefined_inputs[-1][1]**2 + 7 == 0 |
| 108 | + for u, t in undefined_inputs: |
| 109 | + x = xswiftec(u, t) |
| 110 | + self.assertTrue(GE.is_valid_x(x)) |
| 111 | + |
| 112 | + def test_elligator_roundtrip(self): |
| 113 | + """Verify that encoding using xelligatorswift decodes back using xswiftec.""" |
| 114 | + for _ in range(32): |
| 115 | + while True: |
| 116 | + # Loop until we find a valid X coordinate on the curve. |
| 117 | + x = FE(random.randrange(1, FE.SIZE)) |
| 118 | + if GE.is_valid_x(x): |
| 119 | + break |
| 120 | + # Encoding it to (u, t), decode it back, and compare. |
| 121 | + u, t = xelligatorswift(x) |
| 122 | + x2 = xswiftec(u, t) |
| 123 | + self.assertEqual(x2, x) |
| 124 | + |
| 125 | + def test_ellswift_ecdh_xonly(self): |
| 126 | + """Verify that shared secret computed by ellswift_ecdh_xonly match.""" |
| 127 | + for _ in range(32): |
| 128 | + privkey1, encoding1 = ellswift_create() |
| 129 | + privkey2, encoding2 = ellswift_create() |
| 130 | + shared_secret1 = ellswift_ecdh_xonly(encoding1, privkey2) |
| 131 | + shared_secret2 = ellswift_ecdh_xonly(encoding2, privkey1) |
| 132 | + self.assertEqual(shared_secret1, shared_secret2) |
| 133 | + |
| 134 | + def test_elligator_encode_testvectors(self): |
| 135 | + """Implement the BIP324 test vectors for ellswift encoding (read from xswiftec_inv_test_vectors.csv).""" |
| 136 | + vectors_file = os.path.join(os.path.dirname(os.path.realpath(__file__)), 'xswiftec_inv_test_vectors.csv') |
| 137 | + with open(vectors_file, newline='', encoding='utf8') as csvfile: |
| 138 | + reader = csv.DictReader(csvfile) |
| 139 | + for row in reader: |
| 140 | + u = FE.from_bytes(bytes.fromhex(row['u'])) |
| 141 | + x = FE.from_bytes(bytes.fromhex(row['x'])) |
| 142 | + for case in range(8): |
| 143 | + ret = xswiftec_inv(x, u, case) |
| 144 | + if ret is None: |
| 145 | + self.assertEqual(row[f"case{case}_t"], "") |
| 146 | + else: |
| 147 | + self.assertEqual(row[f"case{case}_t"], ret.to_bytes().hex()) |
| 148 | + self.assertEqual(xswiftec(u, ret), x) |
| 149 | + |
| 150 | + def test_elligator_decode_testvectors(self): |
| 151 | + """Implement the BIP324 test vectors for ellswift decoding (read from ellswift_decode_test_vectors.csv).""" |
| 152 | + vectors_file = os.path.join(os.path.dirname(os.path.realpath(__file__)), 'ellswift_decode_test_vectors.csv') |
| 153 | + with open(vectors_file, newline='', encoding='utf8') as csvfile: |
| 154 | + reader = csv.DictReader(csvfile) |
| 155 | + for row in reader: |
| 156 | + encoding = bytes.fromhex(row['ellswift']) |
| 157 | + assert len(encoding) == 64 |
| 158 | + expected_x = FE(int(row['x'], 16)) |
| 159 | + u = FE(int.from_bytes(encoding[:32], 'big')) |
| 160 | + t = FE(int.from_bytes(encoding[32:], 'big')) |
| 161 | + x = xswiftec(u, t) |
| 162 | + self.assertEqual(x, expected_x) |
| 163 | + self.assertTrue(GE.is_valid_x(x)) |
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