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Merge bitcoin#24005: test: add python implementation of Elligator swift
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4f4d039 test: add ellswift test vectors from BIP324 (stratospher)
a312877 test: Add ellswift unit tests (stratospher)
714fb2c test: Add python ellswift implementation to test framework (stratospher)

Pull request description:

  Built on top of bitcoin#26222.

  This PR introduces Elligator swift encoding and decoding in the functional test framework. It's used in bitcoin#24748 for writing p2p encryption tests.

ACKs for top commit:
  sipa:
    ACK 4f4d039
  theStack:
    ACK 4f4d039 🐊

Tree-SHA512: 32bc8e88f715f2cd67dc04cd38db92680872072cb3775478e2c30da89aa2da2742992779ea14da2f1faca09228942cfbd86d6957402b24bf560244b389e03540
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fanquake committed Jun 30, 2023
2 parents 6744d84 + 4f4d039 commit 61d59fe
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163 changes: 163 additions & 0 deletions test/functional/test_framework/ellswift.py
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#!/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))
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