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test: Add python ellswift implementation to test framework
Co-authored-by: Pieter Wuille <pieter.wuille@gmail.com>
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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.""" | ||
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import random | ||
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from test_framework.secp256k1 import FE, G, GE | ||
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# Precomputed constant square root of -3 (mod p). | ||
MINUS_3_SQRT = FE(-3).sqrt() | ||
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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 | ||
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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.""" | ||
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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) | ||
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def xelligatorswift(x): | ||
"""Given a field element X on the curve, find (u, t) that encode them.""" | ||
while True: | ||
u = FE(random.randrange(1, GE.ORDER)) | ||
case = random.randrange(0, 8) | ||
t = xswiftec_inv(x, u, case) | ||
if t is not None: | ||
return u, t | ||
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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() | ||
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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() |