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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 random
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()
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