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86 lines
2.6 KiB
Python
86 lines
2.6 KiB
Python
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#!/usr/bin/env python3
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# Copyright (c) 2022 The Bitcoin Core developers
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# Distributed under the MIT software license, see the accompanying
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# file COPYING or http://www.opensource.org/licenses/mit-license.php.
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"""Test-only Elligator Swift implementation
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WARNING: This code is slow and uses bad randomness.
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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).
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MINUS_3_SQRT = FE(-3).sqrt()
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def xswiftec(u, t):
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"""Decode field elements (u, t) to an X coordinate on the curve."""
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if u == 0:
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u = FE(1)
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if t == 0:
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t = FE(1)
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if u**3 + t**2 + 7 == 0:
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t = 2 * t
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X = (u**3 + 7 - t**2) / (2 * t)
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Y = (X + t) / (MINUS_3_SQRT * u)
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for x in (u + 4 * Y**2, (-X / Y - u) / 2, (X / Y - u) / 2):
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if GE.is_valid_x(x):
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return x
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assert False
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def xswiftec_inv(x, u, case):
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"""Given x and u, find t such that xswiftec(u, t) = x, or return None.
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Case selects which of the up to 8 results to return."""
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if case & 2 == 0:
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if GE.is_valid_x(-x - u):
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return None
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v = x
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s = -(u**3 + 7) / (u**2 + u*v + v**2)
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else:
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s = x - u
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if s == 0:
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return None
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r = (-s * (4 * (u**3 + 7) + 3 * s * u**2)).sqrt()
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if r is None:
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return None
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if case & 1 and r == 0:
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return None
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v = (-u + r / s) / 2
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w = s.sqrt()
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if w is None:
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return None
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if case & 5 == 0:
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return -w * (u * (1 - MINUS_3_SQRT) / 2 + v)
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if case & 5 == 1:
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return w * (u * (1 + MINUS_3_SQRT) / 2 + v)
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if case & 5 == 4:
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return w * (u * (1 - MINUS_3_SQRT) / 2 + v)
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if case & 5 == 5:
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return -w * (u * (1 + MINUS_3_SQRT) / 2 + v)
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def xelligatorswift(x):
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"""Given a field element X on the curve, find (u, t) that encode them."""
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assert GE.is_valid_x(x)
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while True:
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u = FE(random.randrange(1, FE.SIZE))
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case = random.randrange(0, 8)
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t = xswiftec_inv(x, u, case)
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if t is not None:
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return u, t
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def ellswift_create():
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"""Generate a (privkey, ellswift_pubkey) pair."""
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priv = random.randrange(1, GE.ORDER)
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u, t = xelligatorswift((priv * G).x)
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return priv.to_bytes(32, 'big'), u.to_bytes() + t.to_bytes()
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def ellswift_ecdh_xonly(pubkey_theirs, privkey):
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"""Compute X coordinate of shared ECDH point between ellswift pubkey and privkey."""
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u = FE(int.from_bytes(pubkey_theirs[:32], 'big'))
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t = FE(int.from_bytes(pubkey_theirs[32:], 'big'))
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d = int.from_bytes(privkey, 'big')
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return (d * GE.lift_x(xswiftec(u, t))).x.to_bytes()
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