diff --git a/test/functional/test_framework/ellswift.py b/test/functional/test_framework/ellswift.py new file mode 100644 index 0000000000000..33f77ac832b77 --- /dev/null +++ b/test/functional/test_framework/ellswift.py @@ -0,0 +1,83 @@ +#!/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.""" + 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()