test: Add python ellswift implementation to test framework

Co-authored-by: Pieter Wuille <pieter.wuille@gmail.com>

test/functional/test_framework/ellswift.py

@@ -0,0 +1,85 @@
+#!/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()