Add functions to compute ellswift encoding, x-only ECDH

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

Author: stratospher

test/functional/test_framework/ellswift.py

@@ -10,7 +10,7 @@
 import random
 import unittest
 
-from .key import FE, GE
+from .key import FE, GE, SECP256K1_G
 
 MINUS_3_SQRT = FE(-3).sqrt()
 
@@ -56,6 +56,28 @@ def xswiftec_inv(x, u, case):
         w = -w
     return w * (u * (MINUS_3_SQRT - 1) / 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, GE.ORDER))
+        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 * SECP256K1_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()
+
 class TestFrameworkEllSwift(unittest.TestCase):
     def test_elligator_forward(self):
         """Verify that xswiftec maps all inputs to the curve."""
@@ -77,3 +99,11 @@ def test_elligator_roundtrip(self):
             u, t = xelligatorswift(x)
             x2 = xswiftec(u, t)
             self.assertEqual(x2, x)
+
+    def test_ellswift_ecdh_xonly(self):
+        for _ in range(32):
+            privkey1, encoding1 = ellswift_create()
+            privkey2, encoding2 = ellswift_create()
+            shared_secret1 = ellswift_ecdh_xonly(encoding1, privkey2)
+            shared_secret2 = ellswift_ecdh_xonly(encoding2, privkey1)
+            assert shared_secret1 == shared_secret2