def bip32_xpub_from_xprv(xprv: bytes) -> bytes:
"""Neutered Derivation (ND)
Computation of the extended public key corresponding to an extended
private key (“neutered” as it removes the ability to sign transactions)
"""
xprv = b58decode_check(xprv, 78)
assert xprv[45] == 0, "extended key is not a private one"
i = PRIVATE.index(xprv[:4])
# serialization data
xpub = PUBLIC[i] # version
# unchanged serialization data
xpub += xprv[4:5] # depth
xpub += xprv[5:9] # parent pubkey fingerprint
xpub += xprv[9:13] # child index
xpub += xprv[13:45] # chain code
p = xprv[46:]
P = pointMultiply(ec, p, ec.G)
xpub += bytes_from_Point(ec, P, True) # public key
return b58encode_check(xpub)
def test_all_curves(self):
for ec in allcurves:
# the infinity point is represented by None
self.assertEqual(ec.pointMultiply(0, ec.G), None)
self.assertEqual(pointMultiply(ec, 0, ec.G), None)
self.assertEqual(ec.pointMultiply(1, ec.G), ec.G)
self.assertEqual(pointMultiply(ec, 1, ec.G), ec.G)
Gy_odd = ec.y(ec.G[0], True)
self.assertEqual(Gy_odd % 2, 1)
Gy_even = ec.y(ec.G[0], False)
self.assertEqual(Gy_even % 2, 0)
self.assertTrue(ec.G[1] in (Gy_odd, Gy_even))
Gbytes = bytes_from_Point(ec, ec.G, True)
Gbytes = bytes_from_Point(ec, Gbytes, True)
G2 = tuple_from_Point(ec, Gbytes)
G2 = tuple_from_Point(ec, G2)
self.assertEqual(ec.G, G2)
Gbytes = bytes_from_Point(ec, ec.G, False)
Gbytes = bytes_from_Point(ec, Gbytes, False)
G2 = tuple_from_Point(ec, Gbytes)
G2 = tuple_from_Point(ec, G2)
self.assertEqual(ec.G, G2)
P = ec.pointAdd(None, ec.G)
self.assertEqual(P, ec.G)
P = ec.pointAdd(ec.G, None)
self.assertEqual(P, ec.G)
P = ec.pointAdd(None, None)
self.assertEqual(P, None)
P = pointAdd(ec, None, ec.G)
self.assertEqual(P, ec.G)
P = pointAdd(ec, ec.G, None)
self.assertEqual(P, ec.G)
P = pointAdd(ec, None, None)
self.assertEqual(P, None)
P = ec.pointDouble(ec.G)
self.assertEqual(P, ec.pointMultiply(2, ec.G))
P = pointDouble(ec, ec.G)
self.assertEqual(P, pointMultiply(ec, 2, ec.G))
P = ec.pointAdd(ec.G, ec.G)
self.assertEqual(P, ec.pointMultiply(2, ec.G))
P = pointAdd(ec, ec.G, ec.G)
self.assertEqual(P, pointMultiply(ec, 2, ec.G))
P = ec.pointMultiply(ec.order - 1, ec.G)
self.assertEqual(ec.pointAdd(P, ec.G), None)
self.assertEqual(ec.pointMultiply(ec.order, ec.G), None)
P = pointMultiply(ec, ec.order - 1, ec.G)
self.assertEqual(pointAdd(ec, P, ec.G), None)
self.assertEqual(pointMultiply(ec, ec.order, ec.G), None)
self.assertEqual(ec.pointMultiply(0, None), None)
self.assertEqual(ec.pointMultiply(1, None), None)
self.assertEqual(ec.pointMultiply(25, None), None)
self.assertEqual(pointMultiply(ec, 0, None), None)
self.assertEqual(pointMultiply(ec, 1, None), None)
self.assertEqual(pointMultiply(ec, 25, None), None)
ec2 = eval(repr(ec))
self.assertEqual(str(ec2), str(ec2))
if (ec.order % 2 == 0):
P = ec.pointMultiply(ec.order // 2, ec.G)
self.assertEqual(P[1], 0)
self.assertEqual(ec.pointDouble(P), None)
P = pointMultiply(ec, ec.order // 2, ec.G)
self.assertEqual(P[1], 0)
self.assertEqual(pointDouble(ec, P), None)
def pubkey_from_prvkey(prvkey: PrivateKey, compressed: bool = True) -> bytes:
"""Private key to (bytes) public key"""
P = pointMultiply(ec, prvkey, ec.G)
return bytes_from_Point(ec, P, compressed)
def pedersen_commit(ec: EllipticCurve, r: Scalar, v: Scalar) -> Point:
rG = pointMultiply(ec, r, ec.G)
vH = pointMultiply(ec, v, secondGenerator(ec))
return pointAdd(ec, rG, vH)