def test_dhZ(self):
from ecdsa.keys import SigningKey # VerifyingKey
from ecdsa.curves import NIST521p
# Party V(recepient) declares a satic key pair
curve = NIST521p
v_stc = SigningKey.generate(curve=curve)
# and advertise to Party U(Sender) ( U <--(pub key)-- V)
v_pub = v_stc.get_verifying_key()
self.assertEqual(v_pub.curve, curve)
print(v_pub.curve)
# Party U provides a ephemeral key
u_epk = SigningKey.generate(curve=v_pub.curve)
from jose.jwa import ec
# Compute ECDH as shared secret
# This shared secret itself is NOT have to be exchanged.
shared_secret_u = ec.ecdsa_dhZ(v_pub, u_epk)
# Party V recive Epemeral Public Key ( U --(pub key)--> V)
v_epk = u_epk.get_verifying_key()
# Party V compute
shared_secret_v = ec.ecdsa_dhZ(v_epk, v_stc)
# Secrete Agreeed!
self.assertEqual(shared_secret_u, shared_secret_v)
def test_ecdh_check(self):
'''
https://tools.ietf.org/html/draft-ietf-jose-json-web-algorithms-23#appendix-C
'''
v_stc_material = {
"kty": "EC",
"crv": "P-256",
"x": "gI0GAILBdu7T53akrFmMyGcsF3n5dO7MmwNBHKW5SV0",
"y": "SLW_xSffzlPWrHEVI30DHM_4egVwt3NQqeUD7nMFpps",
"d": "0_NxaRPUMQoAJt50Gz8YiTr8gRTwyEaCumd-MToTmIo"
}
u_epk_material = {
"kty": "EC",
"crv": "P-256",
"x": "weNJy2HscCSM6AEDTDg04biOvhFhyyWvOHQfeF_PxMQ",
"y": "e8lnCO-AlStT-NJVX-crhB7QRYhiix03illJOVAOyck",
"d": "VEmDZpDXXK8p8N0Cndsxs924q6nS1RXFASRl6BfUqdw"
}
import re
def _to_pub(km):
return (
int(re.search(r"P-(\d+)$", km['crv']).group(1)),
(base64.long_from_b64(km['x']),
base64.long_from_b64(km['y'])),
)
def _to_pri(km):
return (
int(re.search(r"P-(\d+)$", km['crv']).group(1)),
base64.long_from_b64(km['d']),
)
pub_tuple = _to_pub(v_stc_material)
pri_tuple = _to_pri(v_stc_material)
import pydoc
curve = pydoc.locate('ecdsa.curves.NIST{0}p'.format(pub_tuple[0]))
from ecdsa import (
SigningKey, VerifyingKey,
ellipticcurve as ec)
x, y = pub_tuple[1]
v_pub = VerifyingKey.from_public_point(
ec.Point(curve.curve, x, y, curve.order),
curve,
)
v_stc = SigningKey.from_secret_exponent(pri_tuple[1], curve)
# Party U provides a ephemeral key
pub_tuple = _to_pub(u_epk_material)
pri_tuple = _to_pri(u_epk_material)
x, y = pub_tuple[1]
u_epk = SigningKey.from_secret_exponent(pri_tuple[1], curve)
from jose.jwa.ec import ecdsa_dhZ
# Party U compute
shared_secret_u = ecdsa_dhZ(v_pub, u_epk)
print("Aggreement:", base64.long_to_b64(shared_secret_u))
from Crypto.Util.number import long_to_bytes
from math import ceil
block_size = int(ceil(pub_tuple[0] / 8.0))
# bit number(512 ) / 8 -> octets
Zu = long_to_bytes(shared_secret_u, block_size)
Z_jwa = [158, 86, 217, 29, 129, 113, 53,
211, 114, 131, 66, 131, 191, 132,
38, 156, 251, 49, 110, 163, 218,
128, 106, 72, 246, 218, 167, 121,
140, 254, 144, 196]
self.assertEqual(_ilist(Zu), Z_jwa)
# Other Information used in Concat KDF
# AlgorithmID || PartyUInfo || PartyVInfo || SuppPubInfo
from struct import pack
def _otherInfo(alg, pu, pv, klen):
return b('').join([
pack("!I", len(alg)),
alg,
pack("!I", len(pu)),
pu,
pack("!I", len(pv)),
pv,
pack("!I", klen),
])
oi_u = _otherInfo(
b("A128GCM"),
b("Alice"),
b("Bob"),
16 * 8, # A128GCM
)
oi_jwa = [
0, 0, 0, 7,
65, 49, 50, 56, 71, 67, 77,
0, 0, 0, 5,
65, 108, 105, 99, 101,
0, 0, 0, 3,
66, 111, 98,
0, 0, 0, 128]
print(">>>>>>>", type(oi_u))
print("<<<<<<<", oi_u)
self.assertEqual(_ilist(oi_u), oi_jwa)
# Coccat KDF : NIST defines SHA256
from Crypto.Hash import SHA256
def _ConcatKDF(Z, dkLen, otherInfo,
digest_method=SHA256):
def _src(counter_bytes):
return b("").join([counter_bytes, Z, otherInfo])
from math import ceil
from struct import pack
dkm = b'' # Derived Key Material
counter = 0
klen = int(ceil(dkLen / 8.0))
while len(dkm) < klen:
counter += 1
counter_b = pack("!I", counter)
dkm += digest_method.new(_src(counter_b)).digest()
return dkm[:klen]
_derived_key_u = _ConcatKDF(Zu, 16 * 8, oi_u)
# Party V recive Epemeral Public Key
v_epk = u_epk.get_verifying_key()
Zv = long_to_bytes(ecdsa_dhZ(v_epk, v_stc), block_size)
_derived_key_v = _ConcatKDF(Zv, 16 * 8, oi_u)
self.assertEqual(_derived_key_u, _derived_key_v)
kd_jwa = [
86, 170, 141, 234, 248, 35, 109, 32,
92, 34, 40, 205, 113, 167, 16, 26]
self.assertEqual(_ilist(_derived_key_u), kd_jwa)
self.assertEqual(b("VqqN6vgjbSBcIijNcacQGg"),
base64.base64url_encode(_derived_key_u))
