Merge branch 'hkdf' (COMPATIBILITY BREAK)

This changes password_to_scalar() and arbitrary_element() to a new derivation function, using HKDF and matching the proposed functions in bitwiseshiftleft/sjcl#273 . Users of this library from after this commit will not interoperate with those who use the library from before this commit: they will get "WrongPasswordError" all the time. closes #5 (rebased the original commits)
warner · May 12, 2016 · 067e094 · 067e094
2 parents 94b8009 + eb15e64
commit 067e094
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diff --git a/.travis.yml b/.travis.yml
@@ -10,7 +10,6 @@ python:
   - "3.4"
   - "3.5"
   - "pypy"
-  - "pypy3"
 install:
   - pip install -U tox virtualenv coverage python-coveralls
 script:

diff --git a/README.md b/README.md
@@ -3,7 +3,7 @@
 
 * License: MIT
 * Dependencies: none (pure-python)
-* Compatible With: Python 2.6, 2.7, 3.3, 3.4, 3.5, pypy2, pypy3
+* Compatible With: Python 2.6, 2.7, 3.3, 3.4, 3.5, pypy2
 * [![Build Status](https://travis-ci.org/warner/python-spake2.png?branch=master)](https://travis-ci.org/warner/python-spake2) [![Coverage Status](https://coveralls.io/repos/warner/python-spake2/badge.svg)](https://coveralls.io/r/warner/python-spake2)
 
 This library implements the SPAKE2 password-authenticated key exchange

diff --git a/setup.py b/setup.py
@@ -79,4 +79,5 @@ def abbrev(t):
           "Programming Language :: Python :: 3.5",
           "Topic :: Security :: Cryptography",
           ],
+      install_requires=["hkdf"],
       )
diff --git a/src/spake2/ed25519_basic.py b/src/spake2/ed25519_basic.py
@@ -1,4 +1,5 @@
 import binascii, hashlib, itertools
+from .groups import expand_arbitrary_element_seed
 
 Q = 2**255 - 19
 L = 2**252 + 27742317777372353535851937790883648493
@@ -267,8 +268,11 @@ def subtract(self, other):
 
 
 def arbitrary_element(seed): # unknown DL
-    # TODO: if we don't need uniformity, maybe use just sha256 here?
-    hseed = hashlib.sha512(seed).digest()
+    # We don't strictly need the uniformity provided by hashing to an
+    # oversized string (128 bits more than the field size), then reducing
+    # down to Q. But it's comforting, and it's the same technique we use for
+    # converting passwords/seeds to scalars (which *does* need uniformity).
+    hseed = expand_arbitrary_element_seed(seed, (256/8)+16)
     y = int(binascii.hexlify(hseed), 16) % Q
 
     # we try successive Y values until we find a valid point

diff --git a/src/spake2/ed25519_group.py b/src/spake2/ed25519_group.py
@@ -1,4 +1,5 @@
 from . import ed25519_basic
+from .groups import password_to_scalar
 
 class _Ed25519Group:
     def random_scalar(self, entropy_f):
@@ -8,7 +9,7 @@ def scalar_to_bytes(self, i):
     def bytes_to_scalar(self, b):
         return ed25519_basic.bytes_to_scalar(b)
     def password_to_scalar(self, pw):
-        return ed25519_basic.password_to_scalar(pw)
+        return password_to_scalar(pw, self.scalar_size_bytes, self.order())
     def arbitrary_element(self, seed):
         return ed25519_basic.arbitrary_element(seed)
     def bytes_to_element(self, b):

diff --git a/src/spake2/groups.py b/src/spake2/groups.py
@@ -1,5 +1,6 @@
 from __future__ import division
 import hashlib
+from hkdf import Hkdf
 from .six import integer_types
 from .util import (size_bits, size_bytes, unbiased_randrange,
                    bytes_to_number, number_to_bytes)
@@ -61,6 +62,24 @@
 """
 
 
+def expand_password(data, num_bytes):
+    h = Hkdf(salt=b"", input_key_material=data, hash=hashlib.sha256)
+    info = b"SPAKE2 pw"
+    return h.expand(info, num_bytes)
+
+def password_to_scalar(pw, scalar_size_bytes, q):
+    assert isinstance(pw, bytes)
+    # the oversized hash reduces bias in the result, so
+    # uniformly-random passwords give nearly-uniform scalars
+    oversized = expand_password(pw, scalar_size_bytes+16)
+    assert len(oversized) >= scalar_size_bytes
+    i = bytes_to_number(oversized)
+    return i % q
+
+def expand_arbitrary_element_seed(data, num_bytes):
+    h = Hkdf(salt=b"", input_key_material=data, hash=hashlib.sha256)
+    info = b"SPAKE2 arbitrary element"
+    return h.expand(info, num_bytes)
 
 class _Element:
     def __init__(self, group, e):
@@ -76,7 +95,7 @@ def to_bytes(self):
         return self._group._element_to_bytes(self)
 
 class IntegerGroup:
-    def __init__(self, p, q, g, element_hasher):
+    def __init__(self, p, q, g):
         self.q = q # the subgroup order, used for scalars
         self.scalar_size_bytes = size_bytes(self.q)
         _s = self.scalar_to_bytes(self.password_to_scalar(b""))
@@ -89,10 +108,6 @@ def __init__(self, p, q, g, element_hasher):
         self.p = p # the field size
         self.element_size_bits = size_bits(self.p)
         self.element_size_bytes = size_bytes(self.p)
-        _e = element_hasher(b"")
-        assert isinstance(_e, bytes)
-        assert len(_e) >= self.element_size_bytes
-        self.element_hasher = element_hasher
 
         # double-check that the generator has the right order
         assert pow(g, self.q, self.p) == 1
@@ -119,19 +134,14 @@ def bytes_to_scalar(self, b):
         return i
 
     def password_to_scalar(self, pw):
-        assert isinstance(pw, bytes)
-        # the oversized hash reduces bias in the result, so
-        # uniformly-random passwords give nearly-uniform scalars
-        oversized = hashlib.sha512(pw).digest()
-        assert len(oversized) >= self.scalar_size_bytes
-        i = bytes_to_number(oversized)
-        return i % self.q
+        return password_to_scalar(pw, self.scalar_size_bytes, self.q)
 
 
     def arbitrary_element(self, seed):
         # we do *not* know the discrete log of this one. Nobody should.
         assert isinstance(seed, bytes)
-        processed_seed = self.element_hasher(seed)[:self.element_size_bytes]
+        processed_seed = expand_arbitrary_element_seed(seed,
+                                                       self.element_size_bytes)
         assert isinstance(processed_seed, bytes)
         assert len(processed_seed) == self.element_size_bytes
         # The larger (non-prime-order) group (Zp*) we're using has order
@@ -192,21 +202,6 @@ def _add(self, e1, e2):
         return _Element(self, (e1._e * e2._e) % self.p)
 
 
-def sha256(b):
-    return hashlib.sha256(b).digest()
-def sha512(b):
-    return hashlib.sha512(b).digest()
-def hash1024(b):
-    return b"".join([sha512(b"0:"+b), sha512(b"1:"+b)])
-def hash2048(b):
-    return b"".join([sha512(b"0:"+b), sha512(b"1:"+b),
-                     sha512(b"2:"+b), sha512(b"3:"+b)])
-def hash3072(b):
-    return b"".join([sha512(b"0:"+b), sha512(b"1:"+b),
-                     sha512(b"2:"+b), sha512(b"3:"+b),
-                     sha512(b"4:"+b), sha512(b"5:"+b)])
-
-
 # This 1024-bit group originally came from the J-PAKE demo code,
 # http://haofeng66.googlepages.com/JPAKEDemo.java . That java code
 # recommended these 2048 and 3072 bit groups from this NIST document:
@@ -217,18 +212,18 @@ def hash3072(b):
     p=0xE0A67598CD1B763BC98C8ABB333E5DDA0CD3AA0E5E1FB5BA8A7B4EABC10BA338FAE06DD4B90FDA70D7CF0CB0C638BE3341BEC0AF8A7330A3307DED2299A0EE606DF035177A239C34A912C202AA5F83B9C4A7CF0235B5316BFC6EFB9A248411258B30B839AF172440F32563056CB67A861158DDD90E6A894C72A5BBEF9E286C6B,
     q=0xE950511EAB424B9A19A2AEB4E159B7844C589C4F,
     g=0xD29D5121B0423C2769AB21843E5A3240FF19CACC792264E3BB6BE4F78EDD1B15C4DFF7F1D905431F0AB16790E1F773B5CE01C804E509066A9919F5195F4ABC58189FD9FF987389CB5BEDF21B4DAB4F8B76A055FFE2770988FE2EC2DE11AD92219F0B351869AC24DA3D7BA87011A701CE8EE7BFE49486ED4527B7186CA4610A75,
-    element_hasher = hash1024)
+    )
 
 # L=2048, N=224
 I2048 = IntegerGroup(
     p=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
     q=0x90EAF4D1AF0708B1B612FF35E0A2997EB9E9D263C9CE659528945C0D,
     g=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
-    element_hasher=hash2048)
+    )
 
 # L=3072, N=256
 I3072 = IntegerGroup(
     p=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
     q=0xCFA0478A54717B08CE64805B76E5B14249A77A4838469DF7F7DC987EFCCFB11D,
     g=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
-    element_hasher=hash3072)
+    )
diff --git a/src/spake2/test/myhkdf.py b/src/spake2/test/myhkdf.py
@@ -0,0 +1,166 @@
+from hashlib import sha256, sha1
+from binascii import unhexlify
+import hmac
+
+def HKDF(IKM, dkLen, salt=None, info=b"", digest=sha256,
+         _test_expected_PRK=None):
+    assert isinstance(IKM, bytes)
+    assert isinstance(salt, (bytes,type(None)))
+    assert isinstance(info, bytes)
+    hlen = len(digest(b"").digest())
+    assert dkLen <= hlen*255
+    if salt is None:
+        salt = b"\x00"*hlen
+    # extract
+    PRK = hmac.new(salt, IKM, digest).digest()
+    if _test_expected_PRK and _test_expected_PRK != PRK:
+        raise ValueError("test failed")
+    # expand
+    blocks = []
+    counter = 1
+    t = b""
+    while hlen*len(blocks) < dkLen:
+        t = hmac.new(PRK, t+info+unhexlify("%02x"%counter), digest).digest()
+        blocks.append(t)
+        counter += 1
+    return b"".join(blocks)[:dkLen]
+
+def power_on_self_test():
+    from binascii import hexlify, unhexlify
+
+    def _test(IKM, salt, info, L, PRK, OKM, digest=sha256):
+        def remove_prefix(prefix, s):
+            assert s.startswith(prefix)
+            return s[len(prefix):]
+        ikm = unhexlify(remove_prefix("0x", IKM))
+        salt = unhexlify(remove_prefix("0x", salt))
+        info = unhexlify(remove_prefix("0x", info))
+        prk = unhexlify(remove_prefix("0x", PRK))
+        okm = unhexlify(remove_prefix("0x", OKM))
+        assert isinstance(ikm, bytes)
+        assert isinstance(salt, bytes)
+        assert isinstance(info, bytes)
+        assert isinstance(prk, bytes)
+        assert isinstance(okm, bytes)
+        if digest is None:
+            out = HKDF(ikm, L, salt, info, _test_expected_PRK=prk)
+        else:
+            out = HKDF(ikm, L, salt, info, digest=digest,
+                       _test_expected_PRK=prk)
+        if okm != out:
+            raise ValueError("got %s, expected %s" % (hexlify(out), hexlify(okm)))
+
+    # test vectors from RFC5869
+    _test(IKM="0x0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b",
+          salt="0x000102030405060708090a0b0c",
+          info="0xf0f1f2f3f4f5f6f7f8f9",
+          L=42,
+          PRK=("0x077709362c2e32df0ddc3f0dc47bba63"
+               "90b6c73bb50f9c3122ec844ad7c2b3e5"),
+          OKM=("0x3cb25f25faacd57a90434f64d0362f2a"
+               "2d2d0a90cf1a5a4c5db02d56ecc4c5bf"
+               "34007208d5b887185865"))
+
+    _test(IKM=("0x000102030405060708090a0b0c0d0e0f"
+               "101112131415161718191a1b1c1d1e1f"
+               "202122232425262728292a2b2c2d2e2f"
+               "303132333435363738393a3b3c3d3e3f"
+               "404142434445464748494a4b4c4d4e4f"),
+          salt=("0x606162636465666768696a6b6c6d6e6f"
+                "707172737475767778797a7b7c7d7e7f"
+                "808182838485868788898a8b8c8d8e8f"
+                "909192939495969798999a9b9c9d9e9f"
+                "a0a1a2a3a4a5a6a7a8a9aaabacadaeaf"),
+          info=("0xb0b1b2b3b4b5b6b7b8b9babbbcbdbebf"
+                "c0c1c2c3c4c5c6c7c8c9cacbcccdcecf"
+                "d0d1d2d3d4d5d6d7d8d9dadbdcdddedf"
+                "e0e1e2e3e4e5e6e7e8e9eaebecedeeef"
+                "f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff"),
+          L=82,
+          PRK=("0x06a6b88c5853361a06104c9ceb35b45c"
+               "ef760014904671014a193f40c15fc244"),
+          OKM=("0xb11e398dc80327a1c8e7f78c596a4934"
+               "4f012eda2d4efad8a050cc4c19afa97c"
+               "59045a99cac7827271cb41c65e590e09"
+               "da3275600c2f09b8367793a9aca3db71"
+               "cc30c58179ec3e87c14c01d5c1f3434f"
+               "1d87"))
+
+    _test(IKM="0x0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b",
+          salt="0x",
+          info="0x",
+          L=42,
+          PRK=("0x19ef24a32c717b167f33a91d6f648bdf"
+               "96596776afdb6377ac434c1c293ccb04"),
+          OKM=("0x8da4e775a563c18f715f802a063c5a31"
+               "b8a11f5c5ee1879ec3454e5f3c738d2d"
+               "9d201395faa4b61a96c8"))
+
+    _test(digest=sha1,
+          IKM="0x0b0b0b0b0b0b0b0b0b0b0b",
+          salt="0x000102030405060708090a0b0c",
+          info="0xf0f1f2f3f4f5f6f7f8f9",
+          L=42,
+          PRK="0x9b6c18c432a7bf8f0e71c8eb88f4b30baa2ba243",
+          OKM=("0x085a01ea1b10f36933068b56efa5ad81"
+               "a4f14b822f5b091568a9cdd4f155fda2"
+               "c22e422478d305f3f896"))
+    _test(digest=sha1,
+       IKM=("0x000102030405060708090a0b0c0d0e0f"
+            "101112131415161718191a1b1c1d1e1f"
+            "202122232425262728292a2b2c2d2e2f"
+            "303132333435363738393a3b3c3d3e3f"
+            "404142434445464748494a4b4c4d4e4f"),
+       salt=("0x606162636465666768696a6b6c6d6e6f"
+             "707172737475767778797a7b7c7d7e7f"
+             "808182838485868788898a8b8c8d8e8f"
+             "909192939495969798999a9b9c9d9e9f"
+             "a0a1a2a3a4a5a6a7a8a9aaabacadaeaf"),
+       info=("0xb0b1b2b3b4b5b6b7b8b9babbbcbdbebf"
+             "c0c1c2c3c4c5c6c7c8c9cacbcccdcecf"
+             "d0d1d2d3d4d5d6d7d8d9dadbdcdddedf"
+             "e0e1e2e3e4e5e6e7e8e9eaebecedeeef"
+             "f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff"),
+       L=82,
+       PRK="0x8adae09a2a307059478d309b26c4115a224cfaf6",
+       OKM=("0x0bd770a74d1160f7c9f12cd5912a06eb"
+            "ff6adcae899d92191fe4305673ba2ffe"
+            "8fa3f1a4e5ad79f3f334b3b202b2173c"
+            "486ea37ce3d397ed034c7f9dfeb15c5e"
+            "927336d0441f4c4300e2cff0d0900b52"
+            "d3b4"))
+    _test(digest=sha1,
+          IKM="0x0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b",
+          salt="0x",
+          info="0x",
+          L=42,
+          PRK="0xda8c8a73c7fa77288ec6f5e7c297786aa0d32d01",
+          OKM=("0x0ac1af7002b3d761d1e55298da9d0506"
+               "b9ae52057220a306e07b6b87e8df21d0"
+               "ea00033de03984d34918"))
+
+    _test(digest=sha1,
+          IKM="0x0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c0c",
+          salt="0x",
+          info="0x",
+          L=42,
+          PRK="0x2adccada18779e7c2077ad2eb19d3f3e731385dd",
+          OKM=("0x2c91117204d745f3500d636a62f64f0a"
+               "b3bae548aa53d423b0d1f27ebba6f5e5"
+               "673a081d70cce7acfc48"))
+
+    # finally test that HKDF() without a digest= uses SHA256
+
+    _test(digest=None,
+          IKM="0x0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b",
+          salt="0x",
+          info="0x",
+          L=42,
+          PRK=("0x19ef24a32c717b167f33a91d6f648bdf"
+               "96596776afdb6377ac434c1c293ccb04"),
+          OKM=("0x8da4e775a563c18f715f802a063c5a31"
+               "b8a11f5c5ee1879ec3454e5f3c738d2d"
+               "9d201395faa4b61a96c8"))
+    #print "all test passed"
+
+power_on_self_test()
-Original file line number
+Diff line change
@@ Expand Up / @@ -10,7 +10,6 @@ python: @@
       - "3.4"
       - "3.5"
       - "pypy"
-      - "pypy3"
     install:
       - pip install -U tox virtualenv coverage python-coveralls
     script:
@@ Expand Down @@