Blind signature support in pyelliptic

- add blind signature functionality to pyelliptic as described in #1409
- add tests for blind signatures
- PEP8 fixes for pyelliptic
- some minor refactoring is necessary for further integration, this is just a
  minimal implementation to pass a test

src/pyelliptic/__init__.py

@@ -2,18 +2,20 @@
 # Author: Yann GUIBET
 # Contact: <yannguibet@gmail.com>
 
+from .openssl import OpenSSL
+from .ecc import ECC
+from .eccblind import ECCBlind
+from .cipher import Cipher
+from .hash import hmac_sha256, hmac_sha512, pbkdf2
+
 __version__ = '1.3'
 
 __all__ = [
     'OpenSSL',
     'ECC',
+    'ECCBlind',
     'Cipher',
     'hmac_sha256',
     'hmac_sha512',
     'pbkdf2'
 ]
-
-from .openssl import OpenSSL
-from .ecc import ECC
-from .cipher import Cipher
-from .hash import hmac_sha256, hmac_sha512, pbkdf2

src/pyelliptic/cipher.py

@@ -4,7 +4,7 @@
 #  Copyright (C) 2011 Yann GUIBET <yannguibet@gmail.com>
 #  See LICENSE for details.
 
-from pyelliptic.openssl import OpenSSL
+from openssl import OpenSSL
 
 
 class Cipher:

src/pyelliptic/ecc.py

@@ -12,9 +12,9 @@ src/pyelliptic/ecc.py
 from hashlib import sha512
 from struct import pack, unpack
 
-from pyelliptic.cipher import Cipher
+from cipher import Cipher
-from pyelliptic.hash import equals, hmac_sha256
+from hash import equals, hmac_sha256
-from pyelliptic.openssl import OpenSSL
+from openssl import OpenSSL
 
 
 class ECC(object):

src/pyelliptic/eccblind.py

@@ -0,0 +1,179 @@
+#!/usr/bin/env python
+"""
+ECC blind signature functionality based on "An Efficient Blind Signature Scheme
+Based on the Elliptic CurveDiscrete Logarithm Problem" by Morteza Nikooghadama
+<mnikooghadam@sbu.ac.ir> and Ali Zakerolhosseini <a-zaker@sbu.ac.ir>,
+http://www.isecure-journal.com/article_39171_47f9ec605dd3918c2793565ec21fcd7a.pdf
+"""
+
+# variable names are based on the math in the paper, so they don't conform
+# to PEP8
+# pylint: disable=invalid-name
+
+from .openssl import OpenSSL
+
+
+class ECCBlind(object):  # pylint: disable=too-many-instance-attributes
+    """
+    Class for ECC blind signature functionality
+    """
+
+    # init
+    k = None
+    R = None
+    keypair = None
+    F = None
+    Q = None
+    a = None
+    b = None
+    c = None
+    binv = None
+    r = None
+    m = None
+    m_ = None
+    s_ = None
+    signature = None
+
+    @staticmethod
+    def ec_get_random(group, ctx):
+        """
+        Random point from finite field
+        """
+        order = OpenSSL.BN_new()
+        OpenSSL.EC_GROUP_get_order(group, order, ctx)
+        OpenSSL.BN_rand(order, OpenSSL.BN_num_bits(order), 0, 0)
+        return order
+
+    @staticmethod
+    def ec_invert(group, a, ctx):
+        """
+        ECC inversion
+        """
+        order = OpenSSL.BN_new()
+        OpenSSL.EC_GROUP_get_order(group, order, ctx)
+        inverse = OpenSSL.BN_mod_inverse(0, a, order, ctx)
+        return inverse
+
+    @staticmethod
+    def ec_gen_keypair(group, ctx):
+        """
+        Generate an ECC keypair
+        """
+        d = ECCBlind.ec_get_random(group, ctx)
+        Q = OpenSSL.EC_POINT_new(group)
+        OpenSSL.EC_POINT_mul(group, Q, d, 0, 0, 0)
+        return (d, Q)
+
+    def __init__(self, curve="secp256k1"):
+        self.group = OpenSSL.EC_GROUP_new_by_curve_name(OpenSSL.get_curve(curve))
+        self.ctx = OpenSSL.BN_CTX_new()
+
+        # Order n
+        self.n = OpenSSL.BN_new()
+        OpenSSL.EC_GROUP_get_order(self.group, self.n, self.ctx)
+
+        # Identity O (infinity)
+        self.iO = OpenSSL.EC_POINT_new(self.group)
+        OpenSSL.EC_POINT_set_to_infinity(self.group, self.iO)
+
+        # Generator G
+        self.G = OpenSSL.EC_GROUP_get0_generator(self.group)
+
+        # Certifier's pubkey
+        self.pubkey = (self.group, self.G, self.n)
+
+    def signer_init(self):
+        """
+        Init signer
+        """
+        # Signer: Random integer k
+        self.k = ECCBlind.ec_get_random(self.group, self.ctx)
+
+        # R = kG
+        self.R = OpenSSL.EC_POINT_new(self.group)
+        OpenSSL.EC_POINT_mul(self.group, self.R, self.k, 0, 0, 0)
+
+    def create_signing_request(self, msg):
+        """
+        Requester creates a new signing request
+        """
+        # new keypair
+        self.keypair = ECCBlind.ec_gen_keypair(self.group, self.ctx)
+
+        # Requester: 3 random blinding factors
+        self.F = OpenSSL.EC_POINT_new(self.group)
+        OpenSSL.EC_POINT_set_to_infinity(self.group, self.F)
+        temp = OpenSSL.EC_POINT_new(self.group)
+        self.Q = self.keypair[1]
+        abinv = OpenSSL.BN_new()
+
+        # F != O
+        while OpenSSL.EC_POINT_cmp(self.group, self.F, self.iO, self.ctx) == 0:
+            self.a = ECCBlind.ec_get_random(self.group, self.ctx)
+            self.b = ECCBlind.ec_get_random(self.group, self.ctx)
+            self.c = ECCBlind.ec_get_random(self.group, self.ctx)
+
+            # F = b^-1 * R...
+            self.binv = ECCBlind.ec_invert(self.group, self.b, self.ctx)
+            OpenSSL.EC_POINT_mul(self.group, temp, 0, self.R, self.binv, 0)
+            OpenSSL.EC_POINT_copy(self.F, temp)
+
+            # ... + a*b^-1 * Q...
+            OpenSSL.BN_mul(abinv, self.a, self.binv, self.ctx)
+            OpenSSL.EC_POINT_mul(self.group, temp, 0, self.Q, abinv, 0)
+            OpenSSL.EC_POINT_add(self.group, self.F, self.F, temp, 0)
+
+            # ... + c*G
+            OpenSSL.EC_POINT_mul(self.group, temp, 0, self.G, self.c, 0)
+            OpenSSL.EC_POINT_add(self.group, self.F, self.F, temp, 0)
+
+        # F = (x0, y0)
+        x0 = OpenSSL.BN_new()
+        y0 = OpenSSL.BN_new()
+        OpenSSL.EC_POINT_get_affine_coordinates_GFp(self.group, self.F, x0, y0,
+                                                    self.ctx)
+        self.r = x0
+
+        # Requester: Blinding (m' = br(m) + a)
+        self.m = OpenSSL.BN_new()
+        OpenSSL.BN_bin2bn(msg, len(msg), self.m)
+
+        self.m_ = OpenSSL.BN_new()
+        OpenSSL.BN_mod_mul(self.m_, self.b, self.r, self.n, self.ctx)
+        OpenSSL.BN_mod_mul(self.m_, self.m_, self.m, self.n, self.ctx)
+        OpenSSL.BN_mod_add(self.m_, self.m_, self.a, self.n, self.ctx)
+
+    def blind_sign(self):
+        """
+        Signer blind-signs the request
+        """
+        self.s_ = OpenSSL.BN_new()
+        OpenSSL.BN_mod_mul(self.s_, self.keypair[0], self.m_, self.n, self.ctx)
+        OpenSSL.BN_mod_add(self.s_, self.s_, self.k, self.n, self.ctx)
+
+    def unblind(self):
+        """
+        Requester unblinds the signature
+        """
+        s = OpenSSL.BN_new()
+        OpenSSL.BN_mod_mul(s, self.binv, self.s_, self.n, self.ctx)
+        OpenSSL.BN_mod_add(s, s, self.c, self.n, self.ctx)
+        self.signature = (s, self.F)
+
+    def verify(self):
+        """
+        Verify signature with certifier's pubkey
+        """
+        lhs = OpenSSL.EC_POINT_new(self.group)
+        rhs = OpenSSL.EC_POINT_new(self.group)
+
+        OpenSSL.EC_POINT_mul(self.group, lhs, self.signature[0], 0, 0, 0)
+        OpenSSL.EC_POINT_mul(self.group, rhs, 0, self.Q, self.m, 0)
+        OpenSSL.EC_POINT_mul(self.group, rhs, 0, rhs, self.r, 0)
+        OpenSSL.EC_POINT_add(self.group, rhs, rhs, self.F, self.ctx)
+
+        retval = OpenSSL.EC_POINT_cmp(self.group, lhs, rhs, self.ctx)
+        if retval == -1:
+            raise RuntimeError("EC_POINT_cmp returned an error")
+        else:
+            return retval == 0

src/pyelliptic/hash.py

@@ -4,7 +4,7 @@
 #  Copyright (C) 2011 Yann GUIBET <yannguibet@gmail.com>
 #  See LICENSE for details.
 
-from pyelliptic.openssl import OpenSSL
+from openssl import OpenSSL
 
 
 # For python3

src/pyelliptic/openssl.py

@@ -19,7 +19,9 @@ class CipherName:
         self._blocksize = blocksize
 
     def __str__(self):
-        return "Cipher : " + self._name + " | Blocksize : " + str(self._blocksize) + " | Fonction pointer : " + str(self._pointer)
+        return "Cipher : " + self._name + \
+               " | Blocksize : " + str(self._blocksize) + \
+               " | Function pointer : " + str(self._pointer)
 
     def get_pointer(self):
         return self._pointer()
@@ -130,7 +132,11 @@ class _OpenSSL:
 
         self.EC_POINT_get_affine_coordinates_GFp = self._lib.EC_POINT_get_affine_coordinates_GFp
         self.EC_POINT_get_affine_coordinates_GFp.restype = ctypes.c_int
-        self.EC_POINT_get_affine_coordinates_GFp.argtypes = [ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p]
+        self.EC_POINT_get_affine_coordinates_GFp.argtypes = [ctypes.c_void_p,
+                                                             ctypes.c_void_p,
+                                                             ctypes.c_void_p,
+                                                             ctypes.c_void_p,
+                                                             ctypes.c_void_p]
 
         self.EC_KEY_set_private_key = self._lib.EC_KEY_set_private_key
         self.EC_KEY_set_private_key.restype = ctypes.c_int
@@ -144,11 +150,16 @@ class _OpenSSL:
 
         self.EC_KEY_set_group = self._lib.EC_KEY_set_group
         self.EC_KEY_set_group.restype = ctypes.c_int
-        self.EC_KEY_set_group.argtypes = [ctypes.c_void_p, ctypes.c_void_p]
+        self.EC_KEY_set_group.argtypes = [ctypes.c_void_p,
+                                          ctypes.c_void_p]
 
         self.EC_POINT_set_affine_coordinates_GFp = self._lib.EC_POINT_set_affine_coordinates_GFp
         self.EC_POINT_set_affine_coordinates_GFp.restype = ctypes.c_int
-        self.EC_POINT_set_affine_coordinates_GFp.argtypes = [ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p]
+        self.EC_POINT_set_affine_coordinates_GFp.argtypes = [ctypes.c_void_p,
+                                                             ctypes.c_void_p,
+                                                             ctypes.c_void_p,
+                                                             ctypes.c_void_p,
+                                                             ctypes.c_void_p]
 
         self.EC_POINT_new = self._lib.EC_POINT_new
         self.EC_POINT_new.restype = ctypes.c_void_p
@@ -164,7 +175,11 @@ class _OpenSSL:
 
         self.EC_POINT_mul = self._lib.EC_POINT_mul
         self.EC_POINT_mul.restype = None
-        self.EC_POINT_mul.argtypes = [ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p, ctypes.c_void_p]
+        self.EC_POINT_mul.argtypes = [ctypes.c_void_p,
+                                      ctypes.c_void_p,
+                                      ctypes.c_void_p,
+                                      ctypes.c_void_p,
+                                      ctypes.c_void_p]
 
         self.EC_KEY_set_private_key = self._lib.EC_KEY_set_private_key
         self.EC_KEY_set_private_key.restype = ctypes.c_int
@@ -178,7 +193,8 @@ class _OpenSSL:
 
             self.EC_KEY_set_method = self._lib.EC_KEY_set_method
             self._lib.EC_KEY_set_method.restype = ctypes.c_int
-            self._lib.EC_KEY_set_method.argtypes = [ctypes.c_void_p, ctypes.c_void_p]
+            self._lib.EC_KEY_set_method.argtypes = [ctypes.c_void_p,
+                                                    ctypes.c_void_p]
         else:
             self.ECDH_OpenSSL = self._lib.ECDH_OpenSSL
             self._lib.ECDH_OpenSSL.restype = ctypes.c_void_p
@@ -186,7 +202,8 @@ class _OpenSSL:
 
             self.ECDH_set_method = self._lib.ECDH_set_method
             self._lib.ECDH_set_method.restype = ctypes.c_int
-            self._lib.ECDH_set_method.argtypes = [ctypes.c_void_p, ctypes.c_void_p]
+            self._lib.ECDH_set_method.argtypes = [ctypes.c_void_p,
+                                                  ctypes.c_void_p]
 
         self.BN_CTX_new = self._lib.BN_CTX_new
         self._lib.BN_CTX_new.restype = ctypes.c_void_p
@@ -195,12 +212,15 @@ class _OpenSSL:
         self.ECDH_compute_key = self._lib.ECDH_compute_key
         self.ECDH_compute_key.restype = ctypes.c_int
         self.ECDH_compute_key.argtypes = [ctypes.c_void_p,
-                                          ctypes.c_int, ctypes.c_void_p, ctypes.c_void_p]
+                                          ctypes.c_int,
+                                          ctypes.c_void_p,
+                                          ctypes.c_void_p]
 
         self.EVP_CipherInit_ex = self._lib.EVP_CipherInit_ex
         self.EVP_CipherInit_ex.restype = ctypes.c_int
         self.EVP_CipherInit_ex.argtypes = [ctypes.c_void_p,
-                                           ctypes.c_void_p, ctypes.c_void_p]
+                                           ctypes.c_void_p,
+                                           ctypes.c_void_p]
 
         self.EVP_CIPHER_CTX_new = self._lib.EVP_CIPHER_CTX_new
         self.EVP_CIPHER_CTX_new.restype = ctypes.c_void_p
@@ -377,6 +397,124 @@ class _OpenSSL:
                                            ctypes.c_int, ctypes.c_void_p,
                                            ctypes.c_int, ctypes.c_void_p]
 
+        # Blind signature requirements
+        self.BN_CTX_new = self._lib.BN_CTX_new
+        self.BN_CTX_new.restype = ctypes.c_void_p
+        self.BN_CTX_new.argtypes = []
+
+        self.BN_dup = self._lib.BN_dup
+        self.BN_dup.restype = ctypes.c_void_p
+        self.BN_dup.argtypes = [ctypes.c_void_p]
+
+        self.BN_rand = self._lib.BN_rand
+        self.BN_rand.restype = ctypes.c_int
+        self.BN_rand.argtypes = [ctypes.c_void_p,
+                                 ctypes.c_int,
+                                 ctypes.c_int]
+
+        self.BN_set_word = self._lib.BN_set_word
+        self.BN_set_word.restype = ctypes.c_int
+        self.BN_set_word.argtypes = [ctypes.c_void_p,
+                                     ctypes.c_ulong]
+
+        self.BN_mul = self._lib.BN_mul
+        self.BN_mul.restype = ctypes.c_int
+        self.BN_mul.argtypes = [ctypes.c_void_p,
+                                ctypes.c_void_p,
+                                ctypes.c_void_p,
+                                ctypes.c_void_p]
+
+        self.BN_mod_add = self._lib.BN_mod_add
+        self.BN_mod_add.restype = ctypes.c_int
+        self.BN_mod_add.argtypes = [ctypes.c_void_p,
+                                    ctypes.c_void_p,
+                                    ctypes.c_void_p,
+                                    ctypes.c_void_p,
+                                    ctypes.c_void_p]
+
+        self.BN_mod_inverse = self._lib.BN_mod_inverse
+        self.BN_mod_inverse.restype = ctypes.c_void_p
+        self.BN_mod_inverse.argtypes = [ctypes.c_void_p,
+                                        ctypes.c_void_p,
+                                        ctypes.c_void_p,
+                                        ctypes.c_void_p]
+
+        self.BN_mod_mul = self._lib.BN_mod_mul
+        self.BN_mod_mul.restype = ctypes.c_int
+        self.BN_mod_mul.argtypes = [ctypes.c_void_p,
+                                    ctypes.c_void_p,
+                                    ctypes.c_void_p,
+                                    ctypes.c_void_p,
+                                    ctypes.c_void_p]
+
+        self.BN_lshift = self._lib.BN_lshift
+        self.BN_lshift.restype = ctypes.c_int
+        self.BN_lshift.argtypes = [ctypes.c_void_p,
+                                   ctypes.c_void_p,
+                                   ctypes.c_int]
+
+        self.BN_sub_word = self._lib.BN_sub_word
+        self.BN_sub_word.restype = ctypes.c_int
+        self.BN_sub_word.argtypes = [ctypes.c_void_p,
+                                     ctypes.c_ulong]
+
+        self.BN_cmp = self._lib.BN_cmp
+        self.BN_cmp.restype = ctypes.c_int
+        self.BN_cmp.argtypes = [ctypes.c_void_p,
+                                ctypes.c_void_p]
+
+        self.BN_bn2dec = self._lib.BN_bn2dec
+        self.BN_bn2dec.restype = ctypes.c_char_p
+        self.BN_bn2dec.argtypes = [ctypes.c_void_p]
+
+        self.BN_CTX_free = self._lib.BN_CTX_free
+        self.BN_CTX_free.argtypes = [ctypes.c_void_p]
+
+        self.EC_GROUP_new_by_curve_name = self._lib.EC_GROUP_new_by_curve_name
+        self.EC_GROUP_new_by_curve_name.restype = ctypes.c_void_p
+        self.EC_GROUP_new_by_curve_name.argtypes = [ctypes.c_int]
+
+        self.EC_GROUP_get_order = self._lib.EC_GROUP_get_order
+        self.EC_GROUP_get_order.restype = ctypes.c_int
+        self.EC_GROUP_get_order.argtypes = [ctypes.c_void_p,
+                                            ctypes.c_void_p,
+                                            ctypes.c_void_p]
+
+        self.EC_GROUP_get_cofactor = self._lib.EC_GROUP_get_cofactor
+        self.EC_GROUP_get_cofactor.restype = ctypes.c_int
+        self.EC_GROUP_get_cofactor.argtypes = [ctypes.c_void_p,
+                                               ctypes.c_void_p,
+                                               ctypes.c_void_p]
+
+        self.EC_GROUP_get0_generator = self._lib.EC_GROUP_get0_generator
+        self.EC_GROUP_get0_generator.restype = ctypes.c_void_p
+        self.EC_GROUP_get0_generator.argtypes = [ctypes.c_void_p]
+
+        self.EC_POINT_copy = self._lib.EC_POINT_copy
+        self.EC_POINT_copy.restype = ctypes.c_int
+        self.EC_POINT_copy.argtypes = [ctypes.c_void_p,
+                                       ctypes.c_void_p]
+
+        self.EC_POINT_add = self._lib.EC_POINT_add
+        self.EC_POINT_add.restype = ctypes.c_int
+        self.EC_POINT_add.argtypes = [ctypes.c_void_p,
+                                      ctypes.c_void_p,
+                                      ctypes.c_void_p,
+                                      ctypes.c_void_p,
+                                      ctypes.c_void_p]
+
+        self.EC_POINT_cmp = self._lib.EC_POINT_cmp
+        self.EC_POINT_cmp.restype = ctypes.c_int
+        self.EC_POINT_cmp.argtypes = [ctypes.c_void_p,
+                                      ctypes.c_void_p,
+                                      ctypes.c_void_p,
+                                      ctypes.c_void_p]
+
+        self.EC_POINT_set_to_infinity = self._lib.EC_POINT_set_to_infinity
+        self.EC_POINT_set_to_infinity.restype = ctypes.c_int
+        self.EC_POINT_set_to_infinity.argtypes = [ctypes.c_void_p,
+                                                  ctypes.c_void_p]
+
         self._set_ciphers()
         self._set_curves()
 
@@ -494,6 +632,7 @@ class _OpenSSL:
             buffer = self.create_string_buffer(size)
         return buffer
 
+
 def loadOpenSSL():
     global OpenSSL
     from os import path, environ
@@ -548,4 +687,5 @@ def loadOpenSSL():
             pass
     raise Exception("Couldn't find and load the OpenSSL library. You must install it.")
 
+
 loadOpenSSL()

src/tests/test_blindsig.py

@@ -0,0 +1,22 @@
+"""
+Test for ECC blind signatures
+"""
+import os
+import unittest
+
+from src.pyelliptic.eccblind import ECCBlind
+
+
+class TestBlindSig(unittest.TestCase):
+    """
+    Test case for ECC blind signature
+    """
+    def test_blind_sig(self):
+        """Test full sequence using a random certifier key and a random message"""
+        blind_sig = ECCBlind()
+        blind_sig.signer_init()
+        msg = os.urandom(64)
+        blind_sig.create_signing_request(msg)
+        blind_sig.blind_sign()
+        blind_sig.unblind()
+        self.assertTrue(blind_sig.verify())