- 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 testpython3android
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#!/usr/bin/env python |
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""" |
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ECC blind signature functionality based on "An Efficient Blind Signature Scheme |
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Based on the Elliptic CurveDiscrete Logarithm Problem" by Morteza Nikooghadama |
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<mnikooghadam@sbu.ac.ir> and Ali Zakerolhosseini <a-zaker@sbu.ac.ir>, |
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http://www.isecure-journal.com/article_39171_47f9ec605dd3918c2793565ec21fcd7a.pdf |
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""" |
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# variable names are based on the math in the paper, so they don't conform |
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# to PEP8 |
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# pylint: disable=invalid-name |
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from .openssl import OpenSSL |
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class ECCBlind(object): # pylint: disable=too-many-instance-attributes |
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""" |
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Class for ECC blind signature functionality |
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""" |
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# init |
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k = None |
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R = None |
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keypair = None |
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F = None |
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Q = None |
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a = None |
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b = None |
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c = None |
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binv = None |
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r = None |
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m = None |
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m_ = None |
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s_ = None |
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signature = None |
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@staticmethod |
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def ec_get_random(group, ctx): |
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""" |
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Random point from finite field |
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""" |
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order = OpenSSL.BN_new() |
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OpenSSL.EC_GROUP_get_order(group, order, ctx) |
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OpenSSL.BN_rand(order, OpenSSL.BN_num_bits(order), 0, 0) |
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return order |
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@staticmethod |
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def ec_invert(group, a, ctx): |
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""" |
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ECC inversion |
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""" |
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order = OpenSSL.BN_new() |
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OpenSSL.EC_GROUP_get_order(group, order, ctx) |
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inverse = OpenSSL.BN_mod_inverse(0, a, order, ctx) |
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return inverse |
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@staticmethod |
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def ec_gen_keypair(group, ctx): |
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""" |
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Generate an ECC keypair |
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""" |
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d = ECCBlind.ec_get_random(group, ctx) |
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Q = OpenSSL.EC_POINT_new(group) |
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OpenSSL.EC_POINT_mul(group, Q, d, 0, 0, 0) |
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return (d, Q) |
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def __init__(self, curve="secp256k1"): |
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self.group = OpenSSL.EC_GROUP_new_by_curve_name(OpenSSL.get_curve(curve)) |
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self.ctx = OpenSSL.BN_CTX_new() |
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# Order n |
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self.n = OpenSSL.BN_new() |
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OpenSSL.EC_GROUP_get_order(self.group, self.n, self.ctx) |
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# Identity O (infinity) |
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self.iO = OpenSSL.EC_POINT_new(self.group) |
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OpenSSL.EC_POINT_set_to_infinity(self.group, self.iO) |
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# Generator G |
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self.G = OpenSSL.EC_GROUP_get0_generator(self.group) |
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# Certifier's pubkey |
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self.pubkey = (self.group, self.G, self.n) |
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def signer_init(self): |
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""" |
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Init signer |
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""" |
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# Signer: Random integer k |
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self.k = ECCBlind.ec_get_random(self.group, self.ctx) |
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# R = kG |
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self.R = OpenSSL.EC_POINT_new(self.group) |
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OpenSSL.EC_POINT_mul(self.group, self.R, self.k, 0, 0, 0) |
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def create_signing_request(self, msg): |
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""" |
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Requester creates a new signing request |
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""" |
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# new keypair |
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self.keypair = ECCBlind.ec_gen_keypair(self.group, self.ctx) |
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# Requester: 3 random blinding factors |
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self.F = OpenSSL.EC_POINT_new(self.group) |
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OpenSSL.EC_POINT_set_to_infinity(self.group, self.F) |
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temp = OpenSSL.EC_POINT_new(self.group) |
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self.Q = self.keypair[1] |
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abinv = OpenSSL.BN_new() |
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# F != O |
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while OpenSSL.EC_POINT_cmp(self.group, self.F, self.iO, self.ctx) == 0: |
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self.a = ECCBlind.ec_get_random(self.group, self.ctx) |
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self.b = ECCBlind.ec_get_random(self.group, self.ctx) |
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self.c = ECCBlind.ec_get_random(self.group, self.ctx) |
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# F = b^-1 * R... |
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self.binv = ECCBlind.ec_invert(self.group, self.b, self.ctx) |
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OpenSSL.EC_POINT_mul(self.group, temp, 0, self.R, self.binv, 0) |
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OpenSSL.EC_POINT_copy(self.F, temp) |
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# ... + a*b^-1 * Q... |
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OpenSSL.BN_mul(abinv, self.a, self.binv, self.ctx) |
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OpenSSL.EC_POINT_mul(self.group, temp, 0, self.Q, abinv, 0) |
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OpenSSL.EC_POINT_add(self.group, self.F, self.F, temp, 0) |
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# ... + c*G |
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OpenSSL.EC_POINT_mul(self.group, temp, 0, self.G, self.c, 0) |
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OpenSSL.EC_POINT_add(self.group, self.F, self.F, temp, 0) |
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# F = (x0, y0) |
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x0 = OpenSSL.BN_new() |
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y0 = OpenSSL.BN_new() |
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OpenSSL.EC_POINT_get_affine_coordinates_GFp(self.group, self.F, x0, y0, |
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self.ctx) |
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self.r = x0 |
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# Requester: Blinding (m' = br(m) + a) |
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self.m = OpenSSL.BN_new() |
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OpenSSL.BN_bin2bn(msg, len(msg), self.m) |
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self.m_ = OpenSSL.BN_new() |
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OpenSSL.BN_mod_mul(self.m_, self.b, self.r, self.n, self.ctx) |
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OpenSSL.BN_mod_mul(self.m_, self.m_, self.m, self.n, self.ctx) |
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OpenSSL.BN_mod_add(self.m_, self.m_, self.a, self.n, self.ctx) |
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def blind_sign(self): |
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""" |
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Signer blind-signs the request |
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""" |
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self.s_ = OpenSSL.BN_new() |
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OpenSSL.BN_mod_mul(self.s_, self.keypair[0], self.m_, self.n, self.ctx) |
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OpenSSL.BN_mod_add(self.s_, self.s_, self.k, self.n, self.ctx) |
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def unblind(self): |
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""" |
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Requester unblinds the signature |
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""" |
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s = OpenSSL.BN_new() |
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OpenSSL.BN_mod_mul(s, self.binv, self.s_, self.n, self.ctx) |
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OpenSSL.BN_mod_add(s, s, self.c, self.n, self.ctx) |
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self.signature = (s, self.F) |
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def verify(self): |
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""" |
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Verify signature with certifier's pubkey |
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""" |
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lhs = OpenSSL.EC_POINT_new(self.group) |
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rhs = OpenSSL.EC_POINT_new(self.group) |
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OpenSSL.EC_POINT_mul(self.group, lhs, self.signature[0], 0, 0, 0) |
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OpenSSL.EC_POINT_mul(self.group, rhs, 0, self.Q, self.m, 0) |
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OpenSSL.EC_POINT_mul(self.group, rhs, 0, rhs, self.r, 0) |
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OpenSSL.EC_POINT_add(self.group, rhs, rhs, self.F, self.ctx) |
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retval = OpenSSL.EC_POINT_cmp(self.group, lhs, rhs, self.ctx) |
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if retval == -1: |
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raise RuntimeError("EC_POINT_cmp returned an error") |
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else: |
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return retval == 0 |
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@ -0,0 +1,22 @@ |
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""" |
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Test for ECC blind signatures |
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""" |
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import os |
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import unittest |
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from src.pyelliptic.eccblind import ECCBlind |
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class TestBlindSig(unittest.TestCase): |
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""" |
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Test case for ECC blind signature |
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""" |
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def test_blind_sig(self): |
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"""Test full sequence using a random certifier key and a random message""" |
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blind_sig = ECCBlind() |
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blind_sig.signer_init() |
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msg = os.urandom(64) |
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blind_sig.create_signing_request(msg) |
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blind_sig.blind_sign() |
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blind_sig.unblind() |
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self.assertTrue(blind_sig.verify()) |
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