def extract_attributes(self, policy_str):
util = SecretUtil(self.abe.group)
policy = util.createPolicy(policy_str)
return [
util.strip_index(policy_attr)
for policy_attr in util.getAttributeList(policy)
]
def add_time_periods_to_policy(policy: str, time_period: int,
group: PairingGroup) -> str:
"""
Update the policy to a policy where the attribute have the time period embedded.
:param policy: The policy to update.
:param time_period: The time period to embed.
:param group:
:return: The policy with the time period embedded.
>>> group = PairingGroup('SS512')
>>> add_time_periods_to_policy("STUDENT@UT", 2, group) == "2%STUDENT@UT"
True
>>> add_time_periods_to_policy("STUDENT@UT and TUTOR@VU", 2, group) == "2%STUDENT@UT and 2%TUTOR@VU"
True
>>> add_time_periods_to_policy("(STUDENT@UT and TUTOR@VU) or (FOO@BAR and (TEST@TROLL or A@B))", 5611315, group) \
== "(5611315%STUDENT@UT and 5611315%TUTOR@VU) or (5611315%FOO@BAR and (5611315%TEST@TROLL or 5611315%A@B))"
True
>>> add_time_periods_to_policy(\
"ADMINISTRATION@INSURANCE or (DOCTOR@NDB and REVIEWER@INSURANCE) or (RADIOLOGIST@NDB and REVIEWER@INSURANCE)", 1, group) == \
"1%ADMINISTRATION@INSURANCE or (1%DOCTOR@NDB and 1%REVIEWER@INSURANCE) or (1%RADIOLOGIST@NDB and 1%REVIEWER@INSURANCE)"
True
"""
util = SecretUtil(group, verbose=False)
parsed_policy = util.createPolicy(policy)
attributes = list_attributes(parsed_policy)
return reduce(
lambda p, attribute: p.replace(
attribute, add_time_period_to_attribute(attribute, time_period)),
attributes, policy)
def decrypt(ik, sk, ct, pk=None):
group = PairingGroup('SS512')
if pk is None:
pk = getPK(stsConfig['TS_ip'],stsConfig['api_getPK'])
if type(pk['g']) == type(''):
pk = dictToObject(pk_dict=pk, group=group)
if type(ct['C0']) == type(''):
ct = dictToObject(ct_dict=ct)
if type(ik['K0']) == type(''):
ik = dictToObject(ik_dict=ik)
if type(sk) == type(''):
sk = dictToObject(pairingElement_dict=sk)
group = PairingGroup('SS512')
util = SecretUtil(group, False)
w = pk['w']
u = pk['u']
S = ik['S'] #['THREE', 'ONE', 'TWO']
K0 = ik['K0']
K1 = ik['K1']
Kj2 = ik['Ki2']
Kj3 = ik['Ki3']
C0 = ct['C0']
Ci1 = ct['C_j_1']
Ci2 = ct['C_j_2']
Ci3 = ct['C_j_3']
Ci4 = ct['C_j_4']
Ci5 = ct['C_j_5']
policy = util.createPolicy(ct['policy']) #((ONE or THREE) and (TWO or FOUR))
print('access policy of this file :', policy)
try:
pruned = util.prune(policy, S) #[ONE, TWO]
except Exception,e:
raise Exception('your attributes do not satisfy the policy!')
def predecrypt(pk, ik, ct):
group = PairingGroup('SS512')
util = SecretUtil(group, debug)
w = pk['w']
u = pk['u']
S = ik['S'] #['THREE', 'ONE', 'TWO']
K0 = ik['K0']
K1 = ik['K1']
Kj2 = ik['Ki2']
Kj3 = ik['Ki3']
C0 = ct['C0']
Ci1 = ct['C_j_1']
Ci2 = ct['C_j_2']
Ci3 = ct['C_j_3']
Ci4 = ct['C_j_4']
Ci5 = ct['C_j_5']
policy = util.createPolicy(ct['policy']) #((ONE or THREE) and (TWO or FOUR))
print('policy in predecrypt===', policy)
print('S in predecrypt===', S)
pruned = util.prune(policy, S) #[ONE, TWO]
if pruned is False:
raise Exception('Prune error in pre-decrypt')
wi = util.getCoefficients(policy) #{u'TWO': <pairing.Element>, u'FOUR': <pairing.Element>, u'THREE': <pairing.Element>, u'ONE': <pairing.Element>}
eC0K0 = pair(C0,K0)
ECi4wi = 0
for each in pruned:
i = each.getAttribute()
ECi4wi += Ci4[i] * wi[i]
ewECi4wiK1 = pair(w ** ECi4wi,K1)
PIeCi1K1eCi2uCi5Kj2eCi3Kj3wi = 1
for each in pruned:
j = each.getAttributeAndIndex()
i = each.getAttribute()
eCi1K1 = pair(Ci1[i],K1)
eCi2uCi5Kj2 = pair(Ci2[i] * (u ** -Ci5[i]), Kj2[j])
eCi3Kj3 = pair(Ci3[i],Kj3[j])
PIeCi1K1eCi2uCi5Kj2eCi3Kj3wi *= (eCi1K1 * eCi2uCi5Kj2 * eCi3Kj3) ** wi[i]
return objectToBytes(eC0K0/(ewECi4wiK1 * PIeCi1K1eCi2uCi5Kj2eCi3Kj3wi), group)
def encrypt(policy_str, pool, group=None):
print('policy_str in ABEnc=',policy_str)
if group is None:
group = PairingGroup('SS512')
util = SecretUtil(group, False)
policy = util.createPolicy(policy_str)
secret = pool.pop('s')
print('policy in ABEnc=',policy)
sshares = util.calculateSharesList(secret, policy)
sshares = dict([(x[0].getAttributeAndIndex(), x[1]) for x in sshares])
print('sshares in ABEnc=',sshares)
C0 = pool.pop('C0')
C_x_1, C_x_2, C_x_3, C_x_4, C_x_5 = {},{},{},{},{}
for attr, s_share in sshares.items():
component = pool['components'].pop()
C_x_1[attr] = component['C_j_1']
C_x_2[attr] = component['C_j_2']
C_x_3[attr] = component['C_j_3']
C_x_4[attr] = s_share - component['lambda_prime_j']
C_x_5[attr] = component['t_j'] * (group.hash(unicode(attr),ZR) - component['x_j'])
ct = {'policy':policy_str, 'C0':C0,'C_j_1':C_x_1, 'C_j_2':C_x_2, 'C_j_3':C_x_3, 'C_j_4':C_x_4, 'C_j_5':C_x_5}
print('ct in ABEnc=',ct)
return (pool, ct)
class MAABE(object):
def __init__(self, groupObj):
self.util = SecretUtil(groupObj,
verbose=False) #Create Secret Sharing Scheme
self.group = groupObj #:Prime order group
def setup(self):
'''Global Setup (executed by CA)'''
#:In global setup, a bilinear group G of prime order p is chosen
#:The global public parameters, GP and p, and a generator g of G. A random oracle H maps global identities GID to elements of G
#:group contains
#:the prime order p is contained somewhere within the group object
g = self.group.random(G1)
#: The oracle that maps global identities GID onto elements of G
#:H = lambda str: g** group.hash(str)
H = lambda x: self.group.hash(x, G1)
a = self.group.random()
b = self.group.random()
g_a = g**a
g_b = g**b
GPP = {'g': g, 'g_a': g_a, 'g_b': g_b, 'H': H}
GMK = {'a': a, 'b': b}
return (GPP, GMK)
def registerUser(self, GPP):
'''Generate user keys (executed by the user).'''
g = GPP['g']
ugsk1 = self.group.random()
ugsk2 = self.group.random()
ugpk1 = g**ugsk1
ugpk2 = g**ugsk2
return ((ugpk1, ugsk2), {
'pk': ugpk2,
'sk': ugsk1
}) # (private, public)
def setupAuthority(self, GPP, authorityid, attributes, authorities):
'''Generate attribute authority keys (executed by attribute authority)'''
if authorityid not in authorities:
alpha = self.group.random()
beta = self.group.random()
gamma = self.group.random()
SK = {'alpha': alpha, 'beta': beta, 'gamma': gamma}
PK = {
'e_alpha': pair(GPP['g'], GPP['g'])**alpha,
'g_beta': GPP['g']**beta,
'g_beta_inv': GPP['g']**~beta
}
authAttrs = {}
authorities[authorityid] = (SK, PK, authAttrs)
else:
SK, PK, authAttrs = authorities[authorityid]
for attrib in attributes:
if attrib in authAttrs:
continue
versionKey = self.group.random() # random or really 'choose' ?
h = GPP['H'](attrib)
pk = h**versionKey
authAttrs[attrib] = {
'VK': versionKey, #secret
'PK1': pk, #public
'PK2': pk**SK['gamma'] #public
}
return (SK, PK, authAttrs)
def keygen(self, GPP, authority, attribute, userObj, USK=None):
'''Generate user keys for a specific attribute (executed on attribute authority)'''
if 't' not in userObj:
userObj['t'] = self.group.random() #private to AA
t = userObj['t']
ASK, APK, authAttrs = authority
u = userObj
if USK is None:
USK = {}
if 'K' not in USK or 'KS' not in USK or 'AK' not in USK:
USK['K'] = \
(GPP['g'] ** ASK['alpha']) * \
(GPP['g_a'] ** u['sk']) * \
(GPP['g_b'] ** t)
USK['KS'] = GPP['g']**t
USK['AK'] = {}
AK = (u['pk'] ** (t * ASK['beta'])) * \
((authAttrs[attribute]['PK1'] ** ASK['beta']) ** (u['sk'] + ASK['gamma']))
USK['AK'][attribute] = AK
return USK
def encrypt(self, GPP, policy_str, k, authority):
'''Generate the cipher-text from the content(-key) and a policy (executed by the content owner)'''
#GPP are global parameters
#k is the content key (group element based on AES key)
#policy_str is the policy string
#authority is the authority tuple
_, APK, authAttrs = authority
policy = self.util.createPolicy(policy_str)
secret = self.group.random()
shares = self.util.calculateSharesList(secret, policy)
shares = dict([(x[0].getAttributeAndIndex(), x[1]) for x in shares])
C1 = k * (APK['e_alpha']**secret)
C2 = GPP['g']**secret
C3 = GPP['g_b']**secret
C = {}
CS = {}
D = {}
DS = {}
for attr, s_share in shares.items():
k_attr = self.util.strip_index(attr)
r_i = self.group.random()
attrPK = authAttrs[attr]
C[attr] = (GPP['g_a']**s_share) * ~(attrPK['PK1']**r_i)
CS[attr] = GPP['g']**r_i
D[attr] = APK['g_beta_inv']**r_i
DS[attr] = attrPK['PK2']**r_i
return {
'C1': C1,
'C2': C2,
'C3': C3,
'C': C,
'CS': CS,
'D': D,
'DS': DS,
'policy': policy_str
}
def decrypt(self, GPP, CT, user):
'''Decrypts the content(-key) from the cipher-text (executed by user/content consumer)'''
UASK = user['authoritySecretKeys']
USK = user['keys']
usr_attribs = list(UASK['AK'].keys())
policy = self.util.createPolicy(CT['policy'])
pruned = self.util.prune(policy, usr_attribs)
if pruned == False:
return False
coeffs = self.util.getCoefficients(policy)
first = pair(CT['C2'], UASK['K']) * ~pair(CT['C3'], UASK['KS'])
n_a = 1
ugpk1, ugsk2 = USK
e_gg_auns = 1
for attr in pruned:
x = attr.getAttributeAndIndex()
y = attr.getAttribute()
temp = \
pair(CT['C'][y], ugpk1) * \
pair(CT['D'][y], UASK['AK'][y]) * \
pair(CT['CS'][y], ~(UASK['KS'] ** ugsk2)) * \
~pair(GPP['g'], CT['DS'][y])
e_gg_auns *= temp**(coeffs[x] * n_a)
return CT['C1'] / (first / e_gg_auns)
def ukeygen(self, GPP, authority, attribute, userObj):
'''Generate update keys for users and cloud provider (executed by attribute authority?)'''
ASK, _, authAttrs = authority
oldVersionKey = authAttrs[attribute]['VK']
newVersionKey = oldVersionKey
while oldVersionKey == newVersionKey:
newVersionKey = self.group.random()
authAttrs[attribute]['VK'] = newVersionKey
u_uid = userObj['sk']
UKs = GPP['H'](attribute)**(ASK['beta'] *
(newVersionKey - oldVersionKey) *
(u_uid + ASK['gamma']))
UKc = (newVersionKey / oldVersionKey, (oldVersionKey - newVersionKey) /
(oldVersionKey * ASK['gamma']))
authAttrs[attribute]['PK1'] = authAttrs[attribute]['PK1']**UKc[0]
authAttrs[attribute]['PK2'] = authAttrs[attribute]['PK2']**UKc[0]
return {'UKs': UKs, 'UKc': UKc}
def skupdate(self, USK, attribute, UKs):
'''Updates the user attribute secret key for the specified attribute (executed by non-revoked user)'''
USK['AK'][attribute] = USK['AK'][attribute] * UKs
def ctupdate(self, GPP, CT, attribute, UKc):
'''Updates the cipher-text using the update key, because of the revoked attribute (executed by cloud provider)'''
CT['C'][attribute] = CT['C'][attribute] * (CT['DS'][attribute]**UKc[1])
CT['DS'][attribute] = CT['DS'][attribute]**UKc[0]
class MaabeKPA(ABEncMultiAuth):
"""
A Multiauthority Attribute Based Cryptosystem with Expressive Policies
>>> group = PairingGroup('SS512')
>>> n_users = 8
>>> height = 3
>>> tree = Tree(n_users, height)
>>> maabe = MaabeKPA(group, tree)
>>> public_parameters = maabe.setup()
Setup the attribute authorities
>>> attributes1 = ['ONE', 'TWO', 'THREE']
>>> attributes2 = ['FOUR', 'FIVE', 'SIX']
>>> attributes3 = ['SEVEN', 'EIGHT', 'NINE']
>>> attributes4 = ['TEN', 'ELEVEN', 'TWELVE']
>>> (public_key1, secret_key1) = maabe.authsetup(public_parameters, 'AB')
>>> (public_key2, secret_key2) = maabe.authsetup(public_parameters, 'CD')
>>> (public_key3, secret_key3) = maabe.authsetup(public_parameters, 'EF')
>>> (public_key4, secret_key4) = maabe.authsetup(public_parameters, 'GH')
>>> public_keys = {'AB': public_key1, 'CD': public_key2, 'EF': public_key3, 'GH': public_key4}
>>> secret_keys = {'AB': secret_key1, 'CD': secret_key2, 'EF': secret_key3, 'GH': secret_key4}
Setup a user and give him some keys
>>> gid = 2
>>> user_attributes1 = ['A1@AB', 'B1@AB', 'C1@AB']
>>> user_attributes2 = ['D1@CD', 'E1@CD', 'F1@CD']
>>> user_attributes3 = ['A2@EF', 'B2@EF', 'C2@EF']
>>> user_attributes4 = ['D2@GH', 'E2@GH', 'F2@GH']
>>> path = tree.Path(2)
>>> user_keys1 = maabe.multiple_attributes_keygen(public_parameters, secret_key1, gid, path, user_attributes1)
>>> user_keys2 = maabe.multiple_attributes_keygen(public_parameters, secret_key2, gid, path, user_attributes2)
>>> user_keys3 = maabe.multiple_attributes_keygen(public_parameters, secret_key3, gid, path, user_attributes3)
>>> user_keys4 = maabe.multiple_attributes_keygen(public_parameters, secret_key4, gid, path, user_attributes4)
>>> user_keys = {'GID': gid, 'keys': merge_dicts(user_keys1, user_keys2, user_keys3, user_keys4)}
>>> update_key1 = maabe.update_keygen(public_parameters, gid, public_key1, secret_key1, user_keys1, user_attributes1, 20)
>>> update_key2 = maabe.update_keygen(public_parameters, gid, public_key2, secret_key2, user_keys2, user_attributes2, 20)
>>> update_key3 = maabe.update_keygen(public_parameters, gid, public_key3, secret_key3, user_keys3, user_attributes3, 20)
>>> update_key4 = maabe.update_keygen(public_parameters, gid, public_key4, secret_key4, user_keys4, user_attributes4, 20)
>>> decrypt_key1 = maabe.decrypt_keygen(public_parameters, public_key1, user_keys1, gid, update_key1, user_attributes1, True)
>>> decrypt_key2 = maabe.decrypt_keygen(public_parameters, public_key2, user_keys2, gid, update_key2, user_attributes2, True)
>>> decrypt_key3 = maabe.decrypt_keygen(public_parameters, public_key3, user_keys3, gid, update_key3, user_attributes3, True)
>>> decrypt_key4 = maabe.decrypt_keygen(public_parameters, public_key4, user_keys4, gid, update_key4, user_attributes4, True)
>>> decrypt_keys = {'GID': gid, 'keys': merge_dicts(decrypt_key1, decrypt_key2, decrypt_key3, decrypt_key4)}
Create a random message
>>> message = group.random(GT)
Encrypt the message
>>> access_policy = '(A1@AB or E1@CD) and (C2@EF or D2@GH)'
>>> cipher_text = maabe.encrypt(public_parameters, public_keys, message, access_policy, 20)
print("Decryption key")
print(decrypt_keys['keys'].keys())
print("User key")
print(user_keys['keys'].keys())
Decrypt the message
>>> decrypted_message = maabe.decrypt(gid, public_parameters, user_keys, decrypt_keys, cipher_text)
>>> decrypted_message == message
True
Check for key sanity
>>> sanityCheck = maabe.sanitycheck(public_parameters, secret_keys, public_keys, user_keys)
Sanity Check
SanityCheck1: True
SanityCheck2: True
>>> sanityCheck == True
True
"""
def __init__(self, group, tree, verbose=False):
ABEncMultiAuth.__init__(self)
self.group = group
self.tree = tree
self.util = SecretUtil(group, verbose)
def setup(self):
g1 = self.group.random(G1)
g2 = self.group.random(G2)
egg = pair(g1, g2)
H = lambda x: self.group.hash(x, G2)
F = lambda x: self.group.hash(x, G2)
gp = {'g1': g1, 'g2': g2, 'egg': egg, 'H': H, 'F': F}
if debug:
print("Setup")
print(gp)
return gp
def unpack_attribute(self, attribute):
"""
Unpacks an attribute in attribute name, authority name and index
:param attribute: The attribute to unpack
:return: The attribute name, authority name and the attribute index, if present.
>>> group = PairingGroup('SS512')
>>> n_users = 8
>>> height = 3
>>> tree = Tree(n_users, height)
>>> maabe = MaabeKPA(group, tree)
>>> maabe.unpack_attribute('STUDENT@UT')
('STUDENT', 'UT', None)
>>> maabe.unpack_attribute('STUDENT@UT_2')
('STUDENT', 'UT', '2')
"""
parts = re.split(r"[@_]", attribute)
assert len(parts) > 1, "No @ char in [attribute@authority] name"
return parts[0], parts[1], None if len(parts) < 3 else parts[2]
def authsetup(self, gp, name):
N, d = 8, 5
alpha, y = self.group.random(), self.group.random()
a, b = self.group.random(), self.group.random()
egga = gp['egg']**alpha
gy = gp['g1']**y
ga = gp['g1']**a
gb = gp['g1']**b
g2a = gp['g2']**a
g2b = gp['g2']**b
f_list = list()
r_list = dict()
for i in range(0, d + 1):
f_list.append(self.group.random(G2))
for i in range(1, 2 * N):
r_list[i] = self.group.random()
pk = {
'name': name,
'egga': egga,
'gy': gy,
'ga': ga,
'gb': gb,
'f_list': f_list,
'g2a': g2a,
'g2b': g2b
}
sk = {
'name': name,
'alpha': alpha,
'y': y,
'a': a,
'b': b,
'r_list': r_list
}
if debug:
print("Authsetup: %s" % name)
print(pk)
print(sk)
return pk, sk
def J(self, f_list, d, t):
t_binary = bin(t)[2:]
prod = self.group.init(G2, 1)
prod *= f_list[0]
for i in range(1, d + 1):
if t_binary[i - 1] == '1':
prod *= f_list[i]
return prod
def keygen(self, gp, sk, gid, attribute, w):
"""
Generate a user secret key for the attribute.
:param gp: The global parameters.
:param sk: The secret key of the attribute authority.
:param gid: The global user identifier.
:param attribute: The attribute.
:param w: The node in the path
:return: The secret key for the attribute for the user with identifier gid.
"""
_, auth, _ = self.unpack_attribute(attribute)
assert sk[
'name'] == auth, "Attribute %s does not belong to authority %s" % (
attribute, sk['name'])
tt = self.group.random()
r = self.group.random()
j = (sk['a'] + sk['b'] * r)
K1 = gp['g2']**((sk['alpha'] - sk['r_list'][w]) / (j + gid))
K1 *= gp['H'](str(gid))**(sk['y'] / (j + gid))
K1 *= gp['F'](attribute)**tt
K2 = gid
K3 = r
K4 = gp['g1']**tt
K5 = gp['g1']**(j * tt)
if debug:
print("Keygen")
print("User, Attribute, Node")
print(gid)
print(attribute)
print(w)
print({'K1': K1, 'K2': K2, 'K3': K3, 'K4': K4, 'K5': K5})
return {'K1': K1, 'K2': K2, 'K3': K3, 'K4': K4, 'K5': K5}
def multiple_attributes_keygen(self, gp, sk, gid, path, attributes):
"""
Generate a dictionary of secret keys for a user for a list of attributes.
:param gp: The global parameters.
:param sk: The secret key of the attribute authority.
:param gid: The global user identifier.
:param attributes: The list of attributes.
:return: A dictionary with attribute names as keys, and secret keys for the attributes as values.
"""
usk = {}
for attribute in attributes:
usk[attribute] = {}
for w in path:
usk[attribute][w] = self.keygen(gp, sk, gid, attribute, w)
return usk
def update_keygen(self, gp, gid, pks, sk, user_key, attributes, t):
X, Y = self.tree.get_sets()
gid_hash = gid
uk = {}
for attribute in attributes:
uk[attribute] = {}
for w in Y:
m = self.group.random()
r = user_key[attribute][w]['K3']
j = (sk['a'] + sk['b'] * r)
uk1 = (gp['g2']**((sk['r_list'][w]) /
(j + gid_hash))) * (self.J(
pks['f_list'], 5, t)**(m /
(j + gid_hash)))
uk2 = gp['g1']**m
uk3 = self.J(pks['f_list'], 5, t)**(1 / (j + gid_hash))
uk[attribute][w] = {'U1': uk1, 'U2': uk2, 'U3': uk3}
if debug:
print("Update keygen")
print(uk)
return uk
def decrypt_keygen(self, gp, pks, usk, gid, uk, attributes, first_iter):
X, Y = self.tree.get_sets()
path = set(self.tree.Path(gid))
common = path.intersection(set(Y))
dsk = {}
for w in common:
if first_iter:
m = 0
else:
m = self.group.random()
for attribute in attributes:
D1 = usk[attribute][w]['K1'] * uk[attribute][w]['U1'] * (
uk[attribute][w]['U3']**m)
D2 = usk[attribute][w]['K4']
Dt = uk[attribute][w]['U2'] * gp['g1']**m
dsk[attribute] = {'D1': D1, 'D2': D2, 'Dt': Dt}
if debug:
print("Decrypt keygen")
print(dsk)
return dsk
def encrypt(self, gp, pks, message, policy_str, t):
"""
Encrypt a message under an access policy
:param gp: The global parameters.
:param pks: The public keys of the relevant attribute authorities, as dict from authority name to public key.
:param message: The message to encrypt.
:param policy_str: The access policy to use.
:return: The encrypted message.
"""
s = self.group.random() # secret to be shared
w = self.group.init(ZR, 0) # 0 to be shared
policy = self.util.createPolicy(policy_str)
attribute_list = self.util.getAttributeList(policy)
secret_shares = self.util.calculateSharesDict(
s, policy) # These are correctly set to be exponents in Z_p
zero_shares = self.util.calculateSharesDict(w, policy)
C0 = message * (gp['egg']**s)
C1, C2, C3, C4, C5, C6, Ct = {}, {}, {}, {}, {}, {}, {}
b = bin(t)[2:]
testing = list()
rx_list = {}
for i in attribute_list:
attribute_name, auth, _ = self.unpack_attribute(i)
attr = "%s@%s" % (attribute_name, auth)
rx = self.group.random()
rx_list[i] = rx
C1[i] = gp['egg']**secret_shares[i] * pks[auth]['egga']**rx
C2[i] = gp['g1']**(-rx)
C3[i] = pks[auth]['gy']**rx * gp['g1']**zero_shares[i]
C4[i] = gp['F'](attr)**rx
C5[i] = pks[auth]['ga']**(-rx)
C6[i] = pks[auth]['gb']**(-rx)
Ct[i] = self.group.init(G2, 1)
Ct[i] *= pks[auth]['f_list'][0]
for k in range(0, len(b)):
if b[k] == '1':
Ct[i] *= pks[auth]['f_list'][k + 1]
Ct[i] = Ct[i]**rx
if debug:
print("Encrypt")
print(message)
print({
'policy': policy_str,
'C0': C0,
'C1': C1,
'C2': C2,
'C3': C3,
'C4': C4,
'C5': C5,
'C6': C6,
'Ct': Ct
})
print("Testing value")
print(testing)
return {
'policy': policy_str,
'C0': C0,
'C1': C1,
'C2': C2,
'C3': C3,
'C4': C4,
'C5': C5,
'C6': C6,
'Ct': Ct,
'secret_shares': secret_shares,
'zero_shares': zero_shares,
'rx': rx_list
}
# def update_encrypt(self, gp, pks, ct):
# """
# Encrypt a message under an access policy
# :param gp: The global parameters.
# :param pks: The public keys of the relevant attribute authorities, as dict from authority name to public key.
# :param message: The message to encrypt.
# :param policy_str: The access policy to use.
# :return: The encrypted message.
# """
# s_new = self.group.random() # secret to be shared
# w_new = self.group.init(ZR, 0) # 0 to be shared
# policy = self.util.createPolicy(ct['policy'])
# attribute_list = self.util.getAttributeList(policy)
# secret_shares = self.util.calculateSharesDict(s, policy) # These are correctly set to be exponents in Z_p
# zero_shares = self.util.calculateSharesDict(w, policy)
# C0_new = ct['C0'] * (gp['egg'] ** s_new)
# C1_new, C2_new, C3_new, C4_new, C5_new, C6_new = {}, {}, {}, {}, {}, {}
# for i in attribute_list:
# attribute_name, auth, _ = self.unpack_attribute(i)
# attr = "%s@%s" % (attribute_name, auth)
# rx_new = self.group.random()
# C1_new[i] = ct['C1'][i] * gp['egg'] ** secret_shares[i] * pks[auth]['egga'] ** rx_new
# C2_new[i] = ct['C2'][i] * gp['g1'] ** (-rx_new)
# C3_new[i] = ct['C3'][i] * pks[auth]['gy'] ** rx_new * gp['g1'] ** zero_shares[i]
# C4_new[i] = ct['C4'][i] * gp['F'](attr) ** rx_new
# C5_new[i] = ct['C5'][i] * pks[auth]['ga'] ** (-rx_new)
# C6_new[i] = ct['C6'][i] * pks[auth]['gb'] ** (-rx_new)
# if debug:
# print("Update Encrypt")
# print(message)
# print({'policy': policy_str, 'C0_new': C0_new, 'C1_new': C1_new, 'C2_new': C2_new, 'C3_new': C3_new, 'C4_new': C4_new, 'C5_new': C5_new, 'C6_new': C6_new})
# return {'policy': policy_str, 'C0_new': C0_new, 'C1_new': C1_new, 'C2_new': C2_new, 'C3_new': C3_new, 'C4_new': C4_new, 'C5_new': C5_new, 'C6_new': C6_new}
def decrypt(self, gi, gp, usk, dsk, ct):
"""
Decrypt the ciphertext using the secret keys of the user.
:param gp: The global parameters.
:param sk: The secret keys of the user.
:param ct: The ciphertext to decrypt.
:return: The decrypted message.
:raise Exception: When the access policy can not be satisfied with the user's attributes.
"""
X, Y = self.tree.get_sets()
path = set(self.tree.Path(gi))
common = path.intersection(set(Y))
gid = list(common)[0]
policy = self.util.createPolicy(ct['policy'])
coefficients = self.util.getCoefficients(policy)
pruned_list = self.util.prune(policy, usk['keys'].keys())
if not pruned_list:
raise Exception(
"You don't have the required attributes for decryption!")
B = self.group.init(GT, 1)
for i in range(len(pruned_list)):
x = pruned_list[i].getAttribute() # without the underscore
# y = pruned_list[i].getAttributeAndIndex() # with the underscore
t1 = ct['C2'][x]**usk['keys'][x][gid]['K2']
t1 *= ct['C5'][x]
t1 *= ct['C6'][x]**usk['keys'][x][gid]['K3']
result1 = pair(t1, dsk['keys'][x]['D1'])
result2 = ct['C1'][x]
result3 = pair(dsk['keys'][x]['Dt'], ct['Ct'][x])
result4 = pair((dsk['keys'][x]['D2']**usk['keys'][x][gid]['K2']) *
usk['keys'][x][gid]['K5'], ct['C4'][x])
result5 = pair(ct['C3'][x],
gp['H'](str(usk['keys'][x][gid]['K2'])))
B *= (result1 * result2 * result3 * result4 *
result5)**coefficients[x]
decrypted_message = ct['C0'] / B
if debug:
print("Decrypt")
print("DSK:")
print(dsk)
print("Decrypted Message:")
print(decrypted_message)
return decrypted_message
def sanitycheck(self, gp, sks, pks, usk):
# self.group.StartBenchmark(["RealTime", "Mul", "Exp", "Pair"])
# policy = self.util.createPolicy(policy_ct)
# pruned_list = self.util.prune(policy, sk['keys'].keys())
# if not pruned_list:
# raise Exception("You don't have the required attributes for decryption!")
attributes = usk['keys'].keys()
keySanityCheck = False
for x in attributes:
# x = pruned_list[i].getAttribute()
# keySanityCheck = True
keySanityCheck1 = False
keySanityCheck2 = False
attribute_name, auth, _ = self.unpack_attribute(x)
for w in usk['keys'][x].keys():
keySanityCheck1 = keySanityCheck1 or (pair(
usk['keys'][x][w]['K5'], gp['g2']) == pair(
usk['keys'][x][w]['K4'], pks[auth]['g2a'] *
(pks[auth]['g2b']**usk['keys'][x][w]['K3'])))
keySanityCheck2 = keySanityCheck2 or (
pair(
pks[auth]['ga'] *
(pks[auth]['gb']**usk['keys'][x][w]['K3']) *
(gp['g1']**usk['keys'][x][w]['K2']),
usk['keys'][x][w]['K1'])
== (gp['egg']**
(sks[auth]['alpha'] - sks[auth]['r_list'][w])) *
pair(pks[auth]['gy'], gp['H'](str(
usk['keys'][x][w]['K2']))) * pair(
usk['keys'][x][w]['K5'] *
(usk['keys'][x][w]['K4']**usk['keys'][x][w]['K2']),
gp['F'](x)))
keySanityCheck = (keySanityCheck1 and keySanityCheck2)
if keySanityCheck:
break
if debug:
print("Sanity Check")
print("SanityCheck1:", keySanityCheck1)
print("SanityCheck2:", keySanityCheck2)
return keySanityCheck
class MaabeKPA(ABEncMultiAuth):
"""
A Multiauthority Attribute Based Cryptosystem with Expressive Policies
>>> group = PairingGroup('SS512')
>>> maabe = MaabeKPA(group)
>>> public_parameters = maabe.setup()
Setup the attribute authorities
attributes1 = ['ONE', 'TWO', 'THREE', 'FOUR']
attributes2 = ['THREE', 'FOUR']
>>> (public_key1, secret_key1) = maabe.authsetup(public_parameters, 'AB')
>>> (public_key2, secret_key2) = maabe.authsetup(public_parameters, 'CD')
>>> (public_key3, secret_key3) = maabe.authsetup(public_parameters, 'EF')
>>> (public_key4, secret_key4) = maabe.authsetup(public_parameters, 'GH')
>>> public_keys = {'AB': public_key1, 'CD': public_key2, 'EF': public_key3, 'GH': public_key4 }
Setup a user and give him some keys
>>> gid = "bob"
>>> user_attributes1 = ['A1@AB', 'B1@AB', 'C1@AB', 'D1@AB']
>>> user_attributes2 = ['A2@CD', 'B2@CD', 'C2@CD', 'D2@CD']
>>> user_attributes3 = ['A3@EF', 'B3@EF', 'C3@EF', 'D3@EF']
>>> user_attributes4 = ['A4@GH', 'B4@GH', 'C4@GH', 'D4@GH']
>>> user_keys1 = maabe.multiple_attributes_keygen(public_parameters, secret_key1, gid, user_attributes1)
>>> user_keys2 = maabe.multiple_attributes_keygen(public_parameters, secret_key2, gid, user_attributes2)
>>> user_keys3 = maabe.multiple_attributes_keygen(public_parameters, secret_key3, gid, user_attributes3)
>>> user_keys4 = maabe.multiple_attributes_keygen(public_parameters, secret_key4, gid, user_attributes4)
>>> user_keys = {'GID': gid, 'keys': merge_dicts(user_keys1, user_keys2, user_keys3, user_keys4)}
Create a random message
>>> message = group.random(GT)
Encrypt the message
>>> access_policy = '(A1@AB or D2@CD) and (B3@EF or C4@GH)'
>>> cipher_text = maabe.encrypt(public_parameters, public_keys, message, access_policy)
Decrypt the message
>>> decrypted_message = maabe.decrypt(public_parameters, user_keys, cipher_text)
>>> decrypted_message == message
True
Check for key sanity
>>> sanityCheck = maabe.sanitycheck(public_parameters, public_keys, user_keys, cipher_text['policy'])
Sanity Check
SanityCheck1: True
SanityCheck2: True
>>> sanityCheck == True
True
"""
def __init__(self, group, verbose=False):
ABEncMultiAuth.__init__(self)
self.group = group
self.util = SecretUtil(group, verbose)
f = open('Benchmarks.txt', 'a+')
f.write("\n")
f.close()
def setup(self):
g1 = self.group.random(G1)
g2 = self.group.random(G2)
egg = pair(g1, g2)
H = lambda x: self.group.hash(x, G2)
F = lambda x: self.group.hash(x, G2)
gp = {'g1': g1, 'g2': g2, 'egg': egg, 'H': H, 'F': F}
if debug:
print("Setup")
print(gp)
return gp
def unpack_attribute(self, attribute):
"""
Unpacks an attribute in attribute name, authority name and index
:param attribute: The attribute to unpack
:return: The attribute name, authority name and the attribute index, if present.
>>> group = PairingGroup('SS512')
>>> maabe = MaabeKPA(group)
>>> maabe.unpack_attribute('STUDENT@UT')
('STUDENT', 'UT', None)
>>> maabe.unpack_attribute('STUDENT@UT_2')
('STUDENT', 'UT', '2')
"""
parts = re.split(r"[@_]", attribute)
assert len(parts) > 1, "No @ char in [attribute@authority] name"
return parts[0], parts[1], None if len(parts) < 3 else parts[2]
def authsetup(self, gp, name):
"""
Setup an attribute authority.
:param gp: The global parameters
:param name: The name of the authority
:return: The public and private key of the authority
"""
f = open('Benchmarks.txt', 'a+')
assert self.group.InitBenchmark(), "failed to initialize benchmark"
self.group.StartBenchmark(["RealTime", "Mul", "Exp", "Pair"])
alpha, y = self.group.random(), self.group.random()
a, b = self.group.random(), self.group.random()
egga = gp['egg']**alpha
gy = gp['g1']**y
ga = gp['g1']**a
gb = gp['g1']**b
pk = {'name': name, 'egga': egga, 'gy': gy, 'ga': ga, 'gb': gb}
sk = {'name': name, 'alpha': alpha, 'y': y, 'a': a, 'b': b}
self.group.EndBenchmark()
msmtDict = self.group.GetGeneralBenchmarks()
f.write("\nAuth Setup Benchmarks for %s:" % name)
json.dump(msmtDict, f)
f.close()
if debug:
print("Authsetup: %s" % name)
print(pk)
print(sk)
return pk, sk
def keygen(self, gp, sk, gid, attribute):
"""
Generate a user secret key for the attribute.
:param gp: The global parameters.
:param sk: The secret key of the attribute authority.
:param gid: The global user identifier.
:param attribute: The attribute.
:return: The secret key for the attribute for the user with identifier gid.
"""
_, auth, _ = self.unpack_attribute(attribute)
assert sk[
'name'] == auth, "Attribute %s does not belong to authority %s" % (
attribute, sk['name'])
t = self.group.random()
i = self.group.random()
gid_hash = self.group.hash(gid, ZR)
j = sk['a'] + sk['a'] * sk['b'] * gid_hash
K4 = gp['g2']**i
K1 = gp['g2']**sk['alpha'] * K4**j * gp['H'](gid)**sk['y'] * gp['F'](
attribute)**t
K2 = gid
K3 = K4**sk['b']
K5 = gp['g1']**t
if debug:
print("Keygen")
print("User: %s, Attribute: %s" % (gid, attribute))
print({'K1': K1, 'K2': K2, 'K3': K3, 'K4': K4, 'K5': K5})
return {'K1': K1, 'K2': K2, 'K3': K3, 'K4': K4, 'K5': K5}
def multiple_attributes_keygen(self, gp, sk, gid, attributes):
"""
Generate a dictionary of secret keys for a user for a list of attributes.
:param gp: The global parameters.
:param sk: The secret key of the attribute authority.
:param gid: The global user identifier.
:param attributes: The list of attributes.
:return: A dictionary with attribute names as keys, and secret keys for the attributes as values.
"""
uk = {}
f = open('Benchmarks.txt', 'a+')
# assert self.group.InitBenchmark(), "failed to initialize benchmark"
self.group.StartBenchmark(["RealTime", "Mul", "Exp", "Pair"])
for attribute in attributes:
uk[attribute] = self.keygen(gp, sk, gid, attribute)
self.group.EndBenchmark()
msmtDict = self.group.GetGeneralBenchmarks()
f.write("\nTotal Keygen Benchmarks:")
json.dump(msmtDict, f)
f.close()
return uk
def encrypt(self, gp, pks, message, policy_str):
"""
Encrypt a message under an access policy
:param gp: The global parameters.
:param pks: The public keys of the relevant attribute authorities, as dict from authority name to public key.
:param message: The message to encrypt.
:param policy_str: The access policy to use.
:return: The encrypted message.
"""
f = open('Benchmarks.txt', 'a+')
s = self.group.random() # secret to be shared
w = self.group.init(ZR, 0) # 0 to be shared
policy = self.util.createPolicy(policy_str)
attribute_list = self.util.getAttributeList(policy)
# assert self.group.InitBenchmark(), "failed to initialize benchmark"
self.group.StartBenchmark(["RealTime", "Mul", "Exp", "Pair"])
secret_shares = self.util.calculateSharesDict(
s, policy) # These are correctly set to be exponents in Z_p
zero_shares = self.util.calculateSharesDict(w, policy)
C0 = message * (gp['egg']**s)
C1, C2, C3, C4, C5 = {}, {}, {}, {}, {}
for i in attribute_list:
attribute_name, auth, _ = self.unpack_attribute(i)
attr = "%s@%s" % (attribute_name, auth)
tx = self.group.random()
C1[i] = gp['egg']**secret_shares[i] * pks[auth]['egga']**tx
C2[i] = gp['g1']**(-tx)
C3[i] = pks[auth]['gy']**tx * gp['g1']**zero_shares[i]
C4[i] = gp['F'](attr)**tx
C5[i] = pks[auth]['ga']**tx
self.group.EndBenchmark()
msmtDict = self.group.GetGeneralBenchmarks()
f.write("\nEncryption Benchmarks:")
json.dump(msmtDict, f)
# granDict = self.group.GetGranularBenchmarks()
# print("<=== General Benchmarks ===>")
# print("Results := ", msmtDict)
# print("<=== Granular Benchmarks ===>")
# print("G1 mul := ", granDict["Mul"][G1])
f.close()
if debug:
print("Encrypt")
print(message)
print({
'policy': policy_str,
'C0': C0,
'C1': C1,
'C2': C2,
'C3': C3,
'C4': C4,
'C5': C5
})
return {
'policy': policy_str,
'C0': C0,
'C1': C1,
'C2': C2,
'C3': C3,
'C4': C4,
'C5': C5
}
def decrypt(self, gp, sk, ct):
"""
Decrypt the ciphertext using the secret keys of the user.
:param gp: The global parameters.
:param sk: The secret keys of the user.
:param ct: The ciphertext to decrypt.
:return: The decrypted message.
:raise Exception: When the access policy can not be satisfied with the user's attributes.
"""
f = open('Benchmarks.txt', 'a+')
# assert self.group.InitBenchmark(), "failed to initialize benchmark"
self.group.StartBenchmark(["RealTime", "Mul", "Exp", "Pair"])
policy = self.util.createPolicy(ct['policy'])
coefficients = self.util.getCoefficients(policy)
pruned_list = self.util.prune(policy, sk['keys'].keys())
print(pruned_list)
if not pruned_list:
raise Exception(
"You don't have the required attributes for decryption!")
B = self.group.init(GT, 1)
for i in range(len(pruned_list)):
x = pruned_list[i].getAttribute() # without the underscore
y = pruned_list[i].getAttributeAndIndex() # with the underscore
K2_hash = self.group.hash(sk['keys'][x]['K2'], ZR)
B *= (ct['C1'][y] * pair(ct['C2'][y], sk['keys'][x]['K1']) *
pair(ct['C3'][y], gp['H'](sk['keys'][x]['K2'])) *
pair(sk['keys'][x]['K5'], ct['C4'][y]) *
pair(ct['C5'][y], sk['keys'][x]['K4'] *
sk['keys'][x]['K3']**K2_hash))**coefficients[y]
decrypted_message = ct['C0'] / B
self.group.EndBenchmark()
msmtDict = self.group.GetGeneralBenchmarks()
f.write("\nDecryption Benchmarks:")
json.dump(msmtDict, f)
f.close()
if debug:
print("Decrypt")
print("SK:")
print(sk['keys'].keys())
print(x)
print(y)
print("Decrypted Message:")
print(decrypted_message)
return decrypted_message
def sanitycheck(self, gp, pks, sk, policy_ct):
f = open('Benchmarks.txt', 'a+')
# assert self.group.InitBenchmark(), "failed to initialize benchmark"
self.group.StartBenchmark(["RealTime", "Mul", "Exp", "Pair"])
policy = self.util.createPolicy(policy_ct)
pruned_list = self.util.prune(policy, sk['keys'].keys())
if not pruned_list:
raise Exception(
"You don't have the required attributes for decryption!")
keySanityCheck = False
for i in range(len(pruned_list)):
x = pruned_list[i].getAttribute()
attribute_name, auth, _ = self.unpack_attribute(x)
K2_hash = self.group.hash(sk['keys'][x]['K2'], ZR)
keySanityCheck1 = (pair(gp['g1'], sk['keys'][x]['K3']) == pair(
pks[auth]['gb'], sk['keys'][x]['K4']))
keySanityCheck2 = (
pair(gp['g1'], sk['keys'][x]['K1']) == pks[auth]['egga'] *
pair(pks[auth]['gy'], gp['H'](sk['keys'][x]['K2'])) *
pair(sk['keys'][x]['K5'], gp['F'](x)) *
pair(pks[auth]['ga'],
sk['keys'][x]['K4'] * sk['keys'][x]['K3']**K2_hash))
keySanityCheck = keySanityCheck1 and keySanityCheck2
if keySanityCheck:
break
self.group.EndBenchmark()
msmtDict = self.group.GetGeneralBenchmarks()
f.write("\nSanity Check Benchmarks:")
json.dump(msmtDict, f)
f.close()
if debug:
print("Sanity Check")
print("SanityCheck1:", keySanityCheck1)
print("SanityCheck2:", keySanityCheck2)
return keySanityCheck
class MaabeRW15(ABEncMultiAuth):
"""
Efficient Statically-Secure Large-Universe Multi-Authority Attribute-Based Encryption
Rouselakis - Waters
"""
def __init__(self, group, verbose=False):
ABEncMultiAuth.__init__(self)
self.group = group
self.util = SecretUtil(group, verbose)
def setup(self):
g1 = self.group.random(G1)
g2 = self.group.random(G2)
egg = pair(g1, g2)
H = lambda x: self.group.hash(x, G2)
F = lambda x: self.group.hash(x, G2)
gp = {'g1': g1, 'g2': g2, 'egg': egg, 'H': H, 'F': F}
if debug:
print("Setup")
print(gp)
return gp
def unpack_attribute(self, attribute):
"""
Unpacks an attribute in attribute name, authority name and index
:param attribute: The attribute to unpack
:return: The attribute name, authority name and the attribute index, if present.
group = PairingGroup('SS512')
maabe = MaabeRW15(group)
maabe.unpack_attribute('STUDENT@UT')
('STUDENT', 'UT', None)
maabe.unpack_attribute('STUDENT@UT_2')
('STUDENT', 'UT', '2')
"""
parts = re.split(r"[@_]", attribute)
assert len(parts) > 1, "No @ char in [attribute@authority] name"
return parts[0], parts[1], None if len(parts) < 3 else parts[2]
def authsetup(self, gp, name):
"""
Setup an attribute authority.
:param gp: The global parameters
:param name: The name of the authority
:return: The public and private key of the authority
"""
alpha, y = self.group.random(), self.group.random()
egga = gp['egg']**alpha
gy = gp['g1']**y
pk = {'name': name, 'egga': egga, 'gy': gy}
sk = {'name': name, 'alpha': alpha, 'y': y}
if debug:
print("Authsetup: %s" % name)
print(pk)
print(sk)
return pk, sk
def keygen(self, gp, sk, gid, attribute):
"""
Generate a user secret key for the attribute.
:param gp: The global parameters.
:param sk: The secret key of the attribute authority.
:param gid: The global user identifier.
:param attribute: The attribute.
:return: The secret key for the attribute for the user with identifier gid.
"""
_, auth, _ = self.unpack_attribute(attribute)
assert sk[
'name'] == auth, "Attribute %s does not belong to authority %s" % (
attribute, sk['name'])
t = self.group.random()
K = gp['g2']**sk['alpha'] * gp['H'](gid)**sk['y'] * gp['F'](
attribute)**t
KP = gp['g1']**t
if debug:
print("Keygen")
print("User: %s, Attribute: %s" % (gid, attribute))
print({'K': K, 'KP': KP})
return {'K': K, 'KP': KP}
def multiple_attributes_keygen(self, gp, sk, gid, attributes):
"""
Generate a dictionary of secret keys for a user for a list of attributes.
:param gp: The global parameters.
:param sk: The secret key of the attribute authority.
:param gid: The global user identifier.
:param attributes: The list of attributes.
:return: A dictionary with attribute names as keys, and secret keys for the attributes as values.
"""
uk = {}
for attribute in attributes:
uk[attribute] = self.keygen(gp, sk, gid, attribute)
return uk
def encrypt(self, gp, pks, message, policy_str):
"""
Encrypt a message under an access policy
:param gp: The global parameters.
:param pks: The public keys of the relevant attribute authorities, as dict from authority name to public key.
:param message: The message to encrypt.
:param policy_str: The access policy to use.
:return: The encrypted message.
"""
s = self.group.random() # secret to be shared
w = self.group.init(ZR, 0) # 0 to be shared
policy = self.util.createPolicy(policy_str)
attribute_list = self.util.getAttributeList(policy)
secret_shares = self.util.calculateSharesDict(
s, policy) # These are correctly set to be exponents in Z_p
zero_shares = self.util.calculateSharesDict(w, policy)
C0 = message * (gp['egg']**s)
C1, C2, C3, C4 = {}, {}, {}, {}
for i in attribute_list:
attribute_name, auth, _ = self.unpack_attribute(i)
attr = "%s@%s" % (attribute_name, auth)
tx = self.group.random()
C1[i] = gp['egg']**secret_shares[i] * pks[auth]['egga']**tx
C2[i] = gp['g1']**(-tx)
C3[i] = pks[auth]['gy']**tx * gp['g1']**zero_shares[i]
C4[i] = gp['F'](attr)**tx
if debug:
print("Encrypt")
print(message)
print({
'policy': policy_str,
'C0': C0,
'C1': C1,
'C2': C2,
'C3': C3,
'C4': C4
})
return {
'policy': policy_str,
'C0': C0,
'C1': C1,
'C2': C2,
'C3': C3,
'C4': C4
}
def decrypt(self, gp, sk, ct):
"""
Decrypt the ciphertext using the secret keys of the user.
:param gp: The global parameters.
:param sk: The secret keys of the user.
:param ct: The ciphertext to decrypt.
:return: The decrypted message.
:raise Exception: When the access policy can not be satisfied with the user's attributes.
"""
policy = self.util.createPolicy(ct['policy'])
coefficients = self.util.getCoefficients(policy)
pruned_list = self.util.prune(policy, sk['keys'].keys())
if not pruned_list:
raise Exception(
"You don't have the required attributes for decryption!")
B = self.group.init(GT, 1)
for i in range(len(pruned_list)):
x = pruned_list[i].getAttribute() # without the underscore
y = pruned_list[i].getAttributeAndIndex() # with the underscore
B *= (ct['C1'][y] * pair(ct['C2'][y], sk['keys'][x]['K']) *
pair(ct['C3'][y], gp['H'](sk['GID'])) *
pair(sk['keys'][x]['KP'], ct['C4'][y]))**coefficients[y]
if debug:
print("Decrypt")
print("SK:")
print(sk)
print("Decrypted Message:")
print(ct['C0'] / B)
return ct['C0'] / B
class DACMACS(object):
def __init__(self, groupObj):
self.util = SecretUtil(groupObj,
verbose=False) #Create Secret Sharing Scheme
self.group = groupObj #:Prime order group
def setup(self):
'''Global Setup (executed by CA)'''
#:In global setup, a bilinear group G of prime order p is chosen
#:The global public parameters, GP and p, and a generator g of G. A random oracle H maps global identities GID to elements of G
#:group contains
#:the prime order p is contained somewhere within the group object
g = self.group.random(G1)
#: The oracle that maps global identities GID onto elements of G
#:H = lambda str: g** group.hash(str)
H = lambda x: self.group.hash(x, G1)
a = self.group.random()
g_a = g**a
GPP = {'g': g, 'g_a': g_a, 'H': H}
GMK = {'a': a}
return (GPP, GMK)
def registerUser(self, GPP):
'''Generate user keys (executed by the user).'''
g = GPP['g']
u = self.group.random()
z = self.group.random()
g_u = g**u
g_z = g**(1 / z)
return ((g_u, z), {'g_z': g_z, 'u': u}) # (private, public)
def setupAuthority(self, GPP, authorityid, attributes, authorities):
'''Generate attribute authority keys (executed by attribute authority)'''
if authorityid not in authorities:
alpha = self.group.random()
beta = self.group.random()
gamma = self.group.random()
SK = {'alpha': alpha, 'beta': beta, 'gamma': gamma}
PK = {
'e_alpha': pair(GPP['g'], GPP['g'])**alpha,
'g_beta_inv': GPP['g']**(1 / beta),
'g_beta_gamma': GPP['g']**(gamma / beta)
}
authAttrs = {}
authorities[authorityid] = (SK, PK, authAttrs)
else:
SK, PK, authAttrs = authorities[authorityid]
for attrib in attributes:
if attrib in authAttrs:
continue
versionKey = self.group.random() # random or really 'choose' ?
h = GPP['H'](attrib)
pk = ((GPP['g']**versionKey) * h)**SK['gamma']
authAttrs[attrib] = {
'VK': versionKey, #secret
'PK': pk, #public
}
return (SK, PK, authAttrs)
def keygen(self, GPP, authority, attribute, userObj, USK=None):
'''Generate user keys for a specific attribute (executed on attribute authority)'''
if 't' not in userObj:
userObj['t'] = self.group.random() #private to AA
t = userObj['t']
ASK, APK, authAttrs = authority
u = userObj
if USK is None:
USK = {}
if 'K' not in USK or 'L' not in USK or 'R' not in USK or 'AK' not in USK:
USK['K'] = \
(u['g_z'] ** ASK['alpha']) * \
(GPP['g_a'] ** u['u']) * \
(GPP['g_a'] ** (t / ASK['beta']))
USK['L'] = u['g_z']**(ASK['beta'] * t)
USK['R'] = GPP['g_a']**t
USK['AK'] = {}
AK = (u['g_z'] ** (ASK['beta'] * ASK['gamma'] * t)) * \
(authAttrs[attribute]['PK'] ** (ASK['beta'] * u['u']))
USK['AK'][attribute] = AK
return USK
def encrypt(self, GPP, policy_str, k, authority):
'''Generate the cipher-text from the content(-key) and a policy (executed by the content owner)'''
#GPP are global parameters
#k is the content key (group element based on AES key)
#policy_str is the policy string
#authority is the authority tuple
_, APK, authAttrs = authority
policy = self.util.createPolicy(policy_str)
secret = self.group.random()
shares = self.util.calculateSharesList(secret, policy)
shares = dict([(x[0].getAttributeAndIndex(), x[1]) for x in shares])
C1 = k * (APK['e_alpha']**secret)
C2 = GPP['g']**secret
C3 = APK['g_beta_inv']**secret
C = {}
D = {}
DS = {}
for attr, s_share in shares.items():
k_attr = self.util.strip_index(attr)
r_i = self.group.random()
attrPK = authAttrs[attr]
C[attr] = (GPP['g_a']**s_share) * ~(attrPK['PK']**r_i)
D[attr] = APK['g_beta_inv']**r_i
DS[attr] = ~(APK['g_beta_gamma']**r_i)
return {
'C1': C1,
'C2': C2,
'C3': C3,
'C': C,
'D': D,
'DS': DS,
'policy': policy_str
}
def generateTK(self, GPP, CT, UASK, g_u):
'''Generates a token using the user's attribute secret keys to offload the decryption process (executed by cloud provider)'''
usr_attribs = list(UASK['AK'].keys())
policy = self.util.createPolicy(CT['policy'])
pruned = self.util.prune(policy, usr_attribs)
if pruned == False:
return False
coeffs = self.util.getCoefficients(policy)
dividend = pair(CT['C2'], UASK['K']) * ~pair(UASK['R'], CT['C3'])
n_a = 1
divisor = 1
for attr in pruned:
x = attr.getAttributeAndIndex()
y = attr.getAttribute()
temp = \
pair(CT['C'][y], g_u) * \
pair(CT['D'][y], UASK['AK'][y]) * \
pair(CT['DS'][y], UASK['L'])
divisor *= temp**(coeffs[x] * n_a)
return dividend / divisor
def decrypt(self, CT, TK, z):
'''Decrypts the content(-key) from the cipher-text using the token and the user secret key (executed by user/content consumer)'''
return CT['C1'] / (TK**z)
def ukeygen(self, GPP, authority, attribute, userObj):
'''Generate update keys for users and cloud provider (executed by attribute authority?)'''
ASK, _, authAttrs = authority
oldVersionKey = authAttrs[attribute]['VK']
newVersionKey = oldVersionKey
while oldVersionKey == newVersionKey:
newVersionKey = self.group.random()
authAttrs[attribute]['VK'] = newVersionKey
u = userObj['u']
AUK = ASK['gamma'] * (newVersionKey - oldVersionKey)
KUK = GPP['g']**(u * ASK['beta'] * AUK)
CUK = ASK['beta'] * AUK / ASK['gamma']
authAttrs[attribute]['PK'] = authAttrs[attribute]['PK'] * (GPP['g']**
AUK)
return {'KUK': KUK, 'CUK': CUK}
def skupdate(self, USK, attribute, KUK):
'''Updates the user attribute secret key for the specified attribute (executed by non-revoked user)'''
USK['AK'][attribute] = USK['AK'][attribute] * KUK
def ctupdate(self, GPP, CT, attribute, CUK):
'''Updates the cipher-text using the update key, because of the revoked attribute (executed by cloud provider)'''
CT['C'][attribute] = CT['C'][attribute] * (CT['DS'][attribute]**CUK)
class YLLC15(ABEnc):
"""
Possibly a subclass of BSW07?
"""
def __init__(self, group):
ABEnc.__init__(self)
self.group = group
self.util = SecretUtil(self.group)
@Output(params_t, msk_t)
def setup(self):
g, gp = self.group.random(G1), self.group.random(G2)
alpha, beta = self.group.random(ZR), self.group.random(ZR)
# initialize pre-processing for generators
g.initPP()
gp.initPP()
h = g**beta
e_gg_alpha = pair(g, gp**alpha)
params = {'g': g, 'g2': gp, 'h': h, 'e_gg_alpha': e_gg_alpha}
msk = {'beta': beta, 'alpha': alpha}
return params, msk
@Input(params_t)
@Output(pku_t, sku_t)
def ukgen(self, params):
g2 = params['g2']
x = self.group.random(ZR)
pku = g2**x
sku = x
return pku, sku
@Input(params_t, msk_t, pku_t, pku_t, [str])
# @Output(pxku_t)
def proxy_keygen(self, params, msk, pkcs, pku, attribute_list):
"""
attributes specified in the `attribute_list` are converted to uppercase
"""
r1 = self.group.random(ZR)
r2 = self.group.random(ZR)
g = params['g']
g2 = params['g2']
k = ((pkcs**r1) * (pku**msk['alpha']) * (g2**r2))**~msk['beta']
k_prime = g2**r1
k_attrs = {}
for attr in attribute_list:
attr_caps = attr.upper()
r_attr = self.group.random(ZR)
k_attr1 = (g2**r2) * (self.group.hash(str(attr_caps), G2)**r_attr)
k_attr2 = g**r_attr
k_attrs[attr_caps] = (k_attr1, k_attr2)
proxy_key_user = {'k': k, 'k_prime': k_prime, 'k_attrs': k_attrs}
return proxy_key_user
@Input(params_t, GT, str)
# @Output(ct_t)
def encrypt(self, params, msg, policy_str):
"""
Encrypt a message M under a policy string.
attributes specified in policy_str are converted to uppercase
policy_str must use parentheses e.g. (A) and (B)
"""
policy = self.util.createPolicy(policy_str)
s = self.group.random(ZR)
shares = self.util.calculateSharesDict(s, policy)
C = (params['e_gg_alpha']**s) * msg
c_prime = params['h']**s
c_prime_prime = params['g']**s
c_attrs = {}
for attr in shares.keys():
attr_stripped = self.util.strip_index(attr)
c_i1 = params['g']**shares[attr]
c_i2 = self.group.hash(attr_stripped, G1)**shares[attr]
c_attrs[attr] = (c_i1, c_i2)
ciphertext = {
'policy_str': policy_str,
'C': C,
'C_prime': c_prime,
'C_prime_prime': c_prime_prime,
'c_attrs': c_attrs
}
return ciphertext
# @Input(sku_t, pxku_t, ct_t)
@Output(v_t)
def proxy_decrypt(self, skcs, proxy_key_user, ciphertext):
policy_root_node = ciphertext['policy_str']
k = proxy_key_user['k']
k_prime = proxy_key_user['k_prime']
c_prime = ciphertext['C_prime']
c_prime_prime = ciphertext['C_prime_prime']
c_attrs = ciphertext['c_attrs']
k_attrs = proxy_key_user['k_attrs']
policy = self.util.createPolicy(policy_root_node)
attributes = proxy_key_user['k_attrs'].keys()
pruned_list = self.util.prune(policy, attributes)
if not pruned_list:
return None
z = self.util.getCoefficients(policy)
# reconstitute the policy random secret (A) which was used to encrypt the message
A = 1
for i in pruned_list:
attr_idx = i.getAttributeAndIndex()
attr = i.getAttribute()
A *= (pair(c_attrs[attr_idx][0], k_attrs[attr][0]) /
pair(k_attrs[attr][1], c_attrs[attr_idx][1]))**z[attr_idx]
e_k_c_prime = pair(k, c_prime)
denominator = (pair(k_prime, c_prime_prime)**skcs) * A
encrypted_element_for_user_pkenc_scheme = e_k_c_prime / denominator
intermediate_value = {
'C': ciphertext['C'],
'e_term': encrypted_element_for_user_pkenc_scheme
}
return intermediate_value
@Input(type(None), sku_t, v_t)
@Output(GT)
def decrypt(self, params, sku, intermediate_value):
"""
:param params: Not required - pass None instead. For interface compatibility only.
:param sku: the secret key of the user as generated by `ukgen()`.
:param intermediate_value: the partially decrypted ciphertext returned by `proxy_decrypt()`.
:return: the plaintext message
"""
ciphertext = intermediate_value['C']
e_term = intermediate_value['e_term']
denominator = e_term**(sku**-1)
msg = ciphertext / denominator
return msg
class OMACPABE(object):
def __init__(self, group_object):
# initialize class object with secret sharing utility
# and appropriate group object
self.util = SecretUtil(group_object, verbose=False)
self.group = group_object
# certificate authority (CA) setup function
def abenc_casetup(self):
"""
Global setup function run by the CA to generate the
Global Master Key (GMK) and the Global Public Parameters (GPP)
:return: GMK, GPP
"""
# initialize bilinear group G of prime p with generator g
g = self.group.random(G1)
# initialize hash function that maps to an element of G
H = lambda x: self.group.hash(x, G1)
# select random elements from Z_p
a = self.group.random(ZR)
b = self.group.random(ZR)
g_a = g**a
g_b = g**b
# Global Public Parameters (GPP) = g, g_a, g_b, H
GPP = {
'g': g,
'g_a': g_a,
'g_b': g_b,
'H': H,
}
# Global Master Key (GMK) = a, b
GMK = {
'a': a,
'b': b,
}
#
return (GPP, GMK)
def abenc_userreg(self, GPP, entity='user'):
"""
User registration by Certificate Authority (CA) to generate corresponding
key pairs (i.e. Public and Private keys)
:param GPP: Global Public Parameters (GPP)
:param entity: the entity executing algorithm
# :param registered_users: Dictionary of already registered users
:return: User Global Secret and Public Keys (GSK_uid, GSK_uid_prime, GPK_uid, GPK_uid_prime)
"""
# group generator from GPP
g = GPP['g']
# random numbers as user global secret keys
u_uid = self.group.random(ZR)
u_uid_prime = self.group.random(ZR)
# user global public keys
g_u_uid = g**u_uid
g_u_uid_prime = g**(1 / u_uid_prime)
# secret public key pair sent to user
GSK_uid_prime = u_uid_prime
GPK_uid = g_u_uid
# secret public key pair to be sent to registered Attribute Authorities (AAs)
GSK_uid = u_uid
GPK_uid_prime = g_u_uid_prime
return (GPK_uid, GSK_uid_prime), {
'GSK_uid': GSK_uid,
'GPK_uid_prime': GPK_uid_prime,
'u_uid': u_uid,
}
def abenc_aareg(self, GPP, authority_id, attributes,
registered_authorities):
"""
Registration of Attribute Authorities (AA) by the Certificate Authority (CA)
:param GPP: Global Public Parameters (GPP)
:param authority_id: Unique ID for Attribute Authority
:param attributes: Attributes managed by the authority
:param registered_authorities: Dictionary of already registered authorities
:return: Attribute Authority Secret and Public Key pairs with Version and Public keys for the attributes
"""
# check if authority has already been registered
if authority_id not in registered_authorities:
# generate random values to serves as attribute authority secret key
alpha_aid = self.group.random(ZR)
beta_aid = self.group.random(ZR)
gamma_aid = self.group.random(ZR)
# attribute authority secret key values
SK_aid = {
'alpha_aid': alpha_aid,
'beta_aid': beta_aid,
'gamma_aid': gamma_aid
}
# attribute authority public key values
PK_aid = {
'e_alpha': pair(GPP['g'], GPP['g'])**alpha_aid,
'g_beta_aid': GPP['g']**beta_aid,
'g_beta_aid_inv': GPP['g']**(1 / beta_aid),
}
authority_attributes = {}
registered_authorities[authority_id] = (SK_aid, PK_aid,
authority_attributes)
else:
SK_aid, PK_aid, authority_attributes = registered_authorities[
authority_id]
# generate version and public keys for attributes
for attribute in attributes:
# check if attributes already exist with public and version keys
# if they do, skip generation process
if attribute in authority_attributes:
continue
# generate random element as version key
version_key = self.group.random(ZR)
h = GPP['H'](attribute)
PK_1_attribute = h**version_key
PK_2_attribute = h**(version_key * SK_aid['gamma_aid'])
PK_attribute_aid = [PK_1_attribute, PK_2_attribute]
authority_attributes[attribute] = {
'VK': version_key,
'PK': PK_attribute_aid,
}
return (SK_aid, PK_aid, authority_attributes)
def abenc_keygen(self, GPP, authority, attribute, user_object, USK=None):
"""
Generate attribute authority related secret keys for users (executed by the corresponding attribute authority)
:param GPP: Global Public Parameters
:param authority: Attribute Authority Parameters
:param attribute: Attribute for which secret key is being generated
:param user_object: User
:param USK: Generated attribute authority related user secret key
:return: User Secret Key (USK)
"""
# generate random integer to tie attribute secret key to user
if 't' not in user_object:
user_object['t'] = self.group.random(ZR)
t = user_object['t']
# assign corresponding attribute authority parameters
ASK, APK, authority_attrs = authority
u = user_object
# create USK data set if none exists already
if USK is None:
USK = {}
if 'K_uid_aid' not in USK or 'K_uid_aid_prime' not in USK or 'AK_uid_aid' not in USK:
USK['K_uid_aid'] = (u['GPK_uid_prime']**ASK['alpha_aid']) * (
GPP['g_a']**u['u_uid']) * (GPP['g_b']**t)
USK['K_uid_aid_prime'] = GPP['g']**t
USK['AK_uid_aid'] = {}
# generate attribute specific secret key parameters
AK_uid_aid = (GPP['g'] ** (t * ASK['beta_aid'])) * authority_attrs[attribute]['PK'][0] \
** (ASK['beta_aid'] * (u['u_uid'] + ASK['gamma_aid']))
USK['AK_uid_aid'][attribute] = AK_uid_aid
return USK
def abenc_encrypt(self, GPP, policy_string, k, authority):
"""
Encryption algorithm which encrypts the message given, based on the policy
:param GPP: Global Public Parameters
:param policy_string: Policy
:param k: Content Key (i.e group element based on AES key)
:param authority: Attribute Authority Parameters
:return: Ciphertext
"""
APK = {}
authority_attributes = {}
authority_g_beta_inv = {}
# extract the APK for the different authorities
for authority_temp in authority.keys():
APK[authority_temp] = authority[authority_temp][1]
# extract the PK values of the attributes of the attribute authorities
# extract the corresponding g_beta_inverse values for the attribute authorities
for item in authority[authority_temp][2].keys():
authority_attributes[item] = authority[authority_temp][2][item]
authority_g_beta_inv[item] = APK[authority_temp][
'g_beta_aid_inv']
# extract policy and use policy elements to slit the secret
# into their corresponding shares for encryption
policy = self.util.createPolicy(policy_string)
# generate secret through random element
secret = self.group.random(ZR)
# split secret into shares (this returns a list)
shares = self.util.calculateSharesList(secret, policy)
# process shares list to create a dict with attribute as key
# and corresponding shares as value
shares = dict([(x[0].getAttributeAndIndex(), x[1]) for x in shares])
# initialize blinding factor to hide key
blinding_factor = 1
for authority_temp in authority.keys():
blinding_factor *= APK[authority_temp]['e_alpha']
# create C elements of encrypted file
C = k * (blinding_factor**secret)
C_prime = GPP['g']**secret
C_prime_prime = GPP['g_b']**secret
# create structure (dict) to hold the C_i and D_i elements of the encrypted file
# these are the components related to the attributes
C_i = {}
C_i_prime = {}
D_i = {}
D_i_prime = {}
# generate C_i and D_i elements
for attribute, secret_share in shares.items():
# attribute_temp = self.util.strip_index(attribute)
# generate random r_i element
k_attr = self.util.strip_index(attribute)
r_i = self.group.random(ZR)
attribute_PK = authority_attributes[attribute]
C_i[attribute] = (GPP['g_a']**
secret_share) * ~(attribute_PK['PK'][0]**r_i)
C_i_prime[attribute] = GPP['g']**r_i
D_i[attribute] = authority_g_beta_inv[attribute]**r_i
D_i_prime[attribute] = attribute_PK['PK'][1]**r_i
return {
'C': C,
'C_prime': C_prime,
'C_prime_prime': C_prime_prime,
'C_i': C_i,
'C_i_prime': C_i_prime,
'D_i': D_i,
'D_i_prime': D_i_prime,
'policy': policy_string,
}
def abenc_generatetoken(self, GPP, CT, UASK, user_keys):
"""
Partial decryption of the ciphertext
:param GPP: Global Public Parameters
:param CT: Ciphertext elements
:param UASK: Secret Keys for user gotten from Attribute Authorities
:param user_keys: User global keys
:return: Partially decrypted ciphertext
"""
# list to hold corresponding attributes possessed by the user
user_attributes = []
for authority in UASK.keys():
user_attributes.extend(UASK[authority]['AK_uid_aid'].keys())
# access ciphertext policy
encryption_policy = self.util.createPolicy(CT['policy'])
# generate list of minimum policy elements needed for encryption
# returns False if user fails policy assessment
minimal_policy_list = self.util.prune(encryption_policy,
user_attributes)
# print(minimal_policy_list)
# this is an error handling implementation that should be fixed later
if not minimal_policy_list:
return False
# get attribute coefficients to be able to access their share of the secret
coefficients = self.util.getCoefficients(encryption_policy)
# initialize the dividend value for the token generation computation
dividend = 1
for authority in UASK.keys():
dividend *= (
pair(CT['C_prime'], UASK[authority]['K_uid_aid']) *
~pair(CT['C_prime_prime'], UASK[authority]['K_uid_aid_prime']))
# attribute authority index?
n_a = 1
# initialize divisor value for token generation computation
divisor = 1
# create dict to hold attributes for the authorities and their corresponding secret keys
attribute_keys = {}
# create dict to hold attributes contained in the pruned list and their corresponding secret keys
pruned_attribute_keys = {}
# populate attribute with with corresponding key value pairs
for authority in UASK.keys():
attribute_keys.update(UASK[authority]['AK_uid_aid'])
# populate pruned attribute with corresponding key value pairs
# from attribute list
for attribute in minimal_policy_list:
pruned_attribute_keys[str(attribute)] = attribute_keys[str(
attribute)]
# compute divisor
for authority in UASK.keys():
temp_divisor = 1
for attribute in minimal_policy_list:
x = attribute.getAttributeAndIndex()
y = attribute.getAttribute()
temp_divisor *= (
(pair(CT['C_i'][y], user_keys) *
pair(CT['D_i'][y], pruned_attribute_keys[y]) *
~pair(CT['C_i_prime'][y],
UASK[authority]['K_uid_aid_prime']) *
~pair(GPP['g'], CT['D_i_prime'][y]))**(coefficients[x] *
n_a))
divisor *= temp_divisor
Token = dividend / divisor
return (Token, CT['C'])
def abenc_decrypt(self, CT, TK, user_keys):
"""
Final decryption algorithm to reveal original message. To be run by the user
:param CT: Original component of ciphertext that contains the encrypted message
:param TK: Token generated during partial decryption of ciphertext
:param user_keys: User global keys
:return: Decrypted message
"""
message = CT / (TK**user_keys[1])
return message
def abenc_ukeygen(self, GPP, authority, attribute, user_object):
"""
Generate update keys used in the revocation process for users and the cloud service provider.
This will be run by the Attribute Authority.
:param GPP: Global Public Parameters
:param authority: Attribute Authority
:param attribute: Attribute to be updated
:param user_object: User
:return: User attribute update keys and ciphertext update keys
"""
ASK, _, authAttrs = authority
# attribute version key to be updated
old_version_key = authAttrs[attribute]['VK']
# set new version key to old value
new_version_key = old_version_key
# ensure that new version key is different from original version key
while old_version_key == new_version_key:
new_version_key = self.group.random()
# update version key of the attribute in the dictionary
authAttrs[attribute]['VK'] = new_version_key
u_uid = user_object['u_uid']
# create update key for users i.e to update the attribute involved
KUK = GPP['H'](attribute)**(ASK['beta_aid'] *
(new_version_key - old_version_key) *
(u_uid + ASK['gamma_aid']))
# create update key for ciphertexts encrypted with attribute involved
CUK = (new_version_key / old_version_key,
(old_version_key - new_version_key) /
(old_version_key * ASK['gamma_aid']))
# update the public parameters of the attribute involvedauthAttrs[attribute]['PK'][0] = authAttrs[attribute]['PK'][0] ** CUK[0]
authAttrs[attribute]['PK'][1] = authAttrs[attribute]['PK'][1]**CUK[0]
return {
'KUK': KUK,
'CUK': CUK,
}
def abenc_skupdate(self, USK, attribute, KUK):
"""
Updates the attribute secret key for the specific attribute.
This is executed by a non-revoked user.
:param USK: User secret key
:param attribute: Attribute whose secret key is to be updated
:param KUK: Update key for users
:return: NA
"""
# update the secret key component of the affected attribute
# print(USK)
USK['AK_uid_aid'][attribute] = USK['AK_uid_aid'][attribute] * KUK
def abenc_ctupdate(self, GPP, CT, attribute, CUK):
"""
Updates the ciphertexts that contain the specific attribute (revoked attribute).
This is executed by the cloud service provider.
:param GPP: Global Public Parameters
:param CT: The affected ciphertext
:param attribute: Attribute that is affected by the revocation process
:param CUK: The Ciphertext Update Key
:return: NA
"""
# update the corresponding components of the ciphertext that are related to the affected attribute
CT['C_i'][attribute] = CT['C_i'][attribute] * (
CT['D_i_prime'][attribute]**CUK[1])
CT['D_i_prime'][attribute] = CT['D_i_prime'][attribute]**CUK[0]