def seal_obj():
# params obj
params = EncryptionParameters()
# set params
params.set_poly_modulus("1x^4096 + 1")
params.set_coeff_modulus(seal.coeff_modulus_128(4096))
params.set_plain_modulus(1 << 16)
# get context
context = SEALContext(params)
# get evaluator
evaluator = Evaluator(context)
# gen keys
keygen = KeyGenerator(context)
public_key = keygen.public_key()
private_key = keygen.secret_key()
# evaluator keys
ev_keys = EvaluationKeys()
keygen.generate_evaluation_keys(30, ev_keys)
# get encryptor and decryptor
encryptor = Encryptor(context, public_key)
decryptor = Decryptor(context, private_key)
# float number encoder
encoder = FractionalEncoder(context.plain_modulus(),
context.poly_modulus(), 64, 32, 3)
return evaluator, encoder.encode, encoder.decode, encryptor.encrypt, decryptor.decrypt, ev_keys
def initialize_fractional(
poly_modulus_degree=4096,
security_level_bits=128,
plain_modulus_power_of_two=10,
plain_modulus=None,
encoder_integral_coefficients=1024,
encoder_fractional_coefficients=3072,
encoder_base=2
):
parameters = EncryptionParameters()
poly_modulus = "1x^" + str(poly_modulus_degree) + " + 1"
parameters.set_poly_modulus(poly_modulus)
if security_level_bits == 128:
parameters.set_coeff_modulus(seal.coeff_modulus_128(poly_modulus_degree))
elif security_level_bits == 192:
parameters.set_coeff_modulus(seal.coeff_modulus_192(poly_modulus_degree))
else:
parameters.set_coeff_modulus(seal.coeff_modulus_128(poly_modulus_degree))
print("Info: security_level_bits unknown - using default security_level_bits = 128")
if plain_modulus is None:
plain_modulus = 1 << plain_modulus_power_of_two
parameters.set_plain_modulus(plain_modulus)
context = SEALContext(parameters)
print_parameters(context)
global encoder
encoder = FractionalEncoder(
context.plain_modulus(),
context.poly_modulus(),
encoder_integral_coefficients,
encoder_fractional_coefficients,
encoder_base
)
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
global encryptor
encryptor = Encryptor(context, public_key)
global evaluator
evaluator = Evaluator(context)
global decryptor
decryptor = Decryptor(context, secret_key)
global evaluation_keys
evaluation_keys = EvaluationKeys()
keygen.generate_evaluation_keys(16, evaluation_keys)
def _build_context(self, config):
#set up encryption parameters and context
parms = EncryptionParameters()
parms.set_poly_modulus(config['poly_modulus'])
parms.set_coeff_modulus(seal.coeff_modulus_128(
config['coeff_modulus']))
parms.set_plain_modulus(1 << 18)
context = SEALContext(parms)
return context
def __init__(self):
# set parameters for encryption
parms = EncryptionParameters()
parms.set_poly_modulus("1x^2048 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(2048))
parms.set_plain_modulus(1 << 8)
self.context = SEALContext(parms)
keygen = KeyGenerator(self.context)
self.encoder = IntegerEncoder(self.context.plain_modulus())
public_key = keygen.public_key()
self.encryptor = Encryptor(self.context, public_key)
secret_key = keygen.secret_key()
self.decryptor = Decryptor(self.context, secret_key)
def config():
# PySEAL wrapper for the SEAL library is used.
# SEAL implements somewhat FHE algorithmic solutions =>
# each operation has a limit - 'invariant noise budget' in bits. Operations consume the noise budget
# at a rate determined py the encryption parameters. Additions free of noise budget consumption, multiplications are not
# Noise budget consumption is getting worse in sequential multiplications => multiplicative depth of the arithmetic circuit that needs to be evaluated.
# Noise budget in a ciphertext -> 0 => ciphertext too corrupted to be decrypted => large enough parameters to be eble to restore the result
#############
# noise_budget = log2(coeff_modulus/plain_modulus) bits (in a freshly encrypted ciphertext)
#############
#############
# noise_budget_cnsumption = log2(plain_modulus) + (other terms)
#############
params = EncryptionParameters()
# set the polynomial modulus. (1x^(power of 2) +1) - power of 2 cyclotomic polynomial
# affects the security of the scheme
# larger more secure and larger ciphertext size, computation slower
# from 1024 to 32768
##params.set_poly_modulus("1x^1024 + 1")
params.set_poly_modulus("1x^2048 + 1")
# coefficient modulus determines the noise budget of the ciphertext
# the bigger the more the budget and lower security -> increase the polynomial modulus
# choosing parameters for polynomial modulus http://HomomorphicEncryption.org
###params.set_coeff_modulus(seal.coeff_modulus_128(8192))
params.set_coeff_modulus(
seal.coeff_modulus_128(2048)) #plain_modulus = k*4096+1
#~ log2(coeff_modulus/plain_modulus) (bits)
# plaintext modulus determines the size of the plaintext datatype, affects the noise budget in multiplication => keep the plaintext data type as small as possible
#65537
params.set_plain_modulus(12289)
#####For batching
###params.set_plain_modulus(65537)
#params.set_plain_modulus(2049)
#params.set_plain_modulus(8192)
# check the validity of the parameters set, performs and stores several important pre-computations
context = SEALContext(params)
# print the chosen parameters
#performance_test_st(context)
return context, params
def initialize_encryption():
print_example_banner("Example: Basics I");
parms = EncryptionParameters()
parms.set_poly_modulus("1x^2048 + 1")
# factor: 0xfffffffff00001.
parms.set_coeff_modulus(seal.coeff_modulus_128(2048))
parms.set_plain_modulus(1 << 8)
context = SEALContext(parms)
print_parameters(context);
# Here we choose to create an IntegerEncoder with base b=2.
encoder = IntegerEncoder(context.plain_modulus())
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
encryptor = Encryptor(context, public_key)
evaluator = Evaluator(context)
decryptor = Decryptor(context, secret_key)
return encryptor, evaluator, decryptor, encoder, context
def do_per_amount(amount, subtract_from=15):
"""
Called on every message in the stream
"""
print("Transaction amount ", amount)
parms = EncryptionParameters()
parms.set_poly_modulus("1x^2048 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(2048))
parms.set_plain_modulus(1 << 8)
context = SEALContext(parms)
# Encode
encoder = FractionalEncoder(context.plain_modulus(),
context.poly_modulus(), 64, 32, 3)
# To create a fresh pair of keys one can call KeyGenerator::generate() at any time.
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
encryptor = Encryptor(context, public_key)
plain1 = encoder.encode(amount)
encoded2 = encoder.encode(subtract_from)
# Encrypt
encrypted1 = Ciphertext(parms)
encryptor.encrypt(plain1, encrypted1)
# Evaluate
evaluator = Evaluator(context)
evaluated = evaluate_subtraction_from_plain(evaluator, encrypted1,
encoded2)
# Decrypt and decode
decryptor = Decryptor(context, secret_key)
plain_result = Plaintext()
decryptor.decrypt(evaluated, plain_result)
result = encoder.decode(plain_result)
str_result = "Amount left = " + str(result)
print(str_result)
return str_result
def __init__(self, poly_modulus = 2048 ,bit_strength = 128 ,plain_modulus = 1<<8, integral_coeffs = 64, fractional_coeffs = 32, fractional_base = 3):
parms = EncryptionParameters()
parms.set_poly_modulus("1x^{} + 1".format(poly_modulus))
if (bit_strength == 128):
parms.set_coeff_modulus(seal.coeff_modulus_128(poly_modulus))
else:
parms.set_coeff_modulus(seal.coeff_modulus_192(poly_modulus))
parms.set_plain_modulus(plain_modulus)
self.parms = parms
context = SEALContext(parms)
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
self.encryptor = Encryptor(context, public_key)
self.evaluator = Evaluator(context)
self.decryptor = Decryptor(context, secret_key)
self.encoder = FractionalEncoder(context.plain_modulus(), context.poly_modulus(), integral_coeffs, fractional_coeffs, fractional_base)
class FracContext:
primes = [
0xffffffffffc0001, 0xfffffffff840001, 0xfffffffff240001,
0xffffffffe7c0001, 0xffffffffe740001, 0xffffffffe4c0001,
0xffffffffe440001, 0xffffffffe400001, 0xffffffffdbc0001,
0xffffffffd840001, 0xffffffffd680001, 0xffffffffd000001,
0xffffffffcf00001, 0xffffffffcdc0001, 0xffffffffcc40001,
0xffffffffc300001, 0xffffffffbf40001, 0xffffffffbdc0001,
0xffffffffb880001, 0xffffffffaec0001, 0xffffffffa380001,
0xffffffffa200001, 0xffffffffa0c0001, 0xffffffff9600001,
0xffffffff91c0001, 0xffffffff8f40001, 0xffffffff8680001,
0xffffffff7e40001, 0xffffffff7bc0001, 0xffffffff76c0001,
0xffffffff7680001, 0xffffffff6fc0001, 0xffffffff6880001,
0xffffffff6340001, 0xffffffff5d40001, 0xffffffff54c0001,
0xffffffff4d40001, 0xffffffff4380001, 0xffffffff3e80001,
0xffffffff37c0001, 0xffffffff36c0001, 0xffffffff2100001,
0xffffffff1d80001, 0xffffffff1cc0001, 0xffffffff1900001,
0xffffffff1740001, 0xffffffff15c0001, 0xffffffff0e80001,
0xfffffffeff80001, 0xfffffffeff40001, 0xfffffffeefc0001,
0xfffffffee8c0001, 0xfffffffede40001, 0xfffffffedcc0001,
0xfffffffed040001, 0xfffffffecf40001, 0xfffffffecec0001,
0xfffffffecb00001, 0xfffffffec380001, 0xfffffffebb40001
]
def __init__(self,
poly_modulus="1x^1024 + 1",
coef_modulus_n_primes=20,
plain_modulus=1 << 32):
"""
Set up encryption context for encoder and decoder
:param poly_modulus:
:param coef_modulus_n_primes:
:param plain_modulus:
"""
self.params = EncryptionParameters()
self.params.set_poly_modulus(poly_modulus)
self.params.set_coeff_modulus([
seal.SmallModulus(p)
for p in FracContext.primes[:coef_modulus_n_primes]
])
self.params.set_plain_modulus(plain_modulus)
self.context = SEALContext(self.params)
self.print_parameters(self.context)
self.keygen = KeyGenerator(self.context)
self.public_key = self.keygen.public_key()
self.secret_key = self.keygen.secret_key()
self.evaluator = Evaluator(self.context)
def print_parameters(self, context: SEALContext):
"""
Parameters description
:param context: SEALContext object
"""
print("/ Encryption parameters:")
print("| poly_modulus: " + context.poly_modulus().to_string())
# Print the size of the true (product) coefficient modulus
print("| coeff_modulus_size: " +
(str)(context.total_coeff_modulus().significant_bit_count()) +
" bits")
print("| plain_modulus: " + (str)(context.plain_modulus().value()))
print("| noise_standard_deviation: " +
(str)(context.noise_standard_deviation()))
class CipherMatrix:
"""
"""
def __init__(self, matrix=None):
"""
:param matrix: numpy.ndarray to be encrypted.
"""
self.parms = EncryptionParameters()
self.parms.set_poly_modulus("1x^2048 + 1")
self.parms.set_coeff_modulus(seal.coeff_modulus_128(2048))
self.parms.set_plain_modulus(1 << 8)
self.context = SEALContext(self.parms)
# self.encoder = IntegerEncoder(self.context.plain_modulus())
self.encoder = FractionalEncoder(self.context.plain_modulus(),
self.context.poly_modulus(), 64, 32,
3)
self.keygen = KeyGenerator(self.context)
self.public_key = self.keygen.public_key()
self.secret_key = self.keygen.secret_key()
self.encryptor = Encryptor(self.context, self.public_key)
self.decryptor = Decryptor(self.context, self.secret_key)
self.evaluator = Evaluator(self.context)
self._saved = False
self._encrypted = False
self._id = '{0:04d}'.format(np.random.randint(1000))
if matrix is not None:
assert len(
matrix.shape) == 2, "Only 2D numpy matrices accepted currently"
self.matrix = np.copy(matrix)
self.encrypted_matrix = np.empty(self.matrix.shape, dtype=object)
for i in range(self.matrix.shape[0]):
for j in range(self.matrix.shape[1]):
self.encrypted_matrix[i, j] = Ciphertext()
else:
self.matrix = None
self.encrypted_matrix = None
print(self._id, "Created")
def __repr__(self):
"""
:return:
"""
print("Encrypted:", self._encrypted)
if not self._encrypted:
print(self.matrix)
return ""
else:
return '[]'
def __str__(self):
"""
:return:
"""
print("| Encryption parameters:")
print("| poly_modulus: " + self.context.poly_modulus().to_string())
# Print the size of the true (product) coefficient modulus
print("| coeff_modulus_size: " + (
str)(self.context.total_coeff_modulus().significant_bit_count()) +
" bits")
print("| plain_modulus: " +
(str)(self.context.plain_modulus().value()))
print("| noise_standard_deviation: " +
(str)(self.context.noise_standard_deviation()))
if self.matrix is not None:
print(self.matrix.shape)
return str(type(self))
def __add__(self, other):
"""
:param other:
:return:
"""
assert isinstance(
other, CipherMatrix), "Can only be added with a CipherMatrix"
A_enc = self._encrypted
B_enc = other._encrypted
if A_enc:
A = self.encrypted_matrix
else:
A = self.matrix
if B_enc:
B = other.encrypted_matrix
else:
B = other.matrix
assert A.shape == B.shape, "Dimension mismatch, Matrices must be of same shape. Got {} and {}".format(
A.shape, B.shape)
shape = A.shape
result = CipherMatrix(np.zeros(shape, dtype=np.int32))
result._update_cryptors(self.get_keygen())
if A_enc:
if B_enc:
res_mat = result.encrypted_matrix
for i in range(shape[0]):
for j in range(shape[1]):
self.evaluator.add(A[i, j], B[i, j], res_mat[i, j])
result._encrypted = True
else:
res_mat = result.encrypted_matrix
for i in range(shape[0]):
for j in range(shape[1]):
self.evaluator.add_plain(A[i, j],
self.encoder.encode(B[i, j]),
res_mat[i, j])
result._encrypted = True
else:
if B_enc:
res_mat = result.encrypted_matrix
for i in range(shape[0]):
for j in range(shape[1]):
self.evaluator.add_plain(B[i, j],
self.encoder.encode(A[i, j]),
res_mat[i, j])
result._encrypted = True
else:
result.matrix = A + B
result._encrypted = False
return result
def __sub__(self, other):
"""
:param other:
:return:
"""
assert isinstance(other, CipherMatrix)
if other._encrypted:
shape = other.encrypted_matrix.shape
for i in range(shape[0]):
for j in range(shape[1]):
self.evaluator.negate(other.encrypted_matrix[i, j])
else:
other.matrix = -1 * other.matrix
return self + other
def __mul__(self, other):
"""
:param other:
:return:
"""
assert isinstance(
other, CipherMatrix), "Can only be multiplied with a CipherMatrix"
# print("LHS", self._id, "RHS", other._id)
A_enc = self._encrypted
B_enc = other._encrypted
if A_enc:
A = self.encrypted_matrix
else:
A = self.matrix
if B_enc:
B = other.encrypted_matrix
else:
B = other.matrix
Ashape = A.shape
Bshape = B.shape
assert Ashape[1] == Bshape[0], "Dimensionality mismatch"
result_shape = [Ashape[0], Bshape[1]]
result = CipherMatrix(np.zeros(shape=result_shape))
if A_enc:
if B_enc:
for i in range(Ashape[0]):
for j in range(Bshape[1]):
result_array = []
for k in range(Ashape[1]):
res = Ciphertext()
self.evaluator.multiply(A[i, k], B[k, j], res)
result_array.append(res)
self.evaluator.add_many(result_array,
result.encrypted_matrix[i, j])
result._encrypted = True
else:
for i in range(Ashape[0]):
for j in range(Bshape[1]):
result_array = []
for k in range(Ashape[1]):
res = Ciphertext()
self.evaluator.multiply_plain(
A[i, k], self.encoder.encode(B[k, j]), res)
result_array.append(res)
self.evaluator.add_many(result_array,
result.encrypted_matrix[i, j])
result._encrypted = True
else:
if B_enc:
for i in range(Ashape[0]):
for j in range(Bshape[1]):
result_array = []
for k in range(Ashape[1]):
res = Ciphertext()
self.evaluator.multiply_plain(
B[i, k], self.encoder.encode(A[k, j]), res)
result_array.append(res)
self.evaluator.add_many(result_array,
result.encrypted_matrix[i, j])
result._encrypted = True
else:
result.matrix = np.matmul(A, B)
result._encrypted = False
return result
def save(self, path):
"""
:param path:
:return:
"""
save_dir = os.path.join(path, self._id)
if self._saved:
print("CipherMatrix already saved")
else:
assert not os.path.isdir(save_dir), "Directory already exists"
os.mkdir(save_dir)
if not self._encrypted:
self.encrypt()
shape = self.encrypted_matrix.shape
for i in range(shape[0]):
for j in range(shape[1]):
element_name = str(i) + '-' + str(j) + '.ahem'
self.encrypted_matrix[i, j].save(
os.path.join(save_dir, element_name))
self.secret_key.save("/keys/" + "." + self._id + '.wheskey')
self._saved = True
return save_dir
def load(self, path, load_secret_key=False):
"""
:param path:
:param load_secret_key:
:return:
"""
self._id = path.split('/')[-1]
print("Loading Matrix:", self._id)
file_list = os.listdir(path)
index_list = [[file.split('.')[0].split('-'), file]
for file in file_list]
M = int(max([int(ind[0][0]) for ind in index_list])) + 1
N = int(max([int(ind[0][1]) for ind in index_list])) + 1
del self.encrypted_matrix
self.encrypted_matrix = np.empty([M, N], dtype=object)
for index in index_list:
i = int(index[0][0])
j = int(index[0][1])
self.encrypted_matrix[i, j] = Ciphertext()
self.encrypted_matrix[i, j].load(os.path.join(path, index[1]))
if load_secret_key:
self.secret_key.load("/keys/" + "." + self._id + '.wheskey')
self.matrix = np.empty(self.encrypted_matrix.shape)
self._encrypted = True
def encrypt(self, matrix=None, keygen=None):
"""
:param matrix:
:return:
"""
assert not self._encrypted, "Matrix already encrypted"
if matrix is not None:
assert self.matrix is None, "matrix already exists"
self.matrix = np.copy(matrix)
shape = self.matrix.shape
self.encrypted_matrix = np.empty(shape, dtype=object)
if keygen is not None:
self._update_cryptors(keygen)
for i in range(shape[0]):
for j in range(shape[1]):
val = self.encoder.encode(self.matrix[i, j])
self.encrypted_matrix[i, j] = Ciphertext()
self.encryptor.encrypt(val, self.encrypted_matrix[i, j])
self._encrypted = True
def decrypt(self, encrypted_matrix=None, keygen=None):
"""
:return:
"""
if encrypted_matrix is not None:
self.encrypted_matrix = encrypted_matrix
assert self._encrypted, "No encrypted matrix"
del self.matrix
shape = self.encrypted_matrix.shape
self.matrix = np.empty(shape)
if keygen is not None:
self._update_cryptors(keygen)
for i in range(shape[0]):
for j in range(shape[1]):
plain_text = Plaintext()
self.decryptor.decrypt(self.encrypted_matrix[i, j], plain_text)
self.matrix[i, j] = self.encoder.decode(plain_text)
self._encrypted = False
return np.copy(self.matrix)
def get_keygen(self):
"""
:return:
"""
return self.keygen
def _update_cryptors(self, keygen):
"""
:param keygen:
:return:
"""
self.keygen = keygen
self.public_key = keygen.public_key()
self.secret_key = keygen.secret_key()
self.encryptor = Encryptor(self.context, self.public_key)
self.decryptor = Decryptor(self.context, self.secret_key)
return
class encryption_handler(object):
"""
Methods:
set_encoder: sets specified encoder
encode_encrypt_2D: for encoding list of lists
decrypt_1D: for decoding list
Attributes:
params: seal encrpytion parameters object
batch: bool to batch operations
context: seal context object
secretkey: secret key kept on client side
publickey: public key for encryption
encoder: encoder for numerical inputs
"""
def __init__(
self,
security_level=128, #128 or 192 for now
poly_modulus_pwr2=12, # 11 through 15
coeff_modulus=None,
plain_modulus=2**8,
batch=False,
):
"""
security level: 128 or 192
poly_modulus_pwr2: 11,12,13,14,or 15 poly=x^(2^thisvariable)+1
will define our polynomial ring by Z[x]/poly. Larger
number means more security but longer computations.
coeff_modulus: default None, If set then security level
is ignored. This is important to set for batching as
it needs to be prime.
batch: default False, setting to true will design encryption
scheme to allow parallel predictions
"""
self.params = EncryptionParameters()
self.batch = batch
power = 2**poly_modulus_pwr2
self.params.set_poly_modulus(f"1x^{power} + 1")
if coeff_modulus != None:
st.write("Security level is ignored since coeff_modulus was set.")
self.params.set_coeff_modulus(coeff_modulus)
else:
if security_level == 128:
self.params.set_coeff_modulus(seal.coeff_modulus_128(power))
if security_level == 192:
self.params.set_coeff_modulus(seal.coeff_modulus_192(power))
try:
self.params.set_plain_modulus(plain_modulus)
except:
raise ValueError("There was a problem setting the plain modulus.")
try:
self._cont = SEALContext(self.params)
except Exception as e:
raise ValueError("There was a problem with your parameters.")
st.write(f"There was a problem with your parameters: {e}")
_keygen = KeyGenerator(self._cont)
self._secretkey = _keygen.secret_key()
self._publickey = _keygen.public_key()
@property
def secretkey(self):
return self._secretkey
@property
def publickey(self):
return self._publickey
@property
def context(self):
return self._cont
def pickle_ciphertext():
parms = EncryptionParameters()
parms.set_poly_modulus("1x^2048 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(2048))
parms.set_plain_modulus(1 << 8)
context = SEALContext(parms)
# Print the parameters that we have chosen
print_parameters(context);
encoder = IntegerEncoder(context.plain_modulus())
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
# To be able to encrypt, we need to construct an instance of Encryptor. Note that
# the Encryptor only requires the public key.
encryptor = Encryptor(context, public_key)
# Computations on the ciphertexts are performed with the Evaluator class.
evaluator = Evaluator(context)
# We will of course want to decrypt our results to verify that everything worked,
# so we need to also construct an instance of Decryptor. Note that the Decryptor
# requires the secret key.
decryptor = Decryptor(context, secret_key)
# We start by encoding two integers as plaintext polynomials.
value1 = 5;
plain1 = encoder.encode(value1);
print("Encoded " + (str)(value1) + " as polynomial " + plain1.to_string() + " (plain1)")
value2 = -7;
plain2 = encoder.encode(value2);
print("Encoded " + (str)(value2) + " as polynomial " + plain2.to_string() + " (plain2)")
# Encrypting the values is easy.
encrypted1 = Ciphertext()
encrypted2 = Ciphertext()
print("Encrypting plain1: ", encrypted1)
encryptor.encrypt(plain1, encrypted1)
print("Done (encrypted1)", encrypted1)
print("Encrypting plain2: ")
encryptor.encrypt(plain2, encrypted2)
print("Done (encrypted2)")
# output = open('ciphertest.pkl', 'wb')
# dill.dumps(encrypted_save, output)
# output.close()
# encrypted1 = dill.load(open('ciphertest.pkl', 'rb'))
output = open('session.pkl', 'wb')
dill.dump_session('session.pkl')
del encrypted1
sill.load_session('session.pkl')
# To illustrate the concept of noise budget, we print the budgets in the fresh
# encryptions.
print("Noise budget in encrypted1: " + (str)(decryptor.invariant_noise_budget(encrypted1)) + " bits")
print("Noise budget in encrypted2: " + (str)(decryptor.invariant_noise_budget(encrypted2)) + " bits")
# As a simple example, we compute (-encrypted1 + encrypted2) * encrypted2.
# Negation is a unary operation.
evaluator.negate(encrypted1)
# Negation does not consume any noise budget.
print("Noise budget in -encrypted1: " + (str)(decryptor.invariant_noise_budget(encrypted1)) + " bits")
# Addition can be done in-place (overwriting the first argument with the result,
# or alternatively a three-argument overload with a separate destination variable
# can be used. The in-place variants are always more efficient. Here we overwrite
# encrypted1 with the sum.
evaluator.add(encrypted1, encrypted2)
# It is instructive to think that addition sets the noise budget to the minimum
# of the input noise budgets. In this case both inputs had roughly the same
# budget going on, and the output (in encrypted1) has just slightly lower budget.
# Depending on probabilistic effects, the noise growth consumption may or may
# not be visible when measured in whole bits.
print("Noise budget in -encrypted1 + encrypted2: " + (str)(decryptor.invariant_noise_budget(encrypted1)) + " bits")
# Finally multiply with encrypted2. Again, we use the in-place version of the
# function, overwriting encrypted1 with the product.
evaluator.multiply(encrypted1, encrypted2)
# Multiplication consumes a lot of noise budget. This is clearly seen in the
# print-out. The user can change the plain_modulus to see its effect on the
# rate of noise budget consumption.
print("Noise budget in (-encrypted1 + encrypted2) * encrypted2: " + (str)(
decryptor.invariant_noise_budget(encrypted1)) + " bits")
# Now we decrypt and decode our result.
plain_result = Plaintext()
print("Decrypting result: ")
decryptor.decrypt(encrypted1, plain_result)
print("Done")
# Print the result plaintext polynomial.
print("Plaintext polynomial: " + plain_result.to_string())
# Decode to obtain an integer result.
print("Decoded integer: " + (str)(encoder.decode_int32(plain_result)))
for colIndex in range(rowIndex+1,n):
if M[rowIndex][colIndex]==None:
M[rowIndex][colIndex]=Ciphertext(M[colIndex][rowIndex])
print_plain(M)
if __name__ == '__main__':
multiprocessing.freeze_support()
########################## paramaters required #################################
parms = EncryptionParameters()
parms.set_poly_modulus("1x^16384 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(8192))
parms.set_plain_modulus(1 << 25)
context = SEALContext(parms)
encoderF = FractionalEncoder(context.plain_modulus(), context.poly_modulus(), 34, 30, 3)
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
encryptor = Encryptor(context, public_key)
evaluator = Evaluator(context)
decryptor = Decryptor(context, secret_key)
num_cores = multiprocessing.cpu_count() -1
def example_basics_ii():
print_example_banner("Example: Basics II")
# In this example we explain what relinearization is, how to use it, and how
# it affects noise budget consumption.
# First we set the parameters, create a SEALContext, and generate the public
# and secret keys. We use slightly larger parameters than be fore to be able
# to do more homomorphic multiplications.
parms = EncryptionParameters()
parms.set_poly_modulus("1x^8192 + 1")
# The default coefficient modulus consists of the following primes:
# 0x7fffffffba0001,
# 0x7fffffffaa0001,
# 0x7fffffff7e0001,
# 0x3fffffffd60001.
# The total size is 219 bits.
parms.set_coeff_modulus(seal.coeff_modulus_128(8192))
parms.set_plain_modulus(1 << 10)
context = SEALContext(parms)
print_parameters(context)
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
# We also set up an Encryptor, Evaluator, and Decryptor here. We will
# encrypt polynomials directly in this example, so there is no need for
# an encoder.
encryptor = Encryptor(context, public_key)
evaluator = Evaluator(context)
decryptor = Decryptor(context, secret_key)
# There are actually two more types of keys in SEAL: `evaluation keys' and
# `Galois keys'. Here we will discuss evaluation keys, and Galois keys will
# be discussed later in example_batching().
# In SEAL, a valid ciphertext consists of two or more polynomials with
# coefficients integers modulo the product of the primes in coeff_modulus.
# The current size of a ciphertext can be found using Ciphertext::size().
# A freshly encrypted ciphertext always has size 2.
#plain1 = Plaintext("1x^2 + 2x^1 + 3")
plain1 = Plaintext("1x^2 + 2x^1 + 3")
encrypted = Ciphertext()
print("")
print("Encrypting " + plain1.to_string() + ": ")
encryptor.encrypt(plain1, encrypted)
print("Done")
print("Size of a fresh encryption: " + (str)(encrypted.size()))
print("Noise budget in fresh encryption: " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
# Homomorphic multiplication results in the output ciphertext growing in size.
# More precisely, if the input ciphertexts have size M and N, then the output
# ciphertext after homomorphic multiplication will have size M+N-1. In this
# case we square encrypted twice to observe this growth (also observe noise
# budget consumption).
evaluator.square(encrypted)
print("Size after squaring: " + (str)(encrypted.size()))
print("Noise budget after squaring: " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
plain2 = Plaintext()
decryptor.decrypt(encrypted, plain2)
print("Second power: " + plain2.to_string())
evaluator.square(encrypted)
print("Size after squaring: " + (str)(encrypted.size()))
print("Noise budget after squaring: " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
# It does not matter that the size has grown -- decryption works as usual.
# Observe from the print-out that the coefficients in the plaintext have
# grown quite large. One more squaring would cause some of them to wrap
# around plain_modulus (0x400), and as a result we would no longer obtain
# the expected result as an integer-coefficient polynomial. We can fix this
# problem to some extent by increasing plain_modulus. This would make sense,
# since we still have plenty of noise budget left.
plain2 = Plaintext()
decryptor.decrypt(encrypted, plain2)
print("Fourth power: " + plain2.to_string())
# The problem here is that homomorphic operations on large ciphertexts are
# computationally much more costly than on small ciphertexts. Specifically,
# homomorphic multiplication on input ciphertexts of size M and N will require
# O(M*N) polynomial multiplications to be performed, and an addition will
# require O(M+N) additions. Relinearization reduces the size of the ciphertexts
# after multiplication back to the initial size (2). Thus, relinearizing one
# or both inputs before the next multiplication, or e.g. before serializing the
# ciphertexts, can have a huge positive impact on performance.
# Another problem is that the noise budget consumption in multiplication is
# bigger when the input ciphertexts sizes are bigger. In a complicated
# computation the contribution of the sizes to the noise budget consumption
# can actually become the dominant term. We will point this out again below
# once we get to our example.
# Relinearization itself has both a computational cost and a noise budget cost.
# These both depend on a parameter called `decomposition bit count', which can
# be any integer at least 1 [dbc_min()] and at most 60 [dbc_max()]. A large
# decomposition bit count makes relinearization fast, but consumes more noise
# budget. A small decomposition bit count can make relinearization slower, but
# might not change the noise budget by any observable amount.
# Relinearization requires a special type of key called `evaluation keys'.
# These can be created by the KeyGenerator for any decomposition bit count.
# To relinearize a ciphertext of size M >= 2 back to size 2, we actually need
# M-2 evaluation keys. Attempting to relinearize a too large ciphertext with
# too few evaluation keys will result in an exception being thrown.
# We repeat our computation, but this time relinearize after both squarings.
# Since our ciphertext never grows past size 3 (we relinearize after every
# multiplication), it suffices to generate only one evaluation key.
# First, we need to create evaluation keys. We use a decomposition bit count
# of 16 here, which can be thought of as quite small.
ev_keys16 = EvaluationKeys()
# This function generates one single evaluation key. Another overload takes
# the number of keys to be generated as an argument, but one is all we need
# in this example (see above).
keygen.generate_evaluation_keys(16, ev_keys16)
print("")
print("Encrypting " + plain1.to_string() + ": ")
encryptor.encrypt(plain1, encrypted)
print("Done")
print("Size of a fresh encryption: " + (str)(encrypted.size()))
print("Noise budget in fresh encryption: " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
evaluator.square(encrypted)
print("Size after squaring: " + (str)(encrypted.size()))
print("Noise budget after squaring: " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
evaluator.relinearize(encrypted, ev_keys16)
print("Size after relinearization: " + (str)(encrypted.size()))
print("Noise budget after relinearizing (dbs = " +
(str)(ev_keys16.decomposition_bit_count()) + "): " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
evaluator.square(encrypted)
print("Size after second squaring: " + (str)(encrypted.size()) + " bits")
print("Noise budget after second squaring: " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
evaluator.relinearize(encrypted, ev_keys16)
print("Size after relinearization: " + (str)(encrypted.size()))
print("Noise budget after relinearizing (dbs = " +
(str)(ev_keys16.decomposition_bit_count()) + "): " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
decryptor.decrypt(encrypted, plain2)
print("Fourth power: " + plain2.to_string())
# Of course the result is still the same, but this time we actually
# used less of our noise budget. This is not surprising for two reasons:
# - We used a very small decomposition bit count, which is why
# relinearization itself did not consume the noise budget by any
# observable amount;
# - Since our ciphertext sizes remain small throughout the two
# squarings, the noise budget consumption rate in multiplication
# remains as small as possible. Recall from above that operations
# on larger ciphertexts actually cause more noise growth.
# To make matters even more clear, we repeat the computation a third time,
# now using the largest possible decomposition bit count (60). We are not
# measuring the time here, but relinearization with these evaluation keys
# is significantly faster than with ev_keys16.
ev_keys60 = EvaluationKeys()
keygen.generate_evaluation_keys(seal.dbc_max(), ev_keys60)
print("")
print("Encrypting " + plain1.to_string() + ": ")
encryptor.encrypt(plain1, encrypted)
print("Done")
print("Size of a fresh encryption: " + (str)(encrypted.size()))
print("Noise budget in fresh encryption: " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
evaluator.square(encrypted)
print("Size after squaring: " + (str)(encrypted.size()))
print("Noise budget after squaring: " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
evaluator.relinearize(encrypted, ev_keys60)
print("Size after relinearization: " + (str)(encrypted.size()))
print("Noise budget after relinearizing (dbc = " +
(str)(ev_keys60.decomposition_bit_count()) + "): " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
evaluator.square(encrypted)
print("Size after second squaring: " + (str)(encrypted.size()))
print("Noise budget after second squaring: " +
(str)(decryptor.invariant_noise_budget) + " bits")
evaluator.relinearize(encrypted, ev_keys60)
print("Size after relinearization: " + (str)(encrypted.size()))
print("Noise budget after relinearizing (dbc = " +
(str)(ev_keys60.decomposition_bit_count()) + "): " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
decryptor.decrypt(encrypted, plain2)
print("Fourth power: " + plain2.to_string())
# Observe from the print-out that we have now used significantly more of our
# noise budget than in the two previous runs. This is again not surprising,
# since the first relinearization chops off a huge part of the noise budget.
# However, note that the second relinearization does not change the noise
# budget by any observable amount. This is very important to understand when
# optimal performance is desired: relinearization always drops the noise
# budget from the maximum (freshly encrypted ciphertext) down to a fixed
# amount depending on the encryption parameters and the decomposition bit
# count. On the other hand, homomorphic multiplication always consumes the
# noise budget from its current level. This is why the second relinearization
# does not change the noise budget anymore: it is already consumed past the
# fixed amount determinted by the decomposition bit count and the encryption
# parameters.
# We now perform a third squaring and observe an even further compounded
# decrease in the noise budget. Again, relinearization does not consume the
# noise budget at this point by any observable amount, even with the largest
# possible decomposition bit count.
evaluator.square(encrypted)
print("Size after third squaring " + (str)(encrypted.size()))
print("Noise budget after third squaring: " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
evaluator.relinearize(encrypted, ev_keys60)
print("Size after relinearization: " + (str)(encrypted.size()))
print("Noise budget after relinearizing (dbc = " +
(str)(ev_keys60.decomposition_bit_count()) + "): " +
(str)(decryptor.invariant_noise_budget(encrypted)) + " bits")
decryptor.decrypt(encrypted, plain2)
print("Eighth power: " + plain2.to_string())
def example_basics_i():
print_example_banner("Example: Basics I")
# In this example we demonstrate setting up encryption parameters and other
# relevant objects for performing simple computations on encrypted integers.
# SEAL uses the Fan-Vercauteren (FV) homomorphic encryption scheme. We refer to
# https://eprint.iacr.org/2012/144 for full details on how the FV scheme works.
# For better performance, SEAL implements the "FullRNS" optimization of FV, as
# described in https://eprint.iacr.org/2016/510.
# The first task is to set up an instance of the EncryptionParameters class.
# It is critical to understand how these different parameters behave, how they
# affect the encryption scheme, performance, and the security level. There are
# three encryption parameters that are necessary to set:
# - poly_modulus (polynomial modulus);
# - coeff_modulus ([ciphertext] coefficient modulus);
# - plain_modulus (plaintext modulus).
# A fourth parameter -- noise_standard_deviation -- has a default value of 3.19
# and should not be necessary to modify unless the user has a specific reason
# to and knows what they are doing.
# The encryption scheme implemented in SEAL cannot perform arbitrary computations
# on encrypted data. Instead, each ciphertext has a specific quantity called the
# `invariant noise budget' -- or `noise budget' for short -- measured in bits.
# The noise budget of a freshly encrypted ciphertext (initial noise budget) is
# determined by the encryption parameters. Homomorphic operations consume the
# noise budget at a rate also determined by the encryption parameters. In SEAL
# the two basic homomorphic operations are additions and multiplications, of
# which additions can generally be thought of as being nearly free in terms of
# noise budget consumption compared to multiplications. Since noise budget
# consumption is compounding in sequential multiplications, the most significant
# factor in choosing appropriate encryption parameters is the multiplicative
# depth of the arithmetic circuit that needs to be evaluated. Once the noise
# budget in a ciphertext reaches zero, it becomes too corrupted to be decrypted.
# Thus, it is essential to choose the parameters to be large enough to support
# the desired computation; otherwise the result is impossible to make sense of
# even with the secret key.
parms = EncryptionParameters()
# We first set the polynomial modulus. This must be a power-of-2 cyclotomic
# polynomial, i.e. a polynomial of the form "1x^(power-of-2) + 1". The polynomial
# modulus should be thought of mainly affecting the security level of the scheme;
# larger polynomial modulus makes the scheme more secure. At the same time, it
# makes ciphertext sizes larger, and consequently all operations slower.
# Recommended degrees for poly_modulus are 1024, 2048, 4096, 8192, 16384, 32768,
# but it is also possible to go beyond this. Since we perform only a very small
# computation in this example, it suffices to use a very small polynomial modulus
parms.set_poly_modulus("1x^2048 + 1")
# Next we choose the [ciphertext] coefficient modulus (coeff_modulus). The size
# of the coefficient modulus should be thought of as the most significant factor
# in determining the noise budget in a freshly encrypted ciphertext: bigger means
# more noise budget. Unfortunately, a larger coefficient modulus also lowers the
# security level of the scheme. Thus, if a large noise budget is required for
# complicated computations, a large coefficient modulus needs to be used, and the
# reduction in the security level must be countered by simultaneously increasing
# the polynomial modulus.
# To make parameter selection easier for the user, we have constructed sets of
# largest allowed coefficient moduli for 128-bit and 192-bit security levels
# for different choices of the polynomial modulus. These recommended parameters
# follow the Security white paper at http://HomomorphicEncryption.org. However,
# due to the complexity of this topic, we highly recommend the user to directly
# consult an expert in homomorphic encryption and RLWE-based encryption schemes
# to determine the security of their parameter choices.
# Our recommended values for the coefficient modulus can be easily accessed
# through the functions
# coeff_modulus_128bit(int)
# coeff_modulus_192bit(int)
# for 128-bit and 192-bit security levels. The integer parameter is the degree
# of the polynomial modulus.
# In SEAL the coefficient modulus is a positive composite number -- a product
# of distinct primes of size up to 60 bits. When we talk about the size of the
# coefficient modulus we mean the bit length of the product of the small primes.
# The small primes are represented by instances of the SmallModulus class; for
# example coeff_modulus_128bit(int) returns a vector of SmallModulus instances.
# It is possible for the user to select their own small primes. Since SEAL uses
# the Number Theoretic Transform (NTT) for polynomial multiplications modulo the
# factors of the coefficient modulus, the factors need to be prime numbers
# congruent to 1 modulo 2*degree(poly_modulus). We have generated a list of such
# prime numbers of various sizes, that the user can easily access through the
# functions
# small_mods_60bit(int)
# small_mods_50bit(int)
# small_mods_40bit(int)
# small_mods_30bit(int)
# each of which gives access to an array of primes of the denoted size. These
# primes are located in the source file util/globals.cpp.
# Performance is mainly affected by the size of the polynomial modulus, and the
# number of prime factors in the coefficient modulus. Thus, it is important to
# use as few factors in the coefficient modulus as possible.
# In this example we use the default coefficient modulus for a 128-bit security
# level. Concretely, this coefficient modulus consists of only one 56-bit prime
# factor: 0xfffffffff00001.
parms.set_coeff_modulus(seal.coeff_modulus_128(2048))
# The plaintext modulus can be any positive integer, even though here we take
# it to be a power of two. In fact, in many cases one might instead want it to
# be a prime number; we will see this in example_batching(). The plaintext
# modulus determines the size of the plaintext data type, but it also affects
# the noise budget in a freshly encrypted ciphertext, and the consumption of
# the noise budget in homomorphic multiplication. Thus, it is essential to try
# to keep the plaintext data type as small as possible for good performance.
# The noise budget in a freshly encrypted ciphertext is
# ~ log2(coeff_modulus/plain_modulus) (bits)
# and the noise budget consumption in a homomorphic multiplication is of the
# form log2(plain_modulus) + (other terms).
parms.set_plain_modulus(1 << 8)
# Now that all parameters are set, we are ready to construct a SEALContext
# object. This is a heavy class that checks the validity and properties of
# the parameters we just set, and performs and stores several important
# pre-computations.
context = SEALContext(parms)
# Print the parameters that we have chosen
print_parameters(context)
# Plaintexts in the FV scheme are polynomials with coefficients integers modulo
# plain_modulus. To encrypt for example integers instead, one can use an
# `encoding scheme' to represent the integers as such polynomials. SEAL comes
# with a few basic encoders:
# [IntegerEncoder]
# Given an integer base b, encodes integers as plaintext polynomials as follows.
# First, a base-b expansion of the integer is computed. This expansion uses
# a `balanced' set of representatives of integers modulo b as the coefficients.
# Namely, when b is odd the coefficients are integers between -(b-1)/2 and
# (b-1)/2. When b is even, the integers are between -b/2 and (b-1)/2, except
# when b is two and the usual binary expansion is used (coefficients 0 and 1).
# Decoding amounts to evaluating the polynomial at x=b. For example, if b=2,
# the integer
# 26 = 2^4 + 2^3 + 2^1
# is encoded as the polynomial 1x^4 + 1x^3 + 1x^1. When b=3,
# 26 = 3^3 - 3^0
# is encoded as the polynomial 1x^3 - 1. In memory polynomial coefficients are
# always stored as unsigned integers by storing their smallest non-negative
# representatives modulo plain_modulus. To create a base-b integer encoder,
# use the constructor IntegerEncoder(plain_modulus, b). If no b is given, b=2
# is used.
# [FractionalEncoder]
# The FractionalEncoder encodes fixed-precision rational numbers as follows.
# It expands the number in a given base b, possibly truncating an infinite
# fractional part to finite precision, e.g.
# 26.75 = 2^4 + 2^3 + 2^1 + 2^(-1) + 2^(-2)
# when b=2. For the sake of the example, suppose poly_modulus is 1x^1024 + 1.
# It then represents the integer part of the number in the same way as in
# IntegerEncoder (with b=2 here), and moves the fractional part instead to the
# highest degree part of the polynomial, but with signs of the coefficients
# changed. In this example we would represent 26.75 as the polynomial
# -1x^1023 - 1x^1022 + 1x^4 + 1x^3 + 1x^1.
# In memory the negative coefficients of the polynomial will be represented as
# their negatives modulo plain_modulus.
# [PolyCRTBuilder]
# If plain_modulus is a prime congruent to 1 modulo 2*degree(poly_modulus), the
# plaintext elements can be viewed as 2-by-(degree(poly_modulus) / 2) matrices
# with elements integers modulo plain_modulus. When a desired computation can be
# vectorized, using PolyCRTBuilder can result in massive performance improvements
# over naively encrypting and operating on each input number separately. Thus,
# in more complicated computations this is likely to be by far the most important
# and useful encoder. In example_batching() we show how to use and operate on
# encrypted matrix plaintexts.
# For performance reasons, in homomorphic encryption one typically wants to keep
# the plaintext data types as small as possible, which can make it challenging to
# prevent data type overflow in more complicated computations, especially when
# operating on rational numbers that have been scaled to integers. When using
# PolyCRTBuilder estimating whether an overflow occurs is a fairly standard task,
# as the matrix slots are integers modulo plain_modulus, and each slot is operated
# on independently of the others. When using IntegerEncoder or FractionalEncoder
# it is substantially more difficult to estimate when an overflow occurs in the
# plaintext, and choosing the plaintext modulus very carefully to be large enough
# is critical to avoid unexpected results. Specifically, one needs to estimate how
# large the largest coefficient in the polynomial view of all of the plaintext
# elements becomes, and choose the plaintext modulus to be larger than this value.
# SEAL comes with an automatic parameter selection tool that can help with this
# task, as is demonstrated in example_parameter_selection().
# Here we choose to create an IntegerEncoder with base b=2.
encoder = IntegerEncoder(context.plain_modulus())
# We are now ready to generate the secret and public keys. For this purpose we need
# an instance of the KeyGenerator class. Constructing a KeyGenerator automatically
# generates the public and secret key, which can then be read to local variables.
# To create a fresh pair of keys one can call KeyGenerator::generate() at any time.
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
# To be able to encrypt, we need to construct an instance of Encryptor. Note that
# the Encryptor only requires the public key.
encryptor = Encryptor(context, public_key)
# Computations on the ciphertexts are performed with the Evaluator class.
evaluator = Evaluator(context)
# We will of course want to decrypt our results to verify that everything worked,
# so we need to also construct an instance of Decryptor. Note that the Decryptor
# requires the secret key.
decryptor = Decryptor(context, secret_key)
# We start by encoding two integers as plaintext polynomials.
value1 = 5
plain1 = encoder.encode(value1)
print("Encoded " + (str)(value1) + " as polynomial " + plain1.to_string() +
" (plain1)")
value2 = -7
plain2 = encoder.encode(value2)
print("Encoded " + (str)(value2) + " as polynomial " + plain2.to_string() +
" (plain2)")
# Encrypting the values is easy.
encrypted1 = Ciphertext()
encrypted2 = Ciphertext()
print("Encrypting plain1: ")
encryptor.encrypt(plain1, encrypted1)
print("Done (encrypted1)")
print("Encrypting plain2: ")
encryptor.encrypt(plain2, encrypted2)
print("Done (encrypted2)")
# To illustrate the concept of noise budget, we print the budgets in the fresh
# encryptions.
print("Noise budget in encrypted1: " +
(str)(decryptor.invariant_noise_budget(encrypted1)) + " bits")
print("Noise budget in encrypted2: " +
(str)(decryptor.invariant_noise_budget(encrypted2)) + " bits")
# As a simple example, we compute (-encrypted1 + encrypted2) * encrypted2.
# Negation is a unary operation.
evaluator.negate(encrypted1)
# Negation does not consume any noise budget.
print("Noise budget in -encrypted1: " +
(str)(decryptor.invariant_noise_budget(encrypted1)) + " bits")
# Addition can be done in-place (overwriting the first argument with the result,
# or alternatively a three-argument overload with a separate destination variable
# can be used. The in-place variants are always more efficient. Here we overwrite
# encrypted1 with the sum.
evaluator.add(encrypted1, encrypted2)
# It is instructive to think that addition sets the noise budget to the minimum
# of the input noise budgets. In this case both inputs had roughly the same
# budget going on, and the output (in encrypted1) has just slightly lower budget.
# Depending on probabilistic effects, the noise growth consumption may or may
# not be visible when measured in whole bits.
print("Noise budget in -encrypted1 + encrypted2: " +
(str)(decryptor.invariant_noise_budget(encrypted1)) + " bits")
# Finally multiply with encrypted2. Again, we use the in-place version of the
# function, overwriting encrypted1 with the product.
evaluator.multiply(encrypted1, encrypted2)
# Multiplication consumes a lot of noise budget. This is clearly seen in the
# print-out. The user can change the plain_modulus to see its effect on the
# rate of noise budget consumption.
print("Noise budget in (-encrypted1 + encrypted2) * encrypted2: " +
(str)(decryptor.invariant_noise_budget(encrypted1)) + " bits")
# Now we decrypt and decode our result.
plain_result = Plaintext()
print("Decrypting result: ")
decryptor.decrypt(encrypted1, plain_result)
print("Done")
# Print the result plaintext polynomial.
print("Plaintext polynomial: " + plain_result.to_string())
# Decode to obtain an integer result.
print("Decoded integer: " + (str)(encoder.decode_int32(plain_result)))
Evaluator, \
IntegerEncoder, \
FractionalEncoder, \
KeyGenerator, \
MemoryPoolHandle, \
Plaintext, \
SEALContext, \
EvaluationKeys, \
GaloisKeys, \
PolyCRTBuilder, \
ChooserEncoder, \
ChooserEvaluator, \
ChooserPoly
parms = EncryptionParameters()
parms.set_poly_modulus("1x^8192 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(8192))
parms.set_plain_modulus(1 << 21)
context = SEALContext(parms)
encoder = IntegerEncoder(context.plain_modulus())
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
ev_keys40 = EvaluationKeys()
ev_keys20 = EvaluationKeys()
#keygen.generate_evaluation_keys(40,5,ev_keys40)
keygen.generate_evaluation_keys(20, 3, ev_keys20)
encryptor = Encryptor(context, public_key)
evaluator = Evaluator(context)
decryptor = Decryptor(context, secret_key)
X[rowIndex] += [None] * (n - len(X[rowIndex]))
for rowIndex in range(n):
for colIndex in range(rowIndex + 1, n):
assert (X[rowIndex][colIndex] == None)
X[rowIndex][colIndex] = X[colIndex][rowIndex]
X_array = np.asarray(X)
return (X_array)
########################## paramaters required #################################
#N= int(input("Enter dimension of matrix needed to reverse: "))
parms = EncryptionParameters()
parms.set_poly_modulus("1x^32768 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(16384))
parms.set_plain_modulus(1 << 30)
context = SEALContext(parms)
encoderF = FractionalEncoder(context.plain_modulus(), context.poly_modulus(),
34, 30, 2)
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
ev_keys = EvaluationKeys()
keygen.generate_evaluation_keys(15, ev_keys)
encryptor = Encryptor(context, public_key)
evaluator = Evaluator(context)
Evaluator, \
IntegerEncoder, \
FractionalEncoder, \
KeyGenerator, \
MemoryPoolHandle, \
Plaintext, \
SEALContext, \
EvaluationKeys, \
GaloisKeys, \
PolyCRTBuilder, \
ChooserEncoder, \
ChooserEvaluator, \
ChooserPoly
parms = EncryptionParameters()
parms.set_poly_modulus("1x^4096 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(4096))
# Note that 40961 is a prime number and 2*4096 divides 40960.
parms.set_plain_modulus(40961)
context = SEALContext(parms)
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
def inner_product(cypher1, cypher2):
# We also set up an Encryptor, Evaluator, and Decryptor here.
evaluator = Evaluator(context)
decryptor = Decryptor(context, secret_key)
def example_batching():
print_example_banner("Example: Batching with PolyCRTBuilder");
parms = EncryptionParameters()
parms.set_poly_modulus("1x^4096 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(4096))
parms.set_plain_modulus(40961)
context = SEALContext(parms)
print_parameters(context)
qualifiers = context.qualifiers()
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
gal_keys = GaloisKeys()
keygen.generate_galois_keys(30, gal_keys)
#ev_keys = EvaluationKeys()
#keygen.generate_evaluation_keys(30, ev_keys)
encryptor = Encryptor(context, public_key)
evaluator = Evaluator(context)
decryptor = Decryptor(context, secret_key)
crtbuilder = PolyCRTBuilder(context)
slot_count = (int)(crtbuilder.slot_count())
row_size = (int)(slot_count / 2)
print("Plaintext matrix row size: " + (str)(row_size))
def print_matrix(matrix):
print("")
print_size = 5
current_line = " ["
for i in range(print_size):
current_line += ((str)(matrix[i]) + ", ")
current_line += ("..., ")
for i in range(row_size - print_size, row_size):
current_line += ((str)(matrix[i]))
if i != row_size-1: current_line += ", "
else: current_line += "]"
print(current_line)
current_line = " ["
for i in range(row_size, row_size + print_size):
current_line += ((str)(matrix[i]) + ", ")
current_line += ("..., ")
for i in range(2*row_size - print_size, 2*row_size):
current_line += ((str)(matrix[i]))
if i != 2*row_size-1: current_line += ", "
else: current_line += "]"
print(current_line)
print("")
# [ 0, 1, 2, 3, 0, 0, ..., 0 ]
# [ 4, 5, 6, 7, 0, 0, ..., 0 ]
pod_matrix = [0]*slot_count
pod_matrix[0] = 0
pod_matrix[1] = 1
pod_matrix[2] = 2
pod_matrix[3] = 3
pod_matrix[row_size] = 4
pod_matrix[row_size + 1] = 5
pod_matrix[row_size + 2] = 6
pod_matrix[row_size + 3] = 7
print("Input plaintext matrix:")
print_matrix(pod_matrix)
plain_matrix = Plaintext()
crtbuilder.compose(pod_matrix, plain_matrix)
encrypted_matrix = Ciphertext()
print("Encrypting: ")
encryptor.encrypt(plain_matrix, encrypted_matrix)
print("Done")
print("Noise budget in fresh encryption: " +
(str)(decryptor.invariant_noise_budget(encrypted_matrix)) + " bits")
pod_matrix2 = []
for i in range(slot_count): pod_matrix2.append((i % 2) + 1)
plain_matrix2 = Plaintext()
crtbuilder.compose(pod_matrix2, plain_matrix2)
print("Second input plaintext matrix:")
print_matrix(pod_matrix2)
print("Adding and squaring: ")
evaluator.add_plain(encrypted_matrix, plain_matrix2)
evaluator.square(encrypted_matrix)
evaluator.relinearize(encrypted_matrix, ev_keys)
print("Done")
print("Noise budget in result: " + (str)(decryptor.invariant_noise_budget(encrypted_matrix)) + " bits")
plain_result = Plaintext()
print("Decrypting result: ")
decryptor.decrypt(encrypted_matrix, plain_result)
print("Done")
crtbuilder.decompose(plain_result)
pod_result = [plain_result.coeff_at(i) for i in range(plain_result.coeff_count())]
print("Result plaintext matrix:")
print_matrix(pod_result)
encryptor.encrypt(plain_matrix, encrypted_matrix)
print("Unrotated matrix: ")
print_matrix(pod_matrix)
print("Noise budget in fresh encryption: " +
(str)(decryptor.invariant_noise_budget(encrypted_matrix)) + " bits")
# Now rotate the rows to the left 3 steps, decrypt, decompose, and print.
evaluator.rotate_rows(encrypted_matrix, 3, gal_keys)
print("Rotated rows 3 steps left: ")
decryptor.decrypt(encrypted_matrix, plain_result)
crtbuilder.decompose(plain_result)
pod_result = [plain_result.coeff_at(i) for i in range(plain_result.coeff_count())]
print_matrix(pod_result)
print("Noise budget after rotation" +
(str)(decryptor.invariant_noise_budget(encrypted_matrix)) + " bits")
# Rotate columns (swap rows), decrypt, decompose, and print.
evaluator.rotate_columns(encrypted_matrix, gal_keys)
print("Rotated columns: ")
decryptor.decrypt(encrypted_matrix, plain_result)
crtbuilder.decompose(plain_result)
pod_result = [plain_result.coeff_at(i) for i in range(plain_result.coeff_count())]
print_matrix(pod_result)
print("Noise budget after rotation: " +
(str)(decryptor.invariant_noise_budget(encrypted_matrix)) + " bits")
# Rotate rows to the right 4 steps, decrypt, decompose, and print.
evaluator.rotate_rows(encrypted_matrix, -4, gal_keys)
print("Rotated rows 4 steps right: ")
decryptor.decrypt(encrypted_matrix, plain_result)
crtbuilder.decompose(plain_result)
pod_result = [plain_result.coeff_at(i) for i in range(plain_result.coeff_count())]
print_matrix(pod_result)
print("Noise budget after rotation: " +
(str)(decryptor.invariant_noise_budget(encrypted_matrix)) + " bits")
def dot_product():
print("Example: Weighted Average")
# In this example we demonstrate the FractionalEncoder, and use it to compute
# a weighted average of 10 encrypted rational numbers. In this computation we
# perform homomorphic multiplications of ciphertexts by plaintexts, which is
# much faster than regular multiplications of ciphertexts by ciphertexts.
# Moreover, such `plain multiplications' never increase the ciphertext size,
# which is why we have no need for evaluation keys in this example.
# We start by creating encryption parameters, setting up the SEALContext, keys,
# and other relevant objects. Since our computation has multiplicative depth of
# only two, it suffices to use a small poly_modulus.
parms = EncryptionParameters()
parms.set_poly_modulus("1x^2048 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(2048))
parms.set_plain_modulus(1 << 8)
context = SEALContext(parms)
print_parameters(context)
keygen = KeyGenerator(context)
keygen2 = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
secret_key2 = keygen.secret_key()
# We also set up an Encryptor, Evaluator, and Decryptor here.
encryptor = Encryptor(context, public_key)
evaluator = Evaluator(context)
decryptor = Decryptor(context, secret_key2)
# Create a vector of 10 rational numbers (as doubles).
# rational_numbers = [3.1, 4.159, 2.65, 3.5897, 9.3, 2.3, 8.46, 2.64, 3.383, 2.795]
rational_numbers = np.random.rand(10)
# Create a vector of weights.
# coefficients = [0.1, 0.05, 0.05, 0.2, 0.05, 0.3, 0.1, 0.025, 0.075, 0.05]
coefficients = np.random.rand(10)
my_result = np.dot(rational_numbers, coefficients)
# We need a FractionalEncoder to encode the rational numbers into plaintext
# polynomials. In this case we decide to reserve 64 coefficients of the
# polynomial for the integral part (low-degree terms) and expand the fractional
# part to 32 digits of precision (in base 3) (high-degree terms). These numbers
# can be changed according to the precision that is needed; note that these
# choices leave a lot of unused space in the 2048-coefficient polynomials.
encoder = FractionalEncoder(context.plain_modulus(), context.poly_modulus(), 64, 32, 3)
# We create a vector of ciphertexts for encrypting the rational numbers.
encrypted_rationals = []
rational_numbers_string = "Encoding and encrypting: "
for i in range(10):
# We create our Ciphertext objects into the vector by passing the
# encryption parameters as an argument to the constructor. This ensures
# that enough memory is allocated for a size 2 ciphertext. In this example
# our ciphertexts never grow in size (plain multiplication does not cause
# ciphertext growth), so we can expect the ciphertexts to remain in the same
# location in memory throughout the computation. In more complicated examples
# one might want to call a constructor that reserves enough memory for the
# ciphertext to grow to a specified size to avoid costly memory moves when
# multiplications and relinearizations are performed.
encrypted_rationals.append(Ciphertext(parms))
encryptor.encrypt(encoder.encode(rational_numbers[i]), encrypted_rationals[i])
rational_numbers_string += (str)(rational_numbers[i])[:6]
if i < 9: rational_numbers_string += ", "
print(rational_numbers_string)
# Next we encode the coefficients. There is no reason to encrypt these since they
# are not private data.
encoded_coefficients = []
encoded_coefficients_string = "Encoding plaintext coefficients: "
encrypted_coefficients =[]
for i in range(10):
encoded_coefficients.append(encoder.encode(coefficients[i]))
encrypted_coefficients.append(Ciphertext(parms))
encryptor.encrypt(encoded_coefficients[i], encrypted_coefficients[i])
encoded_coefficients_string += (str)(coefficients[i])[:6]
if i < 9: encoded_coefficients_string += ", "
print(encoded_coefficients_string)
# We also need to encode 0.1. Multiplication by this plaintext will have the
# effect of dividing by 10. Note that in SEAL it is impossible to divide
# ciphertext by another ciphertext, but in this way division by a plaintext is
# possible.
div_by_ten = encoder.encode(0.1)
# Now compute each multiplication.
prod_result = [Ciphertext() for i in range(10)]
prod_result2 = [Ciphertext() for i in range(10)]
print("Computing products: ")
for i in range(10):
# Note how we use plain multiplication instead of usual multiplication. The
# result overwrites the first argument in the function call.
evaluator.multiply_plain(encrypted_rationals[i], encoded_coefficients[i], prod_result[i])
evaluator.multiply(encrypted_rationals[i], encrypted_coefficients[i], prod_result2[i])
print("Done")
# To obtain the linear sum we need to still compute the sum of the ciphertexts
# in encrypted_rationals. There is an easy way to add together a vector of
# Ciphertexts.
encrypted_result = Ciphertext()
encrypted_result2 = Ciphertext()
print("Adding up all 10 ciphertexts: ")
evaluator.add_many(prod_result, encrypted_result)
evaluator.add_many(prod_result2, encrypted_result2)
print("Done")
# Perform division by 10 by plain multiplication with div_by_ten.
# print("Dividing by 10: ")
# evaluator.multiply_plain(encrypted_result, div_by_ten)
# print("Done")
# How much noise budget do we have left?
print("Noise budget in result: " + (str)(decryptor.invariant_noise_budget(encrypted_result)) + " bits")
# Decrypt, decode, and print result.
plain_result = Plaintext()
plain_result2 = Plaintext()
print("Decrypting result: ")
decryptor.decrypt(encrypted_result, plain_result)
decryptor.decrypt(encrypted_result2, plain_result2)
print("Done")
result = encoder.decode(plain_result)
print("Weighted average: " + (str)(result)[:8])
result2 = encoder.decode(plain_result2)
print("Weighted average: " + (str)(result2)[:8])
print('\n\n', my_result)
def unit_test():
parms = EncryptionParameters()
parms.set_poly_modulus("1x^8192 + 1")
parms.set_coeff_modulus(seal.coeff_modulus_128(8192))
parms.set_plain_modulus(1 << 10)
context = SEALContext(parms)
# Print the parameters that we have chosen
print_parameters(context)
encoder = FractionalEncoder(context.plain_modulus(),
context.poly_modulus(), 64, 32, 3)
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
encryptor = Encryptor(context, public_key)
# Computations on the ciphertexts are performed with the Evaluator class.
evaluator = Evaluator(context)
# We will of course want to decrypt our results to verify that everything worked,
# so we need to also construct an instance of Decryptor. Note that the Decryptor
# requires the secret key.
decryptor = Decryptor(context, secret_key)
learningRate = 0.1
learningRate_data = encoder.encode(learningRate)
learningRate_e = Ciphertext()
encryptor.encrypt(learningRate_data, learningRate_e)
updatedVals = []
updatedVals.append(50)
updatedVals.append(50)
updatedVals_unenc = []
updatedVals_unenc.append(updatedVals[0])
updatedVals_unenc.append(updatedVals[1])
for i in range(15):
x = 1
y = 1
updatedVals = learn(x, y, evaluator, updatedVals[0], updatedVals[1],
encoder, encryptor, learningRate_e, decryptor)
ypred = updatedVals_unenc[0] * x + updatedVals_unenc[1]
error = ypred - y
updatedVals_unenc[0] = updatedVals_unenc[0] - x * error * learningRate
updatedVals_unenc[1] = updatedVals_unenc[1] - error * learningRate
print((str)(updatedVals[1]) + ":" + (str)(updatedVals[0]) + ":" +
(str)(updatedVals_unenc[1]) + ":" + (str)(updatedVals_unenc[0]))
x = 2
y = 3
updatedVals = learn(x, y, evaluator, updatedVals[0], updatedVals[1],
encoder, encryptor, learningRate_e, decryptor)
ypred = updatedVals_unenc[0] * x + updatedVals_unenc[1]
error = ypred - y
updatedVals_unenc[0] = updatedVals_unenc[0] - x * error * learningRate
updatedVals_unenc[1] = updatedVals_unenc[1] - error * learningRate
print((str)(updatedVals[1]) + ":" + (str)(updatedVals[0]) + ":" +
(str)(updatedVals_unenc[1]) + ":" + (str)(updatedVals_unenc[0]))
x = 4
y = 3
updatedVals = learn(x, y, evaluator, updatedVals[0], updatedVals[1],
encoder, encryptor, learningRate_e, decryptor)
ypred = updatedVals_unenc[0] * x + updatedVals_unenc[1]
error = ypred - y
updatedVals_unenc[0] = updatedVals_unenc[0] - x * error * learningRate
updatedVals_unenc[1] = updatedVals_unenc[1] - error * learningRate
print((str)(updatedVals[1]) + ":" + (str)(updatedVals[0]) + ":" +
(str)(updatedVals_unenc[1]) + ":" + (str)(updatedVals_unenc[0]))
x = 3
y = 2
updatedVals = learn(x, y, evaluator, updatedVals[0], updatedVals[1],
encoder, encryptor, learningRate_e, decryptor)
ypred = updatedVals_unenc[0] * x + updatedVals_unenc[1]
error = ypred - y
updatedVals_unenc[0] = updatedVals_unenc[0] - x * error * learningRate
updatedVals_unenc[1] = updatedVals_unenc[1] - error * learningRate
print((str)(updatedVals[1]) + ":" + (str)(updatedVals[0]) + ":" +
(str)(updatedVals_unenc[1]) + ":" + (str)(updatedVals_unenc[0]))
x = 5
y = 5
updatedVals = learn(x, y, evaluator, updatedVals[0], updatedVals[1],
encoder, encryptor, learningRate_e, decryptor)
ypred = updatedVals_unenc[0] * x + updatedVals_unenc[1]
error = ypred - y
updatedVals_unenc[0] = updatedVals_unenc[0] - x * error * learningRate
updatedVals_unenc[1] = updatedVals_unenc[1] - error * learningRate
print((str)(updatedVals[1]) + ":" + (str)(updatedVals[0]) + ":" +
(str)(updatedVals_unenc[1]) + ":" + (str)(updatedVals_unenc[0]))
GaloisKeys, \
PolyCRTBuilder, \
ChooserEncoder, \
ChooserEvaluator, \
ChooserPoly
# Set up an instance of the EncryptionParameters class
# three encryption parameters that are necessary to set:
# - poly_modulus (polynomial modulus);
# - coeff_modulus ([ciphertext] coefficient modulus);
# - plain_modulus (plaintext modulus).
parms = EncryptionParameters()
#polynomial modulus must be a power-of-2 cyclotomic polynomial
# Recommended degrees for poly_modulus are 1024, 2048, 4096, 8192, 16384, 32768,
# but it is also possible to go beyond this.
parms.set_poly_modulus("1x^2048 + 1")
# To make parameter selection easier for the user, we have constructed sets of
# largest allowed coefficient moduli for 128-bit and 192-bit security levels
# for different choices of the polynomial modulus. These recommended parameters
# follow the Security white paper at http://HomomorphicEncryption.org. However,
# due to the complexity of this topic, we highly recommend the user to directly
# consult an expert in homomorphic encryption and RLWE-based encryption schemes
# to determine the security of their parameter choices.
# Our recommended values for the coefficient modulus can be easily accessed
# through the functions
# coeff_modulus_128bit(int)
# coeff_modulus_192bit(int)
parms.set_coeff_modulus(seal.coeff_modulus_128(2048))
# The plaintext modulus can be any positive integer, even though here we take
class FHECryptoEngine(CryptoEngine):
def __init__(self):
CryptoEngine.__init__(self, defs.ENC_MODE_FHE)
self.log_id = 'FHECryptoEngine'
self.encrypt_params = None
self.context = None
self.encryptor = None
self.evaluator = None
self.decryptor = None
return
def load_keys(self):
self.private_key = SecretKey()
self.private_key.load(defs.FN_FHE_PRIVATE_KEY)
self.public_key = PublicKey()
self.public_key.load(defs.FN_FHE_PUBLIC_KEY)
return True
def generate_keys(self):
if self.encrypt_params == None or \
self.context == None:
self.init_encrypt_params()
keygen = KeyGenerator(self.context)
# Generate the private key
self.private_key = keygen.secret_key()
self.private_key.save(defs.FN_FHE_PRIVATE_KEY)
# Generate the public key
self.public_key = keygen.public_key()
self.public_key.save(defs.FN_FHE_PUBLIC_KEY)
return True
def init_encrypt_params(self):
self.encrypt_params = EncryptionParameters()
self.encrypt_params.set_poly_modulus("1x^2048 + 1")
self.encrypt_params.set_coeff_modulus(seal.coeff_modulus_128(2048))
self.encrypt_params.set_plain_modulus(1 << 8)
self.context = SEALContext(self.encrypt_params)
return
def initialize(self, use_old_keys=False):
# Initialize encryption params
self.init_encrypt_params()
# Check if the public & private key files exist
if os.path.isfile(defs.FN_FHE_PUBLIC_KEY) and \
os.path.isfile(defs.FN_FHE_PRIVATE_KEY) and \
use_old_keys == True:
self.log("Keys already exist. Reusing them instead.")
if not self.load_keys():
self.log("Failed to load keys")
return False
else:
# If not, then attempt to generate new ones
if not self.generate_keys():
self.log("Failed to generate keys")
return False
# Setup the rest of the crypto engine
self.encryptor = Encryptor(self.context, self.public_key)
self.evaluator = Evaluator(self.context)
self.decryptor = Decryptor(self.context, self.private_key)
# Set the initialized flag
self.initialized = True
return True
def encrypt(self, data):
if not self.initialized:
self.log("Not initialized")
return False
# Setup the encoder
encoder = FractionalEncoder(self.context.plain_modulus(), self.context.poly_modulus(), 64, 32, 3)
# Create the array of encrypted data objects
encrypted_data = []
for raw_data in data:
encrypted_data.append(Ciphertext(self.encrypt_params))
self.encryptor.encrypt( encoder.encode(raw_data), encrypted_data[-1] )
# Pickle each Ciphertext, base64 encode it, and store it in the array
for i in range(0, len(encrypted_data)):
encrypted_data[i].save("fhe_enc.bin")
encrypted_data[i] = base64.b64encode( pickle.dumps(encrypted_data[i]) )
return encrypted_data
def evaluate(self, encrypted_data, lower_idx=0, higher_idx=-1):
result = Ciphertext()
# Setup the encoder
encoder = FractionalEncoder(self.context.plain_modulus(), self.context.poly_modulus(), 64, 32, 3)
# Unpack the data first
unpacked_data = []
for d in encrypted_data[lower_idx:higher_idx]:
unpacked_data.append(pickle.loads(base64.b64decode(d)))
# Perform operations
self.evaluator.add_many(unpacked_data, result)
div = encoder.encode(1/len(unpacked_data))
self.evaluator.multiply_plain(result, div)
# Pack the result
result = base64.b64encode( pickle.dumps(result) )
return result
def decrypt(self, raw_data):
if not self.initialized:
self.log("Not initialized")
return False
# Setup the encoder
encoder = FractionalEncoder(self.context.plain_modulus(), self.context.poly_modulus(), 64, 32, 3)
# Unpickle, base64 decode, and decrypt each ciphertext result
decrypted_data = []
for d in raw_data:
encrypted_data = pickle.loads( base64.b64decode(d) )
plain_data = Plaintext()
self.decryptor.decrypt(encrypted_data, plain_data)
decrypted_data.append( str(encoder.decode(plain_data)) )
return decrypted_data