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 _create_keys(self, context):
keygen = KeyGenerator(context)
public_key = keygen.public_key()
secret_key = keygen.secret_key()
ev_keys16 = EvaluationKeys()
keygen.generate_evaluation_keys(16, ev_keys16)
return public_key, secret_key, ev_keys16
def keygen(context, batching):
#print("Generating secret/public keys: ")
time_start = time.time()
keygen = KeyGenerator(context)
time_end = time.time()
#print("Done in {} miliseconds".format((str)(1000 * (time_end - time_start))))
public_key = keygen.public_key()
secret_key = keygen.secret_key()
#use moderate size decomposition bit count
if batching:
gal_keys = GaloisKeys()
keygen.generate_galois_keys(30, gal_keys)
#since we are going to do some multiplications we are going to relinearize
ev_keys = EvaluationKeys()
keygen.generate_evaluation_keys(30, ev_keys)
return public_key, secret_key, ev_keys, gal_keys
else:
return public_key, secret_key
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)
A = []
n = int(input("Enter dimension: "))
for i in range(n):
a = []
for j in range(n):
encrypted_data1 = Ciphertext()
ran = random.randint(0, 10)
print(ran)
encryptor.encrypt(encoder.encode(ran), encrypted_data1)
a.append(encrypted_data1)
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()
gal_keys = GaloisKeys()
keygen.generate_galois_keys(30, gal_keys)
# Since we are going to do some multiplications we will also relinearize.
ev_keys = EvaluationKeys()
keygen.generate_evaluation_keys(30, ev_keys)
# We also set up an Encryptor, Evaluator, and Decryptor here.
encryptor = Encryptor(context, public_key)
evaluator = Evaluator(context)
decryptor = Decryptor(context, secret_key)
# Batching is done through an instance of the PolyCRTBuilder class so need
# to start by constructing one.
crtbuilder = PolyCRTBuilder(context)
slot_count = (int)(crtbuilder.slot_count())
row_size = (int)(slot_count / 2)
pod_matrix = [1,2,3,4,8,-4,3,2]
plain_matrix = Plaintext()
crtbuilder.compose(pod_matrix, plain_matrix)
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())
