def add(self, ciph1, ciph2):
"""Adds two ciphertexts.
Adds two ciphertexts within the context.
Args:
ciph1 (Ciphertext): First ciphertext.
ciph2 (Ciphertext): Second ciphertext.
Returns:
A Ciphertext which is the sum of the two ciphertexts.
"""
assert isinstance(ciph1, Ciphertext)
assert isinstance(ciph2, Ciphertext)
assert ciph1.scaling_factor == ciph2.scaling_factor, "Scaling factors are not equal. " \
+ "Ciphertext 1 scaling factor: %d bits, Ciphertext 2 scaling factor: %d bits" \
% (math.log(ciph1.scaling_factor, 2), math.log(ciph2.scaling_factor, 2))
assert ciph1.modulus == ciph2.modulus, "Moduli are not equal. " \
+ "Ciphertext 1 modulus: %d bits, Ciphertext 2 modulus: %d bits" \
% (math.log(ciph1.modulus, 2), math.log(ciph2.modulus, 2))
modulus = ciph1.modulus
c0 = ciph1.c0.add(ciph2.c0, modulus)
c0 = c0.mod_small(modulus)
c1 = ciph1.c1.add(ciph2.c1, modulus)
c1 = c1.mod_small(modulus)
return Ciphertext(c0, c1, ciph1.scaling_factor, modulus)
def encrypt(self, plain):
"""Encrypts a message.
Encrypts the message and returns the corresponding ciphertext.
Args:
plain (Plaintext): Plaintext to be encrypted.
Returns:
A ciphertext consisting of a pair of polynomials in the ciphertext
space.
"""
p0 = self.public_key.p0
p1 = self.public_key.p1
random_vec = Polynomial(self.poly_degree,
sample_triangle(self.poly_degree))
error1 = Polynomial(self.poly_degree,
sample_triangle(self.poly_degree))
error2 = Polynomial(self.poly_degree,
sample_triangle(self.poly_degree))
c0 = p0.multiply(random_vec, self.coeff_modulus, crt=self.crt_context)
c0 = error1.add(c0, self.coeff_modulus)
c0 = c0.add(plain.poly, self.coeff_modulus)
c0 = c0.mod_small(self.coeff_modulus)
c1 = p1.multiply(random_vec, self.coeff_modulus, crt=self.crt_context)
c1 = error2.add(c1, self.coeff_modulus)
c1 = c1.mod_small(self.coeff_modulus)
return Ciphertext(c0, c1, plain.scaling_factor, self.coeff_modulus)
def subtract(self, ciph1, ciph2):
"""Subtracts second ciphertext from first ciphertext.
Computes ciph1 - ciph2.
Args:
ciph1 (Ciphertext): First ciphertext.
ciph2 (Ciphertext): Second ciphertext.
Returns:
A Ciphertext which is the difference between the two ciphertexts.
"""
assert isinstance(ciph1, Ciphertext)
assert isinstance(ciph2, Ciphertext)
assert ciph1.scaling_factor == ciph2.scaling_factor, "Scaling factors are not equal. " \
+ "Ciphertext 1 scaling factor: %d bits, Ciphertext 2 scaling factor: %d bits" \
% (math.log(ciph1.scaling_factor, 2), math.log(ciph2.scaling_factor, 2))
assert ciph1.modulus == ciph2.modulus, "Moduli are not equal. " \
+ "Ciphertext 1 modulus: %d bits, Ciphertext 2 modulus: %d bits" \
% (math.log(ciph1.modulus, 2), math.log(ciph2.modulus, 2))
modulus = ciph1.modulus
c0 = ciph1.c0.subtract(ciph2.c0, modulus)
c0 = c0.mod_small(modulus)
c1 = ciph1.c1.subtract(ciph2.c1, modulus)
c1 = c1.mod_small(modulus)
return Ciphertext(c0, c1, ciph1.scaling_factor, modulus)
def switch_key(self, ciph, key):
"""Outputs ciphertext with switching key.
Performs KS procedure as described in CKKS paper.
Args:
ciph (Ciphertext): Ciphertext to change.
switching_key (PublicKey): Switching key.
Returns:
A Ciphertext which encrypts the same message under a different key.
"""
c0 = key.p0.multiply(ciph.c1,
ciph.modulus * self.big_modulus,
crt=self.crt_context)
c0 = c0.mod_small(ciph.modulus * self.big_modulus)
c0 = c0.scalar_integer_divide(self.big_modulus)
c0 = c0.add(ciph.c0, ciph.modulus)
c0 = c0.mod_small(ciph.modulus)
c1 = key.p1.multiply(ciph.c1,
ciph.modulus * self.big_modulus,
crt=self.crt_context)
c1 = c1.mod_small(ciph.modulus * self.big_modulus)
c1 = c1.scalar_integer_divide(self.big_modulus)
c1 = c1.mod_small(ciph.modulus)
return Ciphertext(c0, c1, ciph.scaling_factor, ciph.modulus)
def encrypt(self, message):
"""Encrypts a message.
Encrypts the message and returns the corresponding ciphertext.
Args:
message (Plaintext): Plaintext to be encrypted.
Returns:
A ciphertext consisting of a pair of polynomials in the ciphertext
space.
"""
p0 = self.public_key.p0
p1 = self.public_key.p1
scaled_message = message.poly.scalar_multiply(self.scaling_factor,
self.coeff_modulus)
random_vec = Polynomial(self.poly_degree,
sample_triangle(self.poly_degree))
error1 = Polynomial(self.poly_degree,
sample_triangle(self.poly_degree))
error1 = Polynomial(self.poly_degree, [0] * self.poly_degree)
error2 = Polynomial(self.poly_degree,
sample_triangle(self.poly_degree))
error2 = Polynomial(self.poly_degree, [0] * self.poly_degree)
c0 = error1.add(p0.multiply(random_vec, self.coeff_modulus),
self.coeff_modulus).add(scaled_message,
self.coeff_modulus)
c1 = error2.add(p1.multiply(random_vec, self.coeff_modulus),
self.coeff_modulus)
return Ciphertext(c0, c1)
def relinearize(self, relin_key, c0, c1, c2):
"""Relinearizes a 3-dimensional ciphertext.
Reduces 3-dimensional ciphertext back down to 2 dimensions.
Args:
relin_key (RelinKey): Relinearization keys.
c0 (Polynomial): First component of ciphertext.
c1 (Polynomial): Second component of ciphertext.
c2 (Polynomial): Third component of ciphertext.
Returns:
A Ciphertext which has only two components.
"""
keys = relin_key.keys
base = relin_key.base
num_levels = len(keys)
c2_decomposed = c2.base_decompose(base, num_levels)
new_c0 = c0
new_c1 = c1
for i in range(num_levels):
new_c0 = new_c0.add(
keys[i][0].multiply(c2_decomposed[i], self.coeff_modulus),
self.coeff_modulus)
new_c1 = new_c1.add(
keys[i][1].multiply(c2_decomposed[i], self.coeff_modulus),
self.coeff_modulus)
return Ciphertext(new_c0, new_c1)
def encrypt_with_secret_key(self, plain):
"""Encrypts a message with secret key encryption.
Encrypts the message for secret key encryption and returns the corresponding ciphertext.
Args:
plain (Plaintext): Plaintext to be encrypted.
Returns:
A ciphertext consisting of a pair of polynomials in the ciphertext
space.
"""
assert self.secret_key != None, 'Secret key does not exist'
sk = self.secret_key.s
random_vec = Polynomial(self.poly_degree,
sample_triangle(self.poly_degree))
error = Polynomial(self.poly_degree, sample_triangle(self.poly_degree))
c0 = sk.multiply(random_vec, self.coeff_modulus, crt=self.crt_context)
c0 = error.add(c0, self.coeff_modulus)
c0 = c0.add(plain.poly, self.coeff_modulus)
c0 = c0.mod_small(self.coeff_modulus)
c1 = random_vec.scalar_multiply(-1, self.coeff_modulus)
c1 = c1.mod_small(self.coeff_modulus)
return Ciphertext(c0, c1, plain.scaling_factor, self.coeff_modulus)
def relinearize(self, relin_key, c0, c1, c2, new_scaling_factor, modulus):
"""Relinearizes a 3-dimensional ciphertext.
Reduces 3-dimensional ciphertext back down to 2 dimensions.
Args:
relin_key (PublicKey): Relinearization keys.
c0 (Polynomial): First component of ciphertext.
c1 (Polynomial): Second component of ciphertext.
c2 (Polynomial): Third component of ciphertext.
new_scaling_factor (float): New scaling factor for ciphertext.
modulus (int): Ciphertext modulus.
Returns:
A Ciphertext which has only two components.
"""
new_c0 = relin_key.p0.multiply(c2,
modulus * self.big_modulus,
crt=self.crt_context)
new_c0 = new_c0.mod_small(modulus * self.big_modulus)
new_c0 = new_c0.scalar_integer_divide(self.big_modulus)
new_c0 = new_c0.add(c0, modulus)
new_c0 = new_c0.mod_small(modulus)
new_c1 = relin_key.p1.multiply(c2,
modulus * self.big_modulus,
crt=self.crt_context)
new_c1 = new_c1.mod_small(modulus * self.big_modulus)
new_c1 = new_c1.scalar_integer_divide(self.big_modulus)
new_c1 = new_c1.add(c1, modulus)
new_c1 = new_c1.mod_small(modulus)
return Ciphertext(new_c0, new_c1, new_scaling_factor, modulus)
def add_plain(self, cipher, plain):
assert isinstance(cipher, Ciphertext)
assert isinstance(plain, Plaintext)
assert cipher.scaling_factor == plain.scaling_factor, "Scaling factors are not equal. " \
+ "Ciphertext scaling factor: %d bits, Plaintext scaling factor: %d bits" \
% (math.log(cipher.scaling_factor, 2),
math.log(plain.scaling_factor, 2))
c0 = cipher.c0.add(plain.poly, cipher.modulus)
c0 = c0.mod_small(cipher.modulus)
return Ciphertext(c0, cipher.c1, cipher.scaling_factor, cipher.modulus)
def add(self, cipher1, cipher2):
assert isinstance(cipher1, Ciphertext)
assert isinstance(cipher2, Ciphertext)
assert cipher1.scaling_factor == cipher2.scaling_factor, "Scaling factors are not equal. " \
+ "Ciphertext 1 scaling factor: %d bits, Ciphertext 2 scaling factor: %d bits" \
% (math.log(cipher1.scaling_factor, 2), math.log(cipher2.scaling_factor, 2))
assert cipher1.modulus == cipher2.modulus, "Moduli are not equal. " \
+ "Ciphertext 1 modulus: %d bits, Ciphertext 2 modulus: %d bits" \
% (math.log(cipher1.modulus, 2), math.log(cipher2.modulus, 2))
modulus = cipher1.modulus
c0 = cipher1.c0.add(cipher2.c0, modulus)
c1 = cipher1.c1.add(cipher2.c1, modulus)
return Ciphertext(c0, c1, cipher1.scaling_factor, cipher1.modulus)
def multiply_plain(self, cipher, plain):
assert isinstance(cipher, Ciphertext)
assert isinstance(plain, Plaintext)
c0 = cipher.c0.multiply(plain.poly,
cipher.modulus,
crt=self.crt_context)
c0 = c0.mod_small(cipher.modulus)
c1 = cipher.c1.multiply(plain.poly,
cipher.modulus,
crt=self.crt_context)
c1 = c1.mod_small(cipher.modulus)
return Ciphertext(c0, c1, cipher.scaling_factor * plain.scaling_factor,
cipher.modulus)
def encrypt(self, plain):
p0 = self.public_key[0]
p1 = self.public_key[1]
random_vec = Poly(self.poly_degree, sample_triangle(self.poly_degree))
error1 = Poly(self.poly_degree, sample_triangle(self.poly_degree))
error2 = Poly(self.poly_degree, sample_triangle(self.poly_degree))
c0 = p0.multiply(random_vec, self.coeff_modulus, crt=self.crt_context)
c0 = error1.add(c0, self.coeff_modulus)
c0 = c0.add(plain.poly, self.coeff_modulus)
c0 = c0.mod_small(self.coeff_modulus)
c1 = p1.multiply(random_vec, self.coeff_modulus, crt=self.crt_context)
c1 = error2.add(c1, self.coeff_modulus)
c1 = c1.mod_small(self.coeff_modulus)
return Ciphertext(c0, c1, plain.scaling_factor, self.coeff_modulus)
def rescale(self, ciph, division_factor):
"""Rescales a ciphertext to a new scaling factor.
Divides ciphertext by division factor, and updates scaling factor
and ciphertext. modulus.
Args:
ciph (Ciphertext): Ciphertext to modify.
division_factor (float): Factor to divide by.
Returns:
Rescaled ciphertext.
"""
c0 = ciph.c0.scalar_integer_divide(division_factor)
c1 = ciph.c1.scalar_integer_divide(division_factor)
return Ciphertext(c0, c1, ciph.scaling_factor // division_factor,
ciph.modulus // division_factor)
def lower_modulus(self, ciph, division_factor):
"""Rescales a ciphertext to a new scaling factor.
Divides ciphertext by division factor, and updates scaling factor
and ciphertext modulus.
Args:
ciph (Ciphertext): Ciphertext to modify.
division_factor (float): Factor to divide by.
Returns:
Rescaled ciphertext.
"""
new_modulus = ciph.modulus // division_factor
c0 = ciph.c0.mod_small(new_modulus)
c1 = ciph.c1.mod_small(new_modulus)
return Ciphertext(c0, c1, ciph.scaling_factor, new_modulus)
def add(self, ciph1, ciph2):
"""Adds two ciphertexts.
Adds two ciphertexts within the context.
Args:
ciph1 (Ciphertext): First ciphertext.
ciph2 (Ciphertext): Second ciphertext.
Returns:
A Ciphertext which is the sum of the two ciphertexts.
"""
assert isinstance(ciph1, Ciphertext)
assert isinstance(ciph2, Ciphertext)
new_ciph_c0 = ciph1.c0.add(ciph2.c0, self.coeff_modulus)
new_ciph_c1 = ciph1.c1.add(ciph2.c1, self.coeff_modulus)
return Ciphertext(new_ciph_c0, new_ciph_c1)
def conjugate(self, ciph, conj_key):
"""Conjugates the ciphertext.
Returns a ciphertext for a plaintext which is conjugated.
Args:
ciph (Ciphertext): Ciphertext to conjugate.
conj_key (PublicKey): Conjugation key.
Returns:
A Ciphertext which is the encryption of the conjugation of the original
plaintext.
"""
conj_ciph0 = ciph.c0.conjugate().mod_small(ciph.modulus)
conj_ciph1 = ciph.c1.conjugate().mod_small(ciph.modulus)
conj_ciph = Ciphertext(conj_ciph0, conj_ciph1, ciph.scaling_factor,
ciph.modulus)
return self.switch_key(conj_ciph, conj_key)
def rotate(self, ciph, rotation, rot_key):
"""Rotates a ciphertext by the amount specified in rotation.
Returns a ciphertext for a plaintext which is rotated by the amount
in rotation.
Args:
ciph (Ciphertext): Ciphertext to rotate.
rotation (int): Amount to rotate by.
rot_key (RotationKey): Rotation key corresponding to the rotation.
Returns:
A Ciphertext which is the encryption of the rotation of the original
plaintext.
"""
rot_ciph0 = ciph.c0.rotate(rotation)
rot_ciph1 = ciph.c1.rotate(rotation)
rot_ciph = Ciphertext(rot_ciph0, rot_ciph1, ciph.scaling_factor,
ciph.modulus)
return self.switch_key(rot_ciph, rot_key.key)
def run_test_simple_rotate(self, message, rot):
poly = Polynomial(self.degree // 2, message)
plain = self.encoder.encode(message, self.scaling_factor)
rot_message = [0] * poly.ring_degree
for i in range(poly.ring_degree):
rot_message[i] = poly.coeffs[(i + rot) % poly.ring_degree]
ciph = self.encryptor.encrypt(plain)
ciph_rot0 = ciph.c0.rotate(rot).mod_small(self.ciph_modulus)
ciph_rot1 = ciph.c1.rotate(rot).mod_small(self.ciph_modulus)
ciph_rot = Ciphertext(ciph_rot0, ciph_rot1, ciph.scaling_factor,
self.ciph_modulus)
decryptor = CKKSDecryptor(self.params,
SecretKey(self.secret_key.s.rotate(rot)))
decrypted_rot = decryptor.decrypt(ciph_rot)
decoded_rot = self.encoder.decode(decrypted_rot)
check_complex_vector_approx_eq(rot_message, decoded_rot, error=0.005)
def add_plain(self, ciph, plain):
"""Adds a ciphertext with a plaintext.
Adds a ciphertext with a plaintext polynomial within the context.
Args:
ciph (Ciphertext): A ciphertext to add.
plain (Plaintext): A plaintext to add.
Returns:
A Ciphertext which is the sum of the ciphertext and plaintext.
"""
assert isinstance(ciph, Ciphertext)
assert isinstance(plain, Plaintext)
assert ciph.scaling_factor == plain.scaling_factor, "Scaling factors are not equal. " \
+ "Ciphertext scaling factor: %d bits, Plaintext scaling factor: %d bits" \
% (math.log(ciph.scaling_factor, 2), math.log(plain.scaling_factor, 2))
c0 = ciph.c0.add(plain.poly, ciph.modulus)
c0 = c0.mod_small(ciph.modulus)
return Ciphertext(c0, ciph.c1, ciph.scaling_factor, ciph.modulus)
def multiply_plain(self, ciph, plain):
"""Multiplies a ciphertext with a plaintext.
Multiplies a ciphertext with a plaintext polynomial within the context.
Args:
ciph (Ciphertext): A ciphertext to multiply.
plain (Plaintext): A plaintext to multiply.
Returns:
A Ciphertext which is the product of the ciphertext and plaintext.
"""
assert isinstance(ciph, Ciphertext)
assert isinstance(plain, Plaintext)
c0 = ciph.c0.multiply(plain.poly, ciph.modulus, crt=self.crt_context)
c0 = c0.mod_small(ciph.modulus)
c1 = ciph.c1.multiply(plain.poly, ciph.modulus, crt=self.crt_context)
c1 = c1.mod_small(ciph.modulus)
return Ciphertext(c0, c1, ciph.scaling_factor * plain.scaling_factor,
ciph.modulus)
