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 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 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 run_test_add(self, message1, message2):
poly1 = Polynomial(self.degree, message1)
poly2 = Polynomial(self.degree, message2)
plain1 = Plaintext(poly1)
plain2 = Plaintext(poly2)
plain_sum = Plaintext(poly1.add(poly2, self.plain_modulus))
ciph1 = self.encryptor.encrypt(plain1)
ciph2 = self.encryptor.encrypt(plain2)
ciph_sum = self.evaluator.add(ciph1, ciph2)
decrypted_sum = self.decryptor.decrypt(ciph_sum)
self.assertEqual(str(plain_sum), str(decrypted_sum))
def run_test_secret_key_add(self, message1, message2):
poly1 = Polynomial(self.degree // 2, message1)
poly2 = Polynomial(self.degree // 2, message2)
plain1 = self.encoder.encode(message1, self.scaling_factor)
plain2 = self.encoder.encode(message2, self.scaling_factor)
plain_sum = poly1.add(poly2)
ciph1 = self.encryptor.encrypt_with_secret_key(plain1)
ciph2 = self.encryptor.encrypt_with_secret_key(plain2)
ciph_sum = self.evaluator.add(ciph1, ciph2)
decrypted_sum = self.decryptor.decrypt(ciph_sum)
decoded_sum = self.encoder.decode(decrypted_sum)
check_complex_vector_approx_eq(plain_sum.coeffs, decoded_sum, error=0.001)
def generate_public_key(self, params):
"""Generates a public key for BFV scheme.
Args:
params (Parameters): Parameters including polynomial degree,
plaintext, and ciphertext modulus.
"""
pk_coeff = Polynomial(
params.poly_degree,
sample_uniform(0, params.ciph_modulus, params.poly_degree))
pk_error = Polynomial(params.poly_degree,
sample_triangle(params.poly_degree))
p0 = pk_error.add(
pk_coeff.multiply(self.secret_key.s, params.ciph_modulus),
params.ciph_modulus).scalar_multiply(-1, params.ciph_modulus)
p1 = pk_coeff
self.public_key = PublicKey(p0, p1)
class TestPolynomial(unittest.TestCase):
def setUp(self):
self.degree = 5
self.coeff_modulus = 60
self.poly1 = Polynomial(self.degree, [0, 1, 4, 5, 59])
self.poly2 = Polynomial(self.degree, [1, 2, 4, 3, 2])
def test_add(self):
poly_sum = self.poly1.add(self.poly2, self.coeff_modulus)
poly_sum2 = self.poly2.add(self.poly1, self.coeff_modulus)
self.assertEqual(poly_sum.coeffs, [1, 3, 8, 8, 1])
self.assertEqual(poly_sum.coeffs, poly_sum2.coeffs)
def test_subtract(self):
poly_diff = self.poly1.subtract(self.poly2, self.coeff_modulus)
self.assertEqual(poly_diff.coeffs, [59, 59, 0, 2, 57])
def test_multiply(self):
poly1 = Polynomial(4, [0, 1, 4, 5])
poly2 = Polynomial(4, [1, 2, 4, 3])
poly_prod = poly1.multiply(poly2, 73)
poly_prod2 = poly2.multiply(poly1, 73)
self.assertEqual(poly_prod.coeffs, [44, 42, 64, 17])
self.assertEqual(poly_prod.coeffs, poly_prod2.coeffs)
def test_multiply_crt(self):
log_modulus = 10
modulus = 1 << log_modulus
prime_size = 59
log_poly_degree = 2
poly_degree = 1 << log_poly_degree
num_primes = (2 + log_poly_degree + 4 * log_modulus + prime_size -
1) // prime_size
crt = CRTContext(num_primes, prime_size, poly_degree)
poly1 = Polynomial(poly_degree, [0, 1, 4, 5])
poly2 = Polynomial(poly_degree, [1, 2, 4, 3])
poly_prod = poly1.multiply_crt(poly2, crt)
poly_prod = poly_prod.mod_small(modulus)
poly_prod2 = poly2.multiply_crt(poly1, crt)
poly_prod2 = poly_prod2.mod_small(modulus)
actual = poly1.multiply_naive(poly2, modulus)
actual = actual.mod_small(modulus)
self.assertEqual(poly_prod.coeffs, actual.coeffs)
self.assertEqual(poly_prod.coeffs, poly_prod2.coeffs)
def test_multiply_fft(self):
poly1 = Polynomial(4, [0, 1, 4, 5])
poly2 = Polynomial(4, [1, 2, 4, 3])
poly_prod = poly1.multiply_fft(poly2)
actual_coeffs = [-29, -31, -9, 17]
self.assertEqual(poly_prod.coeffs, actual_coeffs)
def test_multiply_naive(self):
poly_prod = self.poly1.multiply_naive(self.poly2, self.coeff_modulus)
poly_prod2 = self.poly2.multiply_naive(self.poly1, self.coeff_modulus)
self.assertEqual(poly_prod.coeffs, [28, 42, 59, 19, 28])
self.assertEqual(poly_prod.coeffs, poly_prod2.coeffs)
def test_multiply_01(self):
poly1 = Polynomial(4, sample_uniform(0, 30, 4))
poly2 = Polynomial(4, sample_uniform(0, 30, 4))
poly_prod = poly1.multiply_fft(poly2)
poly_prod2 = poly1.multiply_naive(poly2)
self.assertEqual(poly_prod.coeffs, poly_prod2.coeffs)
def test_scalar_multiply(self):
poly_prod = self.poly1.scalar_multiply(-1, self.coeff_modulus)
self.assertEqual(poly_prod.coeffs, [0, 59, 56, 55, 1])
def test_rotate(self):
poly1 = Polynomial(4, [0, 1, 4, 59])
poly_rot = poly1.rotate(3)
self.assertEqual(poly_rot.coeffs, [0, -1, 4, -59])
def test_round(self):
poly = Polynomial(self.degree, [0.51, -3.2, 54.666, 39.01, 0])
poly_rounded = poly.round()
self.assertEqual(poly_rounded.coeffs, [1, -3, 55, 39, 0])
def test_mod(self):
poly = Polynomial(self.degree, [57, -34, 100, 1000, -7999])
poly_rounded = poly.mod(self.coeff_modulus)
self.assertEqual(poly_rounded.coeffs, [57, 26, 40, 40, 41])
def test_base_decompose(self):
base = ceil(sqrt(self.coeff_modulus))
num_levels = floor(log(self.coeff_modulus, base)) + 1
poly_decomposed = self.poly1.base_decompose(base, num_levels)
self.assertEqual(poly_decomposed[0].coeffs, [0, 1, 4, 5, 3])
self.assertEqual(poly_decomposed[1].coeffs, [0, 0, 0, 0, 7])
def test_evaluate(self):
poly = Polynomial(self.degree, [0, 1, 2, 3, 4])
result = poly.evaluate(3)
self.assertEqual(result, 426)
def test_str(self):
string1 = str(self.poly1)
string2 = str(self.poly2)
self.assertEqual(string1, '59x^4 + 5x^3 + 4x^2 + x')
self.assertEqual(string2, '2x^4 + 3x^3 + 4x^2 + 2x + 1')