def inner_product(cypher1, cypher2): # We also set up an Encryptor, Evaluator, and Decryptor here. evaluator = Evaluator(context) decryptor = Decryptor(context, secret_key) for i in range(len(cypher1)): evaluator.multiply(cypher1[i], cypher2[i]) encrypted_result = Ciphertext() evaluator.add_many(cypher1, encrypted_result) return encrypted_result
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) value=7 plain1 = encoder.encode(value1) print("Encoded " + (str)(value) + " as polynomial " + plain1.to_string() + " (plain1)") encrypted _data= Ciphertext() encryptor.encrypt(plain, encrypted_data) print("Noise budget in encrypted1: " + (str)(decryptor.invariant_noise_budget(encrypted_data)) + " bits") # operations that can be performed ---> # result stored in encrypted1 data evaluator.negate(encrypted1_data) # result stored in encrypted1 data, encrpyted1 is modified evaluator.add(encrypted1_data, encrypted2_data) # result stored in encrypted1 data, encrpyted1 is modified evaluator.multiply(encrypted1_data, encrypted2_data) plain_result = Plaintext() decryptor.decrypt(encrypted_data, plain_result) print("Plaintext polynomial: " + plain_result.to_string()) print("Decoded integer: " + (str)(encoder.decode_int32(plain_result)))
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 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)))
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
def example_bfv_basics(): print("Example: BFV Basics") #In this example, we demonstrate performing simple computations (a polynomial #evaluation) on encrypted integers using the BFV encryption scheme. # #The first task is to set up an instance of the EncryptionParameters class. #It is critical to understand how the 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_degree (degree of polynomial modulus); # - coeff_modulus ([ciphertext] coefficient modulus); # - plain_modulus (plaintext modulus; only for the BFV scheme). # #The BFV scheme 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 #in 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 BFV the two basic #operations allowed on encrypted data 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 compounds in sequential multiplications, the most significant #factor in choosing appropriate encryption parameters is the multiplicative #depth of the arithmetic circuit that the user wants to evaluate on encrypted #data. Once the noise budget of 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(scheme_type.BFV) #The first parameter we set is the degree of the `polynomial modulus'. This #must be a positive power of 2, representing the degree of a power-of-two #cyclotomic polynomial; it is not necessary to understand what this means. # #Larger poly_modulus_degree makes ciphertext sizes larger and all operations #slower, but enables more complicated encrypted computations. Recommended #values are 1024, 2048, 4096, 8192, 16384, 32768, but it is also possible #to go beyond this range. # #In this example we use a relatively small polynomial modulus. Anything #smaller than this will enable only very restricted encrypted computations. poly_modulus_degree = 4096 parms.set_poly_modulus_degree(poly_modulus_degree) #Next we set the [ciphertext] `coefficient modulus' (coeff_modulus). This #parameter is a large integer, which is a product of distinct prime numbers, #each up to 60 bits in size. It is represented as a vector of these prime #numbers, each represented by an instance of the SmallModulus class. The #bit-length of coeff_modulus means the sum of the bit-lengths of its prime #factors. # #A larger coeff_modulus implies a larger noise budget, hence more encrypted #computation capabilities. However, an upper bound for the total bit-length #of the coeff_modulus is determined by the poly_modulus_degree, as follows: # # +----------------------------------------------------+ # | poly_modulus_degree | max coeff_modulus bit-length | # +---------------------+------------------------------+ # | 1024 | 27 | # | 2048 | 54 | # | 4096 | 109 | # | 8192 | 218 | # | 16384 | 438 | # | 32768 | 881 | # +---------------------+------------------------------+ # #These numbers can also be found in native/src/seal/util/hestdparms.h encoded #in the function SEAL_HE_STD_PARMS_128_TC, and can also be obtained from the #function # # CoeffModulus::MaxBitCount(poly_modulus_degree). # #For example, if poly_modulus_degree is 4096, the coeff_modulus could consist #of three 36-bit primes (108 bits). # #Microsoft SEAL comes with helper functions for selecting the coeff_modulus. #For new users the easiest way is to simply use # # CoeffModulus::BFVDefault(poly_modulus_degree), # #which returns std::vector<SmallModulus> consisting of a generally good choice #for the given poly_modulus_degree. parms.set_coeff_modulus(CoeffModulus.BFVDefault(poly_modulus_degree)) #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 later examples. The plaintext #modulus determines the size of the plaintext data type and the consumption #of noise budget in multiplications. Thus, it is essential to try to keep the #plaintext data type as small as possible for best 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). # #The plaintext modulus is specific to the BFV scheme, and cannot be set when #using the CKKS scheme. parms.set_plain_modulus(1024) #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. context = SEALContext.Create(parms) #Print the parameters that we have chosen. print("Set encryption parameters and print") print_parameters(context) print("~~~~~~ A naive way to calculate 4(x^2+1)(x+1)^2. ~~~~~~") #The encryption schemes in Microsoft SEAL are public key encryption schemes. #For users unfamiliar with this terminology, a public key encryption scheme #has a separate public key for encrypting data, and a separate secret key for #decrypting data. This way multiple parties can encrypt data using the same #shared public key, but only the proper recipient of the data can decrypt it #with the secret key. # #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 immediately be #read to local variables. 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, as expected. encryptor = Encryptor(context, public_key) #Computations on the ciphertexts are performed with the Evaluator class. In #a real use-case the Evaluator would not be constructed by the same party #that holds the secret key. 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) #As an example, we evaluate the degree 4 polynomial # # 4x^4 + 8x^3 + 8x^2 + 8x + 4 # #over an encrypted x = 6. The coefficients of the polynomial can be considered #as plaintext inputs, as we will see below. The computation is done modulo the #plain_modulus 1024. # #While this examples is simple and easy to understand, it does not have much #practical value. In later examples we will demonstrate how to compute more #efficiently on encrypted integers and real or complex numbers. # #Plaintexts in the BFV scheme are polynomials of degree less than the degree #of the polynomial modulus, and coefficients integers modulo the plaintext #modulus. For readers with background in ring theory, the plaintext space is #the polynomial quotient ring Z_T[X]/(X^N + 1), where N is poly_modulus_degree #and T is plain_modulus. # #To get started, we create a plaintext containing the constant 6. For the #plaintext element we use a constructor that takes the desired polynomial as #a string with coefficients represented as hexadecimal numbers. x = 6 x_plain = Plaintext(str(x)) print("Express x = {} as a plaintext polynomial 0x{}.".format( x, x_plain.to_string())) #We then encrypt the plaintext, producing a ciphertext. x_encrypted = Ciphertext() print("Encrypt x_plain to x_encrypted.") encryptor.encrypt(x_plain, x_encrypted) #In Microsoft SEAL, a valid ciphertext consists of two or more polynomials #whose coefficients are integers modulo the product of the primes in the #coeff_modulus. The number of polynomials in a ciphertext is called its `size' #and is given by Ciphertext::size(). A freshly encrypted ciphertext always #has size 2. print(" + size of freshly encrypted x: {}".format(x_encrypted.size())) #There is plenty of noise budget left in this freshly encrypted ciphertext. print(" + noise budget in freshly encrypted x: {} bits".format( decryptor.invariant_noise_budget(x_encrypted))) #We decrypt the ciphertext and print the resulting plaintext in order to #demonstrate correctness of the encryption. x_decrypted = Plaintext() decryptor.decrypt(x_encrypted, x_decrypted) print(" + decryption of x_encrypted: 0x{} ...... Correct.".format( x_decrypted.to_string())) #When using Microsoft SEAL, it is typically advantageous to compute in a way #that minimizes the longest chain of sequential multiplications. In other #words, encrypted computations are best evaluated in a way that minimizes #the multiplicative depth of the computation, because the total noise budget #consumption is proportional to the multiplicative depth. For example, for #our example computation it is advantageous to factorize the polynomial as # # 4x^4 + 8x^3 + 8x^2 + 8x + 4 = 4(x + 1)^2 * (x^2 + 1) # #to obtain a simple depth 2 representation. Thus, we compute (x + 1)^2 and #(x^2 + 1) separately, before multiplying them, and multiplying by 4. # #First, we compute x^2 and add a plaintext "1". We can clearly see from the #print-out that multiplication has consumed a lot of noise budget. The user #can vary the plain_modulus parameter to see its effect on the rate of noise #budget consumption. print("Compute x_sq_plus_one (x^2+1).") x_sq_plus_one = Ciphertext() evaluator.square(x_encrypted, x_sq_plus_one) plain_one = Plaintext("1") evaluator.add_plain_inplace(x_sq_plus_one, plain_one) #Encrypted 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 perform a squaring, and observe both size growth and noise budget #consumption. print(" + size of x_sq_plus_one: {}".format(x_sq_plus_one.size())) print(" + noise budget in x_sq_plus_one: {} bits".format( decryptor.invariant_noise_budget(x_sq_plus_one))) #Even though the size has grown, decryption works as usual as long as noise #budget has not reached 0. decrypted_result = Plaintext() decryptor.decrypt(x_sq_plus_one, decrypted_result) print(" + decryption of x_sq_plus_one: 0x{} ...... Correct.".format( decrypted_result.to_string())) #Next, we compute (x + 1)^2. print("Compute x_plus_one_sq ((x+1)^2).") x_plus_one_sq = Ciphertext() evaluator.add_plain(x_encrypted, plain_one, x_plus_one_sq) evaluator.square_inplace(x_plus_one_sq) print(" + size of x_plus_one_sq: {}".format(x_plus_one_sq.size())) print(" + noise budget in x_plus_one_sq: {} bits".format( decryptor.invariant_noise_budget(x_plus_one_sq))) decryptor.decrypt(x_plus_one_sq, decrypted_result) print(" + decryption of x_plus_one_sq: 0x{} ...... Correct.".format( decrypted_result.to_string())) #Finally, we multiply (x^2 + 1) * (x + 1)^2 * 4. print("Compute encrypted_result (4(x^2+1)(x+1)^2).") encrypted_result = Ciphertext() plain_four = Plaintext("4") evaluator.multiply_plain_inplace(x_sq_plus_one, plain_four) evaluator.multiply(x_sq_plus_one, x_plus_one_sq, encrypted_result) print(" + size of encrypted_result: {}".format(encrypted_result.size())) print(" + noise budget in encrypted_result: {} bits".format( decryptor.invariant_noise_budget(encrypted_result))) print("NOTE: Decryption can be incorrect if noise budget is zero.") print("~~~~~~ A better way to calculate 4(x^2+1)(x+1)^2. ~~~~~~") #Noise budget has reached 0, which means that decryption cannot be expected #to give the correct result. This is because both ciphertexts x_sq_plus_one #and x_plus_one_sq consist of 3 polynomials due to the previous squaring #operations, and homomorphic operations on large ciphertexts consume much more #noise budget than computations on small ciphertexts. Computing on smaller #ciphertexts is also computationally significantly cheaper. #`Relinearization' is an operation that reduces the size of a ciphertext after #multiplication back to the initial size, 2. Thus, relinearizing one or both #input ciphertexts before the next multiplication can have a huge positive #impact on both noise growth and performance, even though relinearization has #a significant computational cost itself. It is only possible to relinearize #size 3 ciphertexts down to size 2, so often the user would want to relinearize #after each multiplication to keep the ciphertext sizes at 2. #Relinearization requires special `relinearization keys', which can be thought #of as a kind of public key. Relinearization keys can easily be created with #the KeyGenerator. #Relinearization is used similarly in both the BFV and the CKKS schemes, but #in this example we continue using BFV. We repeat our computation from before, #but this time relinearize after every multiplication. #We use KeyGenerator::relin_keys() to create relinearization keys. print("Generate relinearization keys.") relin_keys = keygen.relin_keys() #We now repeat the computation relinearizing after each multiplication. print("Compute and relinearize x_squared (x^2),") print("then compute x_sq_plus_one (x^2+1)") x_squared = Ciphertext() evaluator.square(x_encrypted, x_squared) print(" + size of x_squared: {}".format(x_squared.size())) evaluator.relinearize_inplace(x_squared, relin_keys) print(" + size of x_squared (after relinearization): {}".format( x_squared.size())) evaluator.add_plain(x_squared, plain_one, x_sq_plus_one) print(" + noise budget in x_sq_plus_one: {} bits".format( decryptor.invariant_noise_budget(x_sq_plus_one))) decryptor.decrypt(x_sq_plus_one, decrypted_result) print(" + decryption of x_sq_plus_one: 0x{} ...... Correct.".format( decrypted_result.to_string())) x_plus_one = Ciphertext() print("Compute x_plus_one (x+1),") print("then compute and relinearize x_plus_one_sq ((x+1)^2).") evaluator.add_plain(x_encrypted, plain_one, x_plus_one) evaluator.square(x_plus_one, x_plus_one_sq) print(" + size of x_plus_one_sq: {}".format(x_plus_one_sq.size())) evaluator.relinearize_inplace(x_plus_one_sq, relin_keys) print(" + noise budget in x_plus_one_sq: {} bits".format( decryptor.invariant_noise_budget(x_plus_one_sq))) decryptor.decrypt(x_plus_one_sq, decrypted_result) print(" + decryption of x_plus_one_sq: 0x{} ...... Correct.".format( decrypted_result.to_string())) print("Compute and relinearize encrypted_result (4(x^2+1)(x+1)^2).") evaluator.multiply_plain_inplace(x_sq_plus_one, plain_four) evaluator.multiply(x_sq_plus_one, x_plus_one_sq, encrypted_result) print(" + size of encrypted_result: {}".format(encrypted_result.size())) evaluator.relinearize_inplace(encrypted_result, relin_keys) print(" + size of encrypted_result (after relinearization): {}".format( encrypted_result.size())) print(" + noise budget in encrypted_result: {} bits".format( decryptor.invariant_noise_budget(encrypted_result))) print("NOTE: Notice the increase in remaining noise budget.") #Relinearization clearly improved our noise consumption. We have still plenty #of noise budget left, so we can expect the correct answer when decrypting. print("Decrypt encrypted_result (4(x^2+1)(x+1)^2).") decryptor.decrypt(encrypted_result, decrypted_result) print(" + decryption of 4(x^2+1)(x+1)^2 = 0x{} ...... Correct.".format( decrypted_result.to_string()))
# creates vector matrixPower_vector contaning each element as powers of matrix A upto A^n # Also creates a vector trace_vector which contains trace of matrix A, A^2 ... A^(n-1) for i in range(1, n): matrixPower_vector.append(raise_power(matrixPower_vector[i - 1])) trace_vector.append(trace(matrixPower_vector[i])) # Vector c is defined as coefficint vector for the charactersitic equation of the matrix c = [Ciphertext(trace_vector[0])] evaluator.negate(c[0]) # The following is the implementation of Newton-identities to calculate the value of coeffecients for i in range(1, n): c_new = Ciphertext(trace_vector[i]) for j in range(i): tc = Ciphertext() evaluator.multiply(trace_vector[i - 1 - j], c[j], tc) evaluator.add(c_new, tc) evaluator.negate(c_new) frac = encoderF.encode(1 / (i + 1)) evaluator.multiply_plain(c_new, frac) c.append(c_new) matrixPower_vector = [iden_matrix(n)] + matrixPower_vector c0 = Ciphertext() encryptor.encrypt(encoderF.encode(1), c0) c = [c0] + c # Adding the matrices multiplie by their coefficients for i in range(len(matrixPower_vector) - 1): for j in range(len(c)): if (i + j == n - 1):
D=A_cipherObject #shallow copy # reducing to diagnol matrix for i in range(4): for j in range (8): if (j!=i): plain_result = Plaintext() X=D[i][i] decryptor.decrypt(X, plain_result) E=1/int(encoder.decode_int32(plain_result)) Y=Ciphertext(parms) R=encoderF.encode(E) encryptor.encrypt(R,Y) evaluator.multiply(Y,D[j][i]) for k in range(8): evaluator.multiply(Y,D[i][k]) evaluator.negate(Y) evaluator.add(A_cipherObject[j][k],Y) # reducing to unit matrix for i in range (8): d=A_cipherObject[i][i] Y=Ciphertext() plain_result = Plaintext() decryptor.decrypt(X, plain_result) encryptor.encrpyt(encoder.encode(1/int(encoder.decode_int32(plain_result))),Y) for j in range (8): A_cipherObject[i][j]=evaluator.multiply(A_cipherObject[i][j],Y)
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)))
class SealOps: @classmethod def with_env(cls): parms = EncryptionParameters(scheme_type.CKKS) parms.set_poly_modulus_degree(POLY_MODULUS_DEGREE) parms.set_coeff_modulus( CoeffModulus.Create(POLY_MODULUS_DEGREE, PRIME_SIZE_LIST)) context = SEALContext.Create(parms) keygen = KeyGenerator(context) public_key = keygen.public_key() secret_key = keygen.secret_key() relin_keys = keygen.relin_keys() galois_keys = keygen.galois_keys() return cls(context=context, public_key=public_key, secret_key=secret_key, relin_keys=relin_keys, galois_keys=galois_keys, poly_modulus_degree=POLY_MODULUS_DEGREE, scale=SCALE) def __init__(self, context: SEALContext, scale: float, poly_modulus_degree: int, public_key: PublicKey = None, secret_key: SecretKey = None, relin_keys: RelinKeys = None, galois_keys: GaloisKeys = None): self.scale = scale self.context = context self.encoder = CKKSEncoder(context) self.evaluator = Evaluator(context) self.encryptor = Encryptor(context, public_key) self.decryptor = Decryptor(context, secret_key) self.relin_keys = relin_keys self.galois_keys = galois_keys self.poly_modulus_degree_log = np.log2(poly_modulus_degree) def encrypt(self, matrix: np.array): matrix = Matrix.from_numpy_array(array=matrix) cipher_matrix = CipherMatrix(rows=matrix.rows, cols=matrix.cols) for i in range(matrix.rows): encoded_row = Plaintext() self.encoder.encode(matrix[i], self.scale, encoded_row) self.encryptor.encrypt(encoded_row, cipher_matrix[i]) return cipher_matrix def decrypt(self, cipher_matrix: CipherMatrix) -> Matrix: matrix = Matrix(rows=cipher_matrix.rows, cols=cipher_matrix.cols) for i in range(matrix.rows): row = Vector() encoded_row = Plaintext() self.decryptor.decrypt(cipher_matrix[i], encoded_row) self.encoder.decode(encoded_row, row) matrix[i] = row return matrix def add(self, matrix_a: CipherMatrix, matrix_b: CipherMatrix) -> CipherMatrix: self.validate_same_dimension(matrix_a, matrix_b) result_matrix = CipherMatrix(rows=matrix_a.rows, cols=matrix_a.cols) for i in range(matrix_a.rows): a_tag, b_tag = self.get_matched_scale_vectors( matrix_a[i], matrix_b[i]) self.evaluator.add(a_tag, b_tag, result_matrix[i]) return result_matrix def add_plain(self, matrix_a: CipherMatrix, matrix_b: np.array) -> CipherMatrix: matrix_b = Matrix.from_numpy_array(matrix_b) self.validate_same_dimension(matrix_a, matrix_b) result_matrix = CipherMatrix(rows=matrix_a.rows, cols=matrix_a.cols) for i in range(matrix_a.rows): row = matrix_b[i] encoded_row = Plaintext() self.encoder.encode(row, self.scale, encoded_row) self.evaluator.mod_switch_to_inplace(encoded_row, matrix_a[i].parms_id()) self.evaluator.add_plain(matrix_a[i], encoded_row, result_matrix[i]) return result_matrix def multiply_plain(self, matrix_a: CipherMatrix, matrix_b: np.array) -> CipherMatrix: matrix_b = Matrix.from_numpy_array(matrix_b) self.validate_same_dimension(matrix_a, matrix_b) result_matrix = CipherMatrix(rows=matrix_a.rows, cols=matrix_a.cols) for i in range(matrix_a.rows): row = matrix_b[i] encoded_row = Plaintext() self.encoder.encode(row, self.scale, encoded_row) self.evaluator.mod_switch_to_inplace(encoded_row, matrix_a[i].parms_id()) self.evaluator.multiply_plain(matrix_a[i], encoded_row, result_matrix[i]) return result_matrix def dot_vector(self, a: Ciphertext, b: Ciphertext) -> Ciphertext: result = Ciphertext() self.evaluator.multiply(a, b, result) self.evaluator.relinearize_inplace(result, self.relin_keys) self.vector_sum_inplace(result) self.get_vector_first_element(result) self.evaluator.rescale_to_next_inplace(result) return result def dot_vector_with_plain(self, a: Ciphertext, b: DoubleVector) -> Ciphertext: result = Ciphertext() b_plain = Plaintext() self.encoder.encode(b, self.scale, b_plain) self.evaluator.multiply_plain(a, b_plain, result) self.vector_sum_inplace(result) self.get_vector_first_element(result) self.evaluator.rescale_to_next_inplace(result) return result def get_vector_range(self, vector_a: Ciphertext, i: int, j: int) -> Ciphertext: cipher_range = Ciphertext() one_and_zeros = DoubleVector([0.0 if x < i else 1.0 for x in range(j)]) plain = Plaintext() self.encoder.encode(one_and_zeros, self.scale, plain) self.evaluator.mod_switch_to_inplace(plain, vector_a.parms_id()) self.evaluator.multiply_plain(vector_a, plain, cipher_range) return cipher_range def dot_matrix_with_matrix_transpose(self, matrix_a: CipherMatrix, matrix_b: CipherMatrix): result_matrix = CipherMatrix(rows=matrix_a.rows, cols=matrix_a.cols) rows_a = matrix_a.rows cols_b = matrix_b.rows for i in range(rows_a): vector_dot_products = [] zeros = Plaintext() for j in range(cols_b): vector_dot_products += [ self.dot_vector(matrix_a[i], matrix_b[j]) ] if j == 0: zero = DoubleVector() self.encoder.encode(zero, vector_dot_products[j].scale(), zeros) self.evaluator.mod_switch_to_inplace( zeros, vector_dot_products[j].parms_id()) self.evaluator.add_plain(vector_dot_products[j], zeros, result_matrix[i]) else: self.evaluator.rotate_vector_inplace( vector_dot_products[j], -j, self.galois_keys) self.evaluator.add_inplace(result_matrix[i], vector_dot_products[j]) for vec in result_matrix: self.evaluator.relinearize_inplace(vec, self.relin_keys) self.evaluator.rescale_to_next_inplace(vec) return result_matrix def dot_matrix_with_plain_matrix_transpose(self, matrix_a: CipherMatrix, matrix_b: np.array): matrix_b = Matrix.from_numpy_array(matrix_b) result_matrix = CipherMatrix(rows=matrix_a.rows, cols=matrix_a.cols) rows_a = matrix_a.rows cols_b = matrix_b.rows for i in range(rows_a): vector_dot_products = [] zeros = Plaintext() for j in range(cols_b): vector_dot_products += [ self.dot_vector_with_plain(matrix_a[i], matrix_b[j]) ] if j == 0: zero = DoubleVector() self.encoder.encode(zero, vector_dot_products[j].scale(), zeros) self.evaluator.mod_switch_to_inplace( zeros, vector_dot_products[j].parms_id()) self.evaluator.add_plain(vector_dot_products[j], zeros, result_matrix[i]) else: self.evaluator.rotate_vector_inplace( vector_dot_products[j], -j, self.galois_keys) self.evaluator.add_inplace(result_matrix[i], vector_dot_products[j]) for vec in result_matrix: self.evaluator.relinearize_inplace(vec, self.relin_keys) self.evaluator.rescale_to_next_inplace(vec) return result_matrix @staticmethod def validate_same_dimension(matrix_a, matrix_b): if matrix_a.rows != matrix_b.rows or matrix_a.cols != matrix_b.cols: raise ArithmeticError("Matrices aren't of the same dimension") def vector_sum_inplace(self, cipher: Ciphertext): rotated = Ciphertext() for i in range(int(self.poly_modulus_degree_log - 1)): self.evaluator.rotate_vector(cipher, pow(2, i), self.galois_keys, rotated) self.evaluator.add_inplace(cipher, rotated) def get_vector_first_element(self, cipher: Ciphertext): one_and_zeros = DoubleVector([1.0]) plain = Plaintext() self.encoder.encode(one_and_zeros, self.scale, plain) self.evaluator.multiply_plain_inplace(cipher, plain) def get_matched_scale_vectors(self, a: Ciphertext, b: Ciphertext) -> (Ciphertext, Ciphertext): a_tag = Ciphertext(a) b_tag = Ciphertext(b) a_index = self.context.get_context_data(a.parms_id()).chain_index() b_index = self.context.get_context_data(b.parms_id()).chain_index() # Changing the mod if required, else just setting the scale if a_index < b_index: self.evaluator.mod_switch_to_inplace(b_tag, a.parms_id()) elif a_index > b_index: self.evaluator.mod_switch_to_inplace(a_tag, b.parms_id()) a_tag.set_scale(self.scale) b_tag.set_scale(self.scale) return a_tag, b_tag
parms.set_coeff_modulus(seal.coeff_modulus_128(8192)) parms.set_plain_modulus(1 << 21) context = SEALContext(parms) encoderF = FractionalEncoder(context.plain_modulus(), context.poly_modulus(), 30, 34, 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) ########################## encoding main matrix ################################ A = [Ciphertext(), Ciphertext(), Ciphertext(), Ciphertext()] for i in range(len(A)): encryptor.encrypt(encoderF.encode(i), A[i]) for j in range(10): evaluator.multiply(A[0], A[1]) evaluator.multiply(A[0], A[2]) evaluator.add(A[1], A[2]) for i in range(len(A)): print("Noise budget of [" + str(i) + "] :" + str((decryptor.invariant_noise_budget(A[i]))) + " bits") print("A[%d]: " % (i), ) print_value(A[i])