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 __init__(self): # set parameters for encryption parms = EncryptionParameters() parms.set_poly_modulus("1x^2048 + 1") parms.set_coeff_modulus(seal.coeff_modulus_128(2048)) parms.set_plain_modulus(1 << 8) self.context = SEALContext(parms) keygen = KeyGenerator(self.context) self.encoder = IntegerEncoder(self.context.plain_modulus()) public_key = keygen.public_key() self.encryptor = Encryptor(self.context, public_key) secret_key = keygen.secret_key() self.decryptor = Decryptor(self.context, secret_key)
def initialize_encryption(): print_example_banner("Example: Basics I"); parms = EncryptionParameters() parms.set_poly_modulus("1x^2048 + 1") # factor: 0xfffffffff00001. parms.set_coeff_modulus(seal.coeff_modulus_128(2048)) parms.set_plain_modulus(1 << 8) context = SEALContext(parms) print_parameters(context); # Here we choose to create an IntegerEncoder with base b=2. encoder = IntegerEncoder(context.plain_modulus()) keygen = KeyGenerator(context) public_key = keygen.public_key() secret_key = keygen.secret_key() encryptor = Encryptor(context, public_key) evaluator = Evaluator(context) decryptor = Decryptor(context, secret_key) return encryptor, evaluator, decryptor, encoder, context
def __init__(self, poly_modulus = 2048 ,bit_strength = 128 ,plain_modulus = 1<<8, integral_coeffs = 64, fractional_coeffs = 32, fractional_base = 3): parms = EncryptionParameters() parms.set_poly_modulus("1x^{} + 1".format(poly_modulus)) if (bit_strength == 128): parms.set_coeff_modulus(seal.coeff_modulus_128(poly_modulus)) else: parms.set_coeff_modulus(seal.coeff_modulus_192(poly_modulus)) parms.set_plain_modulus(plain_modulus) self.parms = parms context = SEALContext(parms) keygen = KeyGenerator(context) public_key = keygen.public_key() secret_key = keygen.secret_key() self.encryptor = Encryptor(context, public_key) self.evaluator = Evaluator(context) self.decryptor = Decryptor(context, secret_key) self.encoder = FractionalEncoder(context.plain_modulus(), context.poly_modulus(), integral_coeffs, fractional_coeffs, fractional_base)
def example_basics_ii(): print_example_banner("Example: Basics II") # In this example we explain what relinearization is, how to use it, and how # it affects noise budget consumption. # First we set the parameters, create a SEALContext, and generate the public # and secret keys. We use slightly larger parameters than be fore to be able # to do more homomorphic multiplications. parms = EncryptionParameters() parms.set_poly_modulus("1x^8192 + 1") # The default coefficient modulus consists of the following primes: # 0x7fffffffba0001, # 0x7fffffffaa0001, # 0x7fffffff7e0001, # 0x3fffffffd60001. # The total size is 219 bits. parms.set_coeff_modulus(seal.coeff_modulus_128(8192)) parms.set_plain_modulus(1 << 10) context = SEALContext(parms) print_parameters(context) keygen = KeyGenerator(context) public_key = keygen.public_key() secret_key = keygen.secret_key() # We also set up an Encryptor, Evaluator, and Decryptor here. We will # encrypt polynomials directly in this example, so there is no need for # an encoder. encryptor = Encryptor(context, public_key) evaluator = Evaluator(context) decryptor = Decryptor(context, secret_key) # There are actually two more types of keys in SEAL: `evaluation keys' and # `Galois keys'. Here we will discuss evaluation keys, and Galois keys will # be discussed later in example_batching(). # In SEAL, a valid ciphertext consists of two or more polynomials with # coefficients integers modulo the product of the primes in coeff_modulus. # The current size of a ciphertext can be found using Ciphertext::size(). # A freshly encrypted ciphertext always has size 2. #plain1 = Plaintext("1x^2 + 2x^1 + 3") plain1 = Plaintext("1x^2 + 2x^1 + 3") encrypted = Ciphertext() print("") print("Encrypting " + plain1.to_string() + ": ") encryptor.encrypt(plain1, encrypted) print("Done") print("Size of a fresh encryption: " + (str)(encrypted.size())) print("Noise budget in fresh encryption: " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") # Homomorphic multiplication results in the output ciphertext growing in size. # More precisely, if the input ciphertexts have size M and N, then the output # ciphertext after homomorphic multiplication will have size M+N-1. In this # case we square encrypted twice to observe this growth (also observe noise # budget consumption). evaluator.square(encrypted) print("Size after squaring: " + (str)(encrypted.size())) print("Noise budget after squaring: " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") plain2 = Plaintext() decryptor.decrypt(encrypted, plain2) print("Second power: " + plain2.to_string()) evaluator.square(encrypted) print("Size after squaring: " + (str)(encrypted.size())) print("Noise budget after squaring: " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") # It does not matter that the size has grown -- decryption works as usual. # Observe from the print-out that the coefficients in the plaintext have # grown quite large. One more squaring would cause some of them to wrap # around plain_modulus (0x400), and as a result we would no longer obtain # the expected result as an integer-coefficient polynomial. We can fix this # problem to some extent by increasing plain_modulus. This would make sense, # since we still have plenty of noise budget left. plain2 = Plaintext() decryptor.decrypt(encrypted, plain2) print("Fourth power: " + plain2.to_string()) # The problem here is that homomorphic operations on large ciphertexts are # computationally much more costly than on small ciphertexts. Specifically, # homomorphic multiplication on input ciphertexts of size M and N will require # O(M*N) polynomial multiplications to be performed, and an addition will # require O(M+N) additions. Relinearization reduces the size of the ciphertexts # after multiplication back to the initial size (2). Thus, relinearizing one # or both inputs before the next multiplication, or e.g. before serializing the # ciphertexts, can have a huge positive impact on performance. # Another problem is that the noise budget consumption in multiplication is # bigger when the input ciphertexts sizes are bigger. In a complicated # computation the contribution of the sizes to the noise budget consumption # can actually become the dominant term. We will point this out again below # once we get to our example. # Relinearization itself has both a computational cost and a noise budget cost. # These both depend on a parameter called `decomposition bit count', which can # be any integer at least 1 [dbc_min()] and at most 60 [dbc_max()]. A large # decomposition bit count makes relinearization fast, but consumes more noise # budget. A small decomposition bit count can make relinearization slower, but # might not change the noise budget by any observable amount. # Relinearization requires a special type of key called `evaluation keys'. # These can be created by the KeyGenerator for any decomposition bit count. # To relinearize a ciphertext of size M >= 2 back to size 2, we actually need # M-2 evaluation keys. Attempting to relinearize a too large ciphertext with # too few evaluation keys will result in an exception being thrown. # We repeat our computation, but this time relinearize after both squarings. # Since our ciphertext never grows past size 3 (we relinearize after every # multiplication), it suffices to generate only one evaluation key. # First, we need to create evaluation keys. We use a decomposition bit count # of 16 here, which can be thought of as quite small. ev_keys16 = EvaluationKeys() # This function generates one single evaluation key. Another overload takes # the number of keys to be generated as an argument, but one is all we need # in this example (see above). keygen.generate_evaluation_keys(16, ev_keys16) print("") print("Encrypting " + plain1.to_string() + ": ") encryptor.encrypt(plain1, encrypted) print("Done") print("Size of a fresh encryption: " + (str)(encrypted.size())) print("Noise budget in fresh encryption: " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") evaluator.square(encrypted) print("Size after squaring: " + (str)(encrypted.size())) print("Noise budget after squaring: " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") evaluator.relinearize(encrypted, ev_keys16) print("Size after relinearization: " + (str)(encrypted.size())) print("Noise budget after relinearizing (dbs = " + (str)(ev_keys16.decomposition_bit_count()) + "): " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") evaluator.square(encrypted) print("Size after second squaring: " + (str)(encrypted.size()) + " bits") print("Noise budget after second squaring: " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") evaluator.relinearize(encrypted, ev_keys16) print("Size after relinearization: " + (str)(encrypted.size())) print("Noise budget after relinearizing (dbs = " + (str)(ev_keys16.decomposition_bit_count()) + "): " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") decryptor.decrypt(encrypted, plain2) print("Fourth power: " + plain2.to_string()) # Of course the result is still the same, but this time we actually # used less of our noise budget. This is not surprising for two reasons: # - We used a very small decomposition bit count, which is why # relinearization itself did not consume the noise budget by any # observable amount; # - Since our ciphertext sizes remain small throughout the two # squarings, the noise budget consumption rate in multiplication # remains as small as possible. Recall from above that operations # on larger ciphertexts actually cause more noise growth. # To make matters even more clear, we repeat the computation a third time, # now using the largest possible decomposition bit count (60). We are not # measuring the time here, but relinearization with these evaluation keys # is significantly faster than with ev_keys16. ev_keys60 = EvaluationKeys() keygen.generate_evaluation_keys(seal.dbc_max(), ev_keys60) print("") print("Encrypting " + plain1.to_string() + ": ") encryptor.encrypt(plain1, encrypted) print("Done") print("Size of a fresh encryption: " + (str)(encrypted.size())) print("Noise budget in fresh encryption: " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") evaluator.square(encrypted) print("Size after squaring: " + (str)(encrypted.size())) print("Noise budget after squaring: " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") evaluator.relinearize(encrypted, ev_keys60) print("Size after relinearization: " + (str)(encrypted.size())) print("Noise budget after relinearizing (dbc = " + (str)(ev_keys60.decomposition_bit_count()) + "): " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") evaluator.square(encrypted) print("Size after second squaring: " + (str)(encrypted.size())) print("Noise budget after second squaring: " + (str)(decryptor.invariant_noise_budget) + " bits") evaluator.relinearize(encrypted, ev_keys60) print("Size after relinearization: " + (str)(encrypted.size())) print("Noise budget after relinearizing (dbc = " + (str)(ev_keys60.decomposition_bit_count()) + "): " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") decryptor.decrypt(encrypted, plain2) print("Fourth power: " + plain2.to_string()) # Observe from the print-out that we have now used significantly more of our # noise budget than in the two previous runs. This is again not surprising, # since the first relinearization chops off a huge part of the noise budget. # However, note that the second relinearization does not change the noise # budget by any observable amount. This is very important to understand when # optimal performance is desired: relinearization always drops the noise # budget from the maximum (freshly encrypted ciphertext) down to a fixed # amount depending on the encryption parameters and the decomposition bit # count. On the other hand, homomorphic multiplication always consumes the # noise budget from its current level. This is why the second relinearization # does not change the noise budget anymore: it is already consumed past the # fixed amount determinted by the decomposition bit count and the encryption # parameters. # We now perform a third squaring and observe an even further compounded # decrease in the noise budget. Again, relinearization does not consume the # noise budget at this point by any observable amount, even with the largest # possible decomposition bit count. evaluator.square(encrypted) print("Size after third squaring " + (str)(encrypted.size())) print("Noise budget after third squaring: " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") evaluator.relinearize(encrypted, ev_keys60) print("Size after relinearization: " + (str)(encrypted.size())) print("Noise budget after relinearizing (dbc = " + (str)(ev_keys60.decomposition_bit_count()) + "): " + (str)(decryptor.invariant_noise_budget(encrypted)) + " bits") decryptor.decrypt(encrypted, plain2) print("Eighth power: " + plain2.to_string())
def example_basics_i(): print_example_banner("Example: Basics I") # In this example we demonstrate setting up encryption parameters and other # relevant objects for performing simple computations on encrypted integers. # SEAL uses the Fan-Vercauteren (FV) homomorphic encryption scheme. We refer to # https://eprint.iacr.org/2012/144 for full details on how the FV scheme works. # For better performance, SEAL implements the "FullRNS" optimization of FV, as # described in https://eprint.iacr.org/2016/510. # The first task is to set up an instance of the EncryptionParameters class. # It is critical to understand how these different parameters behave, how they # affect the encryption scheme, performance, and the security level. There are # three encryption parameters that are necessary to set: # - poly_modulus (polynomial modulus); # - coeff_modulus ([ciphertext] coefficient modulus); # - plain_modulus (plaintext modulus). # A fourth parameter -- noise_standard_deviation -- has a default value of 3.19 # and should not be necessary to modify unless the user has a specific reason # to and knows what they are doing. # The encryption scheme implemented in SEAL cannot perform arbitrary computations # on encrypted data. Instead, each ciphertext has a specific quantity called the # `invariant noise budget' -- or `noise budget' for short -- measured in bits. # The noise budget of a freshly encrypted ciphertext (initial noise budget) is # determined by the encryption parameters. Homomorphic operations consume the # noise budget at a rate also determined by the encryption parameters. In SEAL # the two basic homomorphic operations are additions and multiplications, of # which additions can generally be thought of as being nearly free in terms of # noise budget consumption compared to multiplications. Since noise budget # consumption is compounding in sequential multiplications, the most significant # factor in choosing appropriate encryption parameters is the multiplicative # depth of the arithmetic circuit that needs to be evaluated. Once the noise # budget in a ciphertext reaches zero, it becomes too corrupted to be decrypted. # Thus, it is essential to choose the parameters to be large enough to support # the desired computation; otherwise the result is impossible to make sense of # even with the secret key. parms = EncryptionParameters() # We first set the polynomial modulus. This must be a power-of-2 cyclotomic # polynomial, i.e. a polynomial of the form "1x^(power-of-2) + 1". The polynomial # modulus should be thought of mainly affecting the security level of the scheme; # larger polynomial modulus makes the scheme more secure. At the same time, it # makes ciphertext sizes larger, and consequently all operations slower. # Recommended degrees for poly_modulus are 1024, 2048, 4096, 8192, 16384, 32768, # but it is also possible to go beyond this. Since we perform only a very small # computation in this example, it suffices to use a very small polynomial modulus parms.set_poly_modulus("1x^2048 + 1") # Next we choose the [ciphertext] coefficient modulus (coeff_modulus). The size # of the coefficient modulus should be thought of as the most significant factor # in determining the noise budget in a freshly encrypted ciphertext: bigger means # more noise budget. Unfortunately, a larger coefficient modulus also lowers the # security level of the scheme. Thus, if a large noise budget is required for # complicated computations, a large coefficient modulus needs to be used, and the # reduction in the security level must be countered by simultaneously increasing # the polynomial modulus. # To make parameter selection easier for the user, we have constructed sets of # largest allowed coefficient moduli for 128-bit and 192-bit security levels # for different choices of the polynomial modulus. These recommended parameters # follow the Security white paper at http://HomomorphicEncryption.org. However, # due to the complexity of this topic, we highly recommend the user to directly # consult an expert in homomorphic encryption and RLWE-based encryption schemes # to determine the security of their parameter choices. # Our recommended values for the coefficient modulus can be easily accessed # through the functions # coeff_modulus_128bit(int) # coeff_modulus_192bit(int) # for 128-bit and 192-bit security levels. The integer parameter is the degree # of the polynomial modulus. # In SEAL the coefficient modulus is a positive composite number -- a product # of distinct primes of size up to 60 bits. When we talk about the size of the # coefficient modulus we mean the bit length of the product of the small primes. # The small primes are represented by instances of the SmallModulus class; for # example coeff_modulus_128bit(int) returns a vector of SmallModulus instances. # It is possible for the user to select their own small primes. Since SEAL uses # the Number Theoretic Transform (NTT) for polynomial multiplications modulo the # factors of the coefficient modulus, the factors need to be prime numbers # congruent to 1 modulo 2*degree(poly_modulus). We have generated a list of such # prime numbers of various sizes, that the user can easily access through the # functions # small_mods_60bit(int) # small_mods_50bit(int) # small_mods_40bit(int) # small_mods_30bit(int) # each of which gives access to an array of primes of the denoted size. These # primes are located in the source file util/globals.cpp. # Performance is mainly affected by the size of the polynomial modulus, and the # number of prime factors in the coefficient modulus. Thus, it is important to # use as few factors in the coefficient modulus as possible. # In this example we use the default coefficient modulus for a 128-bit security # level. Concretely, this coefficient modulus consists of only one 56-bit prime # factor: 0xfffffffff00001. parms.set_coeff_modulus(seal.coeff_modulus_128(2048)) # The plaintext modulus can be any positive integer, even though here we take # it to be a power of two. In fact, in many cases one might instead want it to # be a prime number; we will see this in example_batching(). The plaintext # modulus determines the size of the plaintext data type, but it also affects # the noise budget in a freshly encrypted ciphertext, and the consumption of # the noise budget in homomorphic multiplication. Thus, it is essential to try # to keep the plaintext data type as small as possible for good performance. # The noise budget in a freshly encrypted ciphertext is # ~ log2(coeff_modulus/plain_modulus) (bits) # and the noise budget consumption in a homomorphic multiplication is of the # form log2(plain_modulus) + (other terms). parms.set_plain_modulus(1 << 8) # Now that all parameters are set, we are ready to construct a SEALContext # object. This is a heavy class that checks the validity and properties of # the parameters we just set, and performs and stores several important # pre-computations. context = SEALContext(parms) # Print the parameters that we have chosen print_parameters(context) # Plaintexts in the FV scheme are polynomials with coefficients integers modulo # plain_modulus. To encrypt for example integers instead, one can use an # `encoding scheme' to represent the integers as such polynomials. SEAL comes # with a few basic encoders: # [IntegerEncoder] # Given an integer base b, encodes integers as plaintext polynomials as follows. # First, a base-b expansion of the integer is computed. This expansion uses # a `balanced' set of representatives of integers modulo b as the coefficients. # Namely, when b is odd the coefficients are integers between -(b-1)/2 and # (b-1)/2. When b is even, the integers are between -b/2 and (b-1)/2, except # when b is two and the usual binary expansion is used (coefficients 0 and 1). # Decoding amounts to evaluating the polynomial at x=b. For example, if b=2, # the integer # 26 = 2^4 + 2^3 + 2^1 # is encoded as the polynomial 1x^4 + 1x^3 + 1x^1. When b=3, # 26 = 3^3 - 3^0 # is encoded as the polynomial 1x^3 - 1. In memory polynomial coefficients are # always stored as unsigned integers by storing their smallest non-negative # representatives modulo plain_modulus. To create a base-b integer encoder, # use the constructor IntegerEncoder(plain_modulus, b). If no b is given, b=2 # is used. # [FractionalEncoder] # The FractionalEncoder encodes fixed-precision rational numbers as follows. # It expands the number in a given base b, possibly truncating an infinite # fractional part to finite precision, e.g. # 26.75 = 2^4 + 2^3 + 2^1 + 2^(-1) + 2^(-2) # when b=2. For the sake of the example, suppose poly_modulus is 1x^1024 + 1. # It then represents the integer part of the number in the same way as in # IntegerEncoder (with b=2 here), and moves the fractional part instead to the # highest degree part of the polynomial, but with signs of the coefficients # changed. In this example we would represent 26.75 as the polynomial # -1x^1023 - 1x^1022 + 1x^4 + 1x^3 + 1x^1. # In memory the negative coefficients of the polynomial will be represented as # their negatives modulo plain_modulus. # [PolyCRTBuilder] # If plain_modulus is a prime congruent to 1 modulo 2*degree(poly_modulus), the # plaintext elements can be viewed as 2-by-(degree(poly_modulus) / 2) matrices # with elements integers modulo plain_modulus. When a desired computation can be # vectorized, using PolyCRTBuilder can result in massive performance improvements # over naively encrypting and operating on each input number separately. Thus, # in more complicated computations this is likely to be by far the most important # and useful encoder. In example_batching() we show how to use and operate on # encrypted matrix plaintexts. # For performance reasons, in homomorphic encryption one typically wants to keep # the plaintext data types as small as possible, which can make it challenging to # prevent data type overflow in more complicated computations, especially when # operating on rational numbers that have been scaled to integers. When using # PolyCRTBuilder estimating whether an overflow occurs is a fairly standard task, # as the matrix slots are integers modulo plain_modulus, and each slot is operated # on independently of the others. When using IntegerEncoder or FractionalEncoder # it is substantially more difficult to estimate when an overflow occurs in the # plaintext, and choosing the plaintext modulus very carefully to be large enough # is critical to avoid unexpected results. Specifically, one needs to estimate how # large the largest coefficient in the polynomial view of all of the plaintext # elements becomes, and choose the plaintext modulus to be larger than this value. # SEAL comes with an automatic parameter selection tool that can help with this # task, as is demonstrated in example_parameter_selection(). # Here we choose to create an IntegerEncoder with base b=2. encoder = IntegerEncoder(context.plain_modulus()) # We are now ready to generate the secret and public keys. For this purpose we need # an instance of the KeyGenerator class. Constructing a KeyGenerator automatically # generates the public and secret key, which can then be read to local variables. # To create a fresh pair of keys one can call KeyGenerator::generate() at any time. keygen = KeyGenerator(context) public_key = keygen.public_key() secret_key = keygen.secret_key() # To be able to encrypt, we need to construct an instance of Encryptor. Note that # the Encryptor only requires the public key. encryptor = Encryptor(context, public_key) # Computations on the ciphertexts are performed with the Evaluator class. evaluator = Evaluator(context) # We will of course want to decrypt our results to verify that everything worked, # so we need to also construct an instance of Decryptor. Note that the Decryptor # requires the secret key. decryptor = Decryptor(context, secret_key) # We start by encoding two integers as plaintext polynomials. value1 = 5 plain1 = encoder.encode(value1) print("Encoded " + (str)(value1) + " as polynomial " + plain1.to_string() + " (plain1)") value2 = -7 plain2 = encoder.encode(value2) print("Encoded " + (str)(value2) + " as polynomial " + plain2.to_string() + " (plain2)") # Encrypting the values is easy. encrypted1 = Ciphertext() encrypted2 = Ciphertext() print("Encrypting plain1: ") encryptor.encrypt(plain1, encrypted1) print("Done (encrypted1)") print("Encrypting plain2: ") encryptor.encrypt(plain2, encrypted2) print("Done (encrypted2)") # To illustrate the concept of noise budget, we print the budgets in the fresh # encryptions. print("Noise budget in encrypted1: " + (str)(decryptor.invariant_noise_budget(encrypted1)) + " bits") print("Noise budget in encrypted2: " + (str)(decryptor.invariant_noise_budget(encrypted2)) + " bits") # As a simple example, we compute (-encrypted1 + encrypted2) * encrypted2. # Negation is a unary operation. evaluator.negate(encrypted1) # Negation does not consume any noise budget. print("Noise budget in -encrypted1: " + (str)(decryptor.invariant_noise_budget(encrypted1)) + " bits") # Addition can be done in-place (overwriting the first argument with the result, # or alternatively a three-argument overload with a separate destination variable # can be used. The in-place variants are always more efficient. Here we overwrite # encrypted1 with the sum. evaluator.add(encrypted1, encrypted2) # It is instructive to think that addition sets the noise budget to the minimum # of the input noise budgets. In this case both inputs had roughly the same # budget going on, and the output (in encrypted1) has just slightly lower budget. # Depending on probabilistic effects, the noise growth consumption may or may # not be visible when measured in whole bits. print("Noise budget in -encrypted1 + encrypted2: " + (str)(decryptor.invariant_noise_budget(encrypted1)) + " bits") # Finally multiply with encrypted2. Again, we use the in-place version of the # function, overwriting encrypted1 with the product. evaluator.multiply(encrypted1, encrypted2) # Multiplication consumes a lot of noise budget. This is clearly seen in the # print-out. The user can change the plain_modulus to see its effect on the # rate of noise budget consumption. print("Noise budget in (-encrypted1 + encrypted2) * encrypted2: " + (str)(decryptor.invariant_noise_budget(encrypted1)) + " bits") # Now we decrypt and decode our result. plain_result = Plaintext() print("Decrypting result: ") decryptor.decrypt(encrypted1, plain_result) print("Done") # Print the result plaintext polynomial. print("Plaintext polynomial: " + plain_result.to_string()) # Decode to obtain an integer result. print("Decoded integer: " + (str)(encoder.decode_int32(plain_result)))
class encryption_handler(object): """ Methods: set_encoder: sets specified encoder encode_encrypt_2D: for encoding list of lists decrypt_1D: for decoding list Attributes: params: seal encrpytion parameters object batch: bool to batch operations context: seal context object secretkey: secret key kept on client side publickey: public key for encryption encoder: encoder for numerical inputs """ def __init__( self, security_level=128, #128 or 192 for now poly_modulus_pwr2=12, # 11 through 15 coeff_modulus=None, plain_modulus=2**8, batch=False, ): """ security level: 128 or 192 poly_modulus_pwr2: 11,12,13,14,or 15 poly=x^(2^thisvariable)+1 will define our polynomial ring by Z[x]/poly. Larger number means more security but longer computations. coeff_modulus: default None, If set then security level is ignored. This is important to set for batching as it needs to be prime. batch: default False, setting to true will design encryption scheme to allow parallel predictions """ self.params = EncryptionParameters() self.batch = batch power = 2**poly_modulus_pwr2 self.params.set_poly_modulus(f"1x^{power} + 1") if coeff_modulus != None: st.write("Security level is ignored since coeff_modulus was set.") self.params.set_coeff_modulus(coeff_modulus) else: if security_level == 128: self.params.set_coeff_modulus(seal.coeff_modulus_128(power)) if security_level == 192: self.params.set_coeff_modulus(seal.coeff_modulus_192(power)) try: self.params.set_plain_modulus(plain_modulus) except: raise ValueError("There was a problem setting the plain modulus.") try: self._cont = SEALContext(self.params) except Exception as e: raise ValueError("There was a problem with your parameters.") st.write(f"There was a problem with your parameters: {e}") _keygen = KeyGenerator(self._cont) self._secretkey = _keygen.secret_key() self._publickey = _keygen.public_key() @property def secretkey(self): return self._secretkey @property def publickey(self): return self._publickey @property def context(self): return self._cont
class FHECryptoEngine(CryptoEngine): def __init__(self): CryptoEngine.__init__(self, defs.ENC_MODE_FHE) self.log_id = 'FHECryptoEngine' self.encrypt_params = None self.context = None self.encryptor = None self.evaluator = None self.decryptor = None return def load_keys(self): self.private_key = SecretKey() self.private_key.load(defs.FN_FHE_PRIVATE_KEY) self.public_key = PublicKey() self.public_key.load(defs.FN_FHE_PUBLIC_KEY) return True def generate_keys(self): if self.encrypt_params == None or \ self.context == None: self.init_encrypt_params() keygen = KeyGenerator(self.context) # Generate the private key self.private_key = keygen.secret_key() self.private_key.save(defs.FN_FHE_PRIVATE_KEY) # Generate the public key self.public_key = keygen.public_key() self.public_key.save(defs.FN_FHE_PUBLIC_KEY) return True def init_encrypt_params(self): self.encrypt_params = EncryptionParameters() self.encrypt_params.set_poly_modulus("1x^2048 + 1") self.encrypt_params.set_coeff_modulus(seal.coeff_modulus_128(2048)) self.encrypt_params.set_plain_modulus(1 << 8) self.context = SEALContext(self.encrypt_params) return def initialize(self, use_old_keys=False): # Initialize encryption params self.init_encrypt_params() # Check if the public & private key files exist if os.path.isfile(defs.FN_FHE_PUBLIC_KEY) and \ os.path.isfile(defs.FN_FHE_PRIVATE_KEY) and \ use_old_keys == True: self.log("Keys already exist. Reusing them instead.") if not self.load_keys(): self.log("Failed to load keys") return False else: # If not, then attempt to generate new ones if not self.generate_keys(): self.log("Failed to generate keys") return False # Setup the rest of the crypto engine self.encryptor = Encryptor(self.context, self.public_key) self.evaluator = Evaluator(self.context) self.decryptor = Decryptor(self.context, self.private_key) # Set the initialized flag self.initialized = True return True def encrypt(self, data): if not self.initialized: self.log("Not initialized") return False # Setup the encoder encoder = FractionalEncoder(self.context.plain_modulus(), self.context.poly_modulus(), 64, 32, 3) # Create the array of encrypted data objects encrypted_data = [] for raw_data in data: encrypted_data.append(Ciphertext(self.encrypt_params)) self.encryptor.encrypt( encoder.encode(raw_data), encrypted_data[-1] ) # Pickle each Ciphertext, base64 encode it, and store it in the array for i in range(0, len(encrypted_data)): encrypted_data[i].save("fhe_enc.bin") encrypted_data[i] = base64.b64encode( pickle.dumps(encrypted_data[i]) ) return encrypted_data def evaluate(self, encrypted_data, lower_idx=0, higher_idx=-1): result = Ciphertext() # Setup the encoder encoder = FractionalEncoder(self.context.plain_modulus(), self.context.poly_modulus(), 64, 32, 3) # Unpack the data first unpacked_data = [] for d in encrypted_data[lower_idx:higher_idx]: unpacked_data.append(pickle.loads(base64.b64decode(d))) # Perform operations self.evaluator.add_many(unpacked_data, result) div = encoder.encode(1/len(unpacked_data)) self.evaluator.multiply_plain(result, div) # Pack the result result = base64.b64encode( pickle.dumps(result) ) return result def decrypt(self, raw_data): if not self.initialized: self.log("Not initialized") return False # Setup the encoder encoder = FractionalEncoder(self.context.plain_modulus(), self.context.poly_modulus(), 64, 32, 3) # Unpickle, base64 decode, and decrypt each ciphertext result decrypted_data = [] for d in raw_data: encrypted_data = pickle.loads( base64.b64decode(d) ) plain_data = Plaintext() self.decryptor.decrypt(encrypted_data, plain_data) decrypted_data.append( str(encoder.decode(plain_data)) ) return decrypted_data