Method of blocking or passing messages sent via a firewall based on parsing of symbols strings contained in messages among different keywords

Abstract

This invention relates to a method of blocking or passing messages sent via a firewall, based on parsing, of symbols strings contained in said messages, among different keywords, assigning to said messages either a blocking class or a passing class, comprising: performing a dimensionality reduction step for said different classes on a training set of messages whose classes are known, and then classifying one or more unknown messages among said different classes with reduced dimensionality, said dimensionality reduction step being performed on said training set of messages by machine learning including processing, for several first matrices and for several second matrices, a parameter representative of a product of two first and second matrices to assess to which given class a given message belongs: first matrix representing a first array of keywords versus symbols strings contained in a first given message, second matrix representing the values of differences between said first array and a second array of keywords versus symbols strings contained in a second given message different from first given message but known to belong to same class as first given message, wherein: a quantum singular value estimation is performed on first matrix, a quantum singular value estimation is performed on second matrix, both quantum singular value estimation of first matrix and quantum singular value estimation of second matrix are combined together, via quantum calculation, so as to get at a quantum singular value estimation of said product of both first and second matrices, said quantum singular value estimation of said product of both first and second matrices being said parameter representative of said product of two first and second matrices processed to assess to which given class said first given message belongs.

Claims

1. A computer-implemented method of blocking or passing transmitted messages within a firewall, based on parsing, of symbols strings contained in said messages, among different classes, comprising: performing a dimensionality reduction step, by processing, for several first matrices and for several second matrices, a parameter representative of a product of both first and second matrices respectively representing first and second arrays of keywords versus symbols strings related to one or more messages, wherein: a quantum singular value estimation is performed on first matrix, a quantum singular value estimation is performed on second matrix, both quantum singular value estimation of first matrix and quantum singular value estimation of second matrix are combined together, via quantum calculation, so as to get at a quantum singular value estimation of said product of both first and second matrices, said quantum singular value estimation of said product of both first and second matrices being said parameter representative of said product of both first and second matrices.

2. The computer-implemented method according to claim 1, based on parsing, of symbols strings contained in said messages, among different keywords, assigning to said messages either a blocking class or a passing class, wherein: said dimensionality reduction step is performed for said different classes on a training set of messages whose classes are known, and then one or more unknown messages are classified among said different classes with reduced dimensionality, said dimensionality reduction step being performed on said training set of messages by machine learning including processing, for several first matrices and for several second matrices, a parameter representative of a product of two first and second matrices to assess to which given class a given message belongs: first matrix representing a first array of keywords versus symbols strings contained in a first given message, second matrix representing the values of differences between said first array and a second array of keywords versus symbols strings contained in a second given message different from first given message but known to belong to same class as first given message, and wherein said quantum singular value estimation of said product of both first and second matrices being said parameter representative of said product of two first and second matrices are processed to assess to which given class said first given message belongs.

3. The computer-implemented method according to claim 1, wherein: both quantum singular value estimation of first matrix and quantum singular value estimation of second matrix are estimated each and are combined together so as to get at a quantum singular value estimation of said product of both first and second matrices, by making a phase estimation of an entity at least successively performing: quantum singular value estimation of first matrix, quantum rotations, proportional to estimated singular values of first matrix, quantum singular value estimation of second matrix, quantum rotations, proportional to estimated singular values of second matrix, said quantum singular value estimation of said product of both first and second matrices being said parameter representative of said product of both first and second matrices.

4. The computer-implemented method according to claim 3, wherein the step of performing quantum rotations proportional to estimated singular values of first matrix, comprises performing quantum rotations on Y axis of Bloch sphere, proportional to estimated singular values of first matrix.

5. The computer-implemented method according to claim 4, wherein the step of performing quantum rotations proportional to estimated singular values of second matrix, comprises performing quantum rotations on Y axis of Bloch sphere, proportional to estimated singular values of second matrix.

6. The computer-implemented method according to claim 3, wherein the step of performing quantum rotations proportional to estimated singular values of second matrix, comprises performing quantum rotations on Y axis of Bloch sphere, proportional to estimated singular values of second matrix.

7. The computer-implemented method according to claim 1, wherein the method performs blocking or passing messages sent via a firewall, based on parsing, of symbols strings contained in said messages, among different keywords, assigning to said messages either a blocking class or a passing class, and wherein: said dimensionality reduction step is performed for said different classes on a training set of messages whose classes are known, and then classifying one or more unknown messages among said different classes with reduced dimensionality, said dimensionality reduction step is performed on said training set of messages by machine learning including processing, for several first matrices and for several second matrices, a parameter representative of a product of two first and second matrices to assess to which given class a given message belongs: first matrix representing a first array of keywords versus symbols strings contained in a first given message, second matrix representing the values of differences between said first array and a second array of keywords versus symbols strings contained in a second given message different from first given message but known to belong to same class as first given message.

8. The computer-implemented method according to claim 1, wherein said first matrices and said second matrices are sparse matrices.

9. The computer-implemented method according to claim 1, wherein operation of said combination of both quantum singular value estimation of first matrix and quantum singular value estimation of second matrix together, via quantum calculation, so as to get at a quantum singular value estimation of said product of both first and second matrices, is used to replace either an operation of matrices multiplication and/or an operation of matrix inversion on matrices multiplication.

10. A computer-implemented method of blocking or passing transmitted messages within a firewall, based on parsing, of symbols strings contained in said messages, among different classes, comprising: performing a dimensionality reduction step, by processing, for several first matrices and for several second matrices, a parameter representative of a product of both first and second matrices respectively representing first and second arrays of keywords versus symbols strings related to one or more messages, wherein both quantum singular value estimation of first matrix and quantum singular value estimation of second matrix are estimated each and are combined together so as to get at a quantum singular value estimation of said product of both first and second matrices, by applying to both first and second matrices following quantum circuit including: a first Hadamard gate whose output is the input of a first inverted quantum Fourier transform, said first Hadamard output controlling following sub-circuit, a second Hadamard gate whose output is the input of a second inverted quantum Fourier transform, said second Hadamard output controlling a quantum memory, output of said first inverted quantum Fourier transform will give said quantum singular value estimation of said product of both first and second matrices, once said quantum memory has successively contained first matrix and second matrix, said quantum singular value estimation of said product of both first and second matrices being said parameter representative of said product of both first and second matrices.

11. A computer-implemented method of blocking or passing transmitted messages within a firewall, based on parsing, of symbols strings contained in said messages, among different classes, comprising: performing a dimensionality reduction step, by processing, for several first matrices and for several second matrices, a parameter representative of a product of both first and second matrices respectively representing first and second arrays of keywords versus symbols strings related to one or more messages, wherein: both quantum singular value estimation of first matrix and quantum singular value estimation of second matrix are estimated each and are combined together so as to get at a quantum singular value estimation of said product of both first and second matrices, by making a phase estimation of an entity at least successively performing: quantum singular value estimation of first matrix, quantum rotations, proportional to estimated singular values of first matrix, quantum singular value estimation of second matrix, quantum rotations, proportional to estimated singular values of second matrix, while applying to both first and second matrices following quantum circuit including: a first Hadamard gate whose output is the input of a first inverted quantum Fourier transform, said first Hadamard output controlling following sub-circuit, a second Hadamard gate whose output is the input of a second inverted quantum Fourier transform, said second Hadamard output controlling a quantum memory, output of said first inverted quantum Fourier transform will give said quantum singular value estimation of said product of both first and second matrices, once said quantum memory has successively contained first matrix and second matrix, said quantum singular value estimation of said product of both first and second matrices being said parameter representative of said product of both first and second matrices.

12. The computer-implemented method according to claim 11, wherein the step of performing quantum rotations proportional to estimated singular values of first matrix, comprises performing quantum rotations on Y axis of Bloch sphere, proportional to estimated singular values of first matrix.

13. The computer-implemented method according to claim 12, wherein the step of performing quantum rotations, proportional to estimated singular values of second matrix, comprises performing quantum rotations on Y axis of Bloch sphere, proportional to estimated singular values of second matrix.

14. The computer-implemented method according to claim 11, wherein the step of performing quantum rotations, proportional to estimated singular values of second matrix, comprises performing quantum rotations on Y axis of Bloch sphere, proportional to estimated singular values of second matrix.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows an example of a block diagram representing a quantum subroutine called UW used in a method of blocking or passing messages sent via a firewall according to an embodiment of the invention.

(2) FIG. 2 shows an example of a block diagram representing a quantum subroutine called UP used in a method of blocking or passing messages sent via a firewall according to an embodiment of the invention.

(3) FIG. 3 shows an example of a block diagram representing a quantum subroutine called UL used in a method of blocking or passing messages sent via a firewall according to an embodiment of the invention.

(4) FIG. 4 shows an example of a block diagram representing the relationships existing between the different quantum subroutines used in a method of blocking or passing messages sent via a firewall according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

(5) Qubit or qbit will be indifferently used throughout whole text, it means a quantum bit.

(6) Using a quantum computer with the procedure discussed here, it is possible to increase the accuracy of the classifier by extracting more meaningful features form the tokenization matrix.

(7) The quantum computation that is performed is a hyperparameter-free quantum procedure that is used to perform the feature extraction. This procedure to classify a domain consists in a quantum algorithm to perform the feature extraction and in a classical computer to perform classification which uses classical features, along with the feature extracted from the quantum computer. The procedure described is parameterized by a value theta, a parameter that depends on a given dataset. Details will be given below on how to estimate theta for a given dataset in the procedure.

(8) This is the setting that is considered: assumption is made to have a dataset of N domains with 2 different labels: good and malicious. Supposition is made that a new domain is given with an unknown label, and there is a need to find the correct label for the domain under consideration. The quantum algorithm for feature extraction uses a recent scientific breakthrough, called singular value estimation. Quantum singular value estimation allows for building a superposition of the singular values of a given matrix stored in QRAM in time poly logarithmic in the matrix dimension.

(9) The following procedure uses a quantum computer to execute the operations on step number 8a. This quantum procedure will use a data structure called QRAM that is described in “Kerenidis 2016” [Kerenidis, Iordanis, and Anupam Prakash. 2017. “Quantum gradient descent for linear systems and least squares,” April. http://arxiv.org/abs/1704.04992] hereby incorporated by reference. A QRAM is a data structure where the quantum computer can have quantum access, and it is the device used to input data in a quantum computer.

(10) According to embodiments of the invention, following steps 1 to 10 are performed successively, with sub-steps a, b, c etc. . . . for part of them:

(11) 1. Collection the domains to be used as training set. This step is important, as the elements in the dataset should resemble as much as possible the elements that the system will have to classify when executed. Possibly, they should not have misclassified elements; otherwise the performance of the classifier may be affected. For this, publicly available datasets of malware domains can be taken, or even the source code of malware that is publicly available, and use it to generate the training set.

(12) 2. Create the tokenization matrix. Map the good domains in a feature matrix as follow: This consists in splitting each domain in the training set in a series of n-grams of length 2, 3, 4. Then, create a matrix where the rows are the good domains and the columns are the n-grams extracted. Fill the matrix with 1 if in a domain there is a given n-gram. This will result in a sparse matrix. this matrix can be saved in a QRAM or stored in another data structure that can offer quantum access to this matrix.

(13) 3. This row is then eventually polynomially expanded (usually a polynomial of degree 2 or 3 suffices).

(14) 4. Each vector is eventually normalized by removing the mean of the vectors in the training set.

(15) 5. Each component is eventually scaled such that each component of the input vectors has unitary variance if calculated among all the vectors in the dataset.

(16) 6. This resulting matrix is stored into QRAM, that is called QRAM for X.

(17) 7. Construction of QRAM for X_DOT. X_DOT is defined to be a matrix whose rows are samples of the pairwise derivatives of the data which is constructed. Take a number of samples that is at least linear in the number of elements in the dataset X.

(18) 8. For each vector in the training set, do the following operation:

(19) a. With the quantum computer, apply routine UFE on the selected vector, perform tomography of the resulting quantum state. This is the resulting state that can be found after the application of quantum slow feature analysis with 2 as parameter for the number of classes.

(20) 9. Run the training procedure. Use the feature extracted using the quantum computer along with entropy, length. Other relevant information might include the time frequency of DNS queries of a given IP address of the network.

(21) 10. When a new domain served to the detection system in order to be classified,

(22) a. Tokenize the domain using the previously learned decomposition, and get its representation as vector.

(23) b. Perform quantum feature extraction on this vector using UFE, a quantum procedure (described below) on the vector just created.

(24) c. Extract classically other feature like length and entropy.

(25) d. Perform the classification using the model trained in the previous step.

(26) Once the system to perform classification is ready, the problem of finding an estimate for the parameter theta is the task to be done. In case of binary classification, the parameter theta is determined by checking (using tomography) that the resulting vectors are 1 dimensional (i.e. a single number). This is because the parameter theta influences the number of dimensions the output vector has.

(27) At the end of the quantum computation, the register holds the feature that has been extracted from an input vector (or a superposition of vectors).

(28) FIG. 1 shows an example of a block diagram representing a quantum subroutine called UW used in a method of blocking or passing messages sent via a firewall according to an embodiment of the invention.

(29) A QRAM of X 1 is connected to an input of a SVE 2 of X. A first output of SVE 2 is connected to the input of an inverted arcsine function 3 whose output is connected to an arcsine function 5 and controls a Y rotation 4. A second output of SVE 2 is directly connected to a second input of an inverted SVE 6 of X. Y rotation 4 is connected between a third output of SVE 2 and a third input of inverted SVE 6. A qubit measure 7 is performed on third output of inverted SVE 6.

(30) This procedure takes as input a quantum register and two ancillary register, and output a quantum register. It uses multiple calls to the QRAM of X. Following steps 1 to 5 will be successively performed:

(31) 1. Perform Singular Value Estimation (as in Kerenidis 2016 already incorporated by reference) to write in a register the singular values of the matrix X in superposition.

(32) 2. Then, by using arithmetic operations on quantum register, exploit the symmetry of trigonometric functions to map each singular value in its inverse. This can be done using a library for arithmetic operations on a quantum computer.

(33) 3. Execute a Y rotation over an ancillary qubit controlled on the register created in the previous step.

(34) 4. Execute the inverse of the trigonometric function and the inverse of the circuit used to perform SVE (singular value estimation) on X, in this way the quantum register used to store the superposition of singular values is emptied.

(35) 5. Optionally, measure the ancilla qubits until 0 is read. In case 1 is read, repeat the procedure. This step can be postponed to the end of the quantum program. This will allow for applying techniques of amplitude amplification to speedup even further the estimation of the final result, which is contained in the middle register.

(36) FIG. 2 shows an example of a block diagram representing a quantum subroutine called UP used in a method of blocking or passing messages sent via a firewall according to an embodiment of the invention.

(37) The quantum subroutine UW 11 of FIG. 1 is connected to an input of quantum subroutine UL 12 which will be described in FIG. 3. A first output of quantum subroutine UL 12 is connected to the input of a square function of X 13 whose output is connected to an inverted square function of register X 15 and controls X referenced 14. A second output of subroutine UL 12 is directly connected to a second input of an inverted subroutine UL 16. Register X 14 is connected between a third output of subroutine UL 12 and a third input of inverted subroutine UL 16. A qubit measure 7 is performed on third output of inverted subroutine UL 16.

(38) This procedure takes as input a quantum register and two ancillary register, and output a quantum register. Following steps 1 to 5 will be successively performed:

(39) 1. Use UL to store in a quantum register the singular values of the matrix in superposition.

(40) 2. Using a quantum linear algebra library, square the values of the first register, as shown in the image.

(41) 3. Execute a controlled negation gate over an ancillary qubit parameterized by theta.

(42) 4. Execute the inverse of the square of the first register and the inverse of UL, in this way the quantum register used to store the superposition of singular values will be emptied.

(43) 5. Optionally, measure the ancilla qubits until 0 is read. In case 1 is read, repeat the procedure. This step can be postponed to the end of the quantum program. This will allow for applying techniques of amplitude amplification to speedup even further the estimation of the final result, which is contained in the middle register.

(44) FIG. 3 shows an example of a block diagram representing a quantum subroutine called UL used in a method of blocking or passing messages sent via a firewall according to an embodiment of the invention.

(45) Output of an Hadamard 21 is connected to input of an inverted Quantum Fourier Transform 23 (QFT) and controls a quantum subroutine called e{circumflex over ( )}(iH) 22 which will be described below in more details through following sub-steps 2.1 to 2.3.

(46) This step is used to create a quantum register with the superposition of the singular values of the product of two matrices X and X_dot, having them stored in QRAM. This procedure takes as input a quantum register, and two ancillary register. It is to be noted that, since calculating the singular values of the product of two matrixes has never been done before, this represents an unprecedented step that no one has ever done before on a quantum computer. This new step is an effort combining previous results in quantum information, using phase estimation and singular value estimation algorithms. Following steps 1 to 3 will be successively performed:

(47) 1. Create, using an Hadamard, a uniform superposition of elements in an index register. Use this register to perform phase estimation as such.

(48) 2. Controlled on the index register, do the following unitary:

(49) 2.1. Apply a Hadamard gate in order to create a uniform superposition of values on another register.

(50) 2.2. Controlled on the second index register, execute on a new register SVE on X and controlled operation to apply the matrix X to the quantum state, and execute on a new register SVE on X_dot and controlled operation to apply the matrix X_dot on the state.

(51) 2.3. Perform amplitude amplification on 0 on the second index register.

(52) 3. Perform a QFT on the first register.

(53) In the image that represents the quantum circuit, steps 2.1 to 2.3 are executed inside the controlled unitary matrix that is called e{circumflex over ( )}(iH) 22.

(54) To be more precise and more detailed about what is done in quantum subroutine UL and in the controlled unitary matrix that is called e{circumflex over ( )}(iH) 22, here are some complementary explanations.

(55) Performing “controlled operations” means that there are two register: A and B. Generically, an operation on the register B is performed if the register A is in a certain state. Since the register A is in a superposition of states, multiple operations are performed on the second register as well.

(56) For doing quantum subroutine UL, following operations are done:

(57) On the first register the superposition (with Hadamard matrix) of all the numbers from 0 to some integer N is created. Then, controlled on this register, all the following operations are done: apply the first matrix, apply the second matrix,

(58) Then, perform the QFT{circumflex over ( )}{−1} (inverted Quantum Fourier Transform) to read (magically) the eigenvalues (singular values) of the product of the two matrices stored in QRAM.

(59) “apply the matrix” means the following steps: perform singular value estimation to write the eigenvalues of a matrix in a new register, add a new ancilla qubit, perform a rotation on the Y axis on the ancilla qubit controlled on the register that has the superposition of singular values. The rotation is proportional to the singular value written in the register. Since there are many of them (is a superposition), basically more controlled rotations are performed “at the same time”. perform the inverse of singular value estimation to empty the register with the singular values. The Y axis is really the Y axis in X, Y, Z axis of a 3-Dimensional sphere that represents the qubit, which is also called the Bloch Sphere.

(60) Now, UFE is described as well as its use in classification.

(61) This procedure uses access to the QRAM of the tokenized matrix X and the derived matrix X_dot, and ensures a vector which can be used as feature for subsequent classification. In practice, tomography is performed after UFE. Basically extract features using the quantum computer.

(62) FIG. 4 shows an example of a block diagram representing the relationships existing between the different quantum subroutines used in a method of blocking or passing messages sent via a firewall according to an embodiment of the invention.

(63) QRAM of X 101 is used by quantum subroutine UW 103 and by quantum subroutine UL 104. QRAM of X_dot 102 is used by quantum subroutine UL 104. Quantum subroutine UW 103 is used by quantum subroutine UP 105. Quantum subroutine UL 104 is used by quantum subroutine UP 105. Quantum subroutine UP 105 is used by quantum subroutine UFE 106.

(64) On FIG. 4, there is the description of the relationship between the quantum operations which are executed on the quantum computer.

(65) Due to the nature of quantum computers, each step might use multiple oracle calls to other subroutines. For instance, the quantum circuit that named U.sub.L is used inside the subroutine named U.sub.P. The quantum circuit named U.sub.W is used only inside the quantum circuit U.sub.P. The subroutine UFE used to calculate the extracted feature, (which will be used to perform classification) calls U.sub.P for each domain in the dataset. The two oracles (called QRAM in quantum machine learning context) for X and for X_dot are used both to create the quantum states that represent the data, and inside the function calls of singular values estimation that are used inside UL and U.sub.W.

(66) Now a specific example will be described in more details.

(67) In order to prove that a new classification procedure works, in practice, it is usually tested on public datasets. The previous procedure is tested with classical software that simulates the quantum procedure, and tested against a dataset specifically suited for this task.

(68) This dataset has been generated from publicly available databases of source code of malware called “cryptolocker”, which has been used to generate 8.056 malicious domains. The well-known “Alexa's list” of the top 1 million domains was used as sample of non-malicious domains.

(69) The previous procedure thus finds implementation on real data in the following steps 1 to 7:

(70) 1. Generate some domain using the malware database found in “Andrew Aeva 2017” [Reference: Andrev Abakumov https://github.com/andrewaeva/DGA] hereby incorporated by reference. Since the data structures which are going to be created in the simulation are too big for classical computers, the dataset has been reduced in the following way. First, the 16 most used letters in the “Alexa” list of good domains were found. Then, only good domains containing only those letters were tested. This reduced the dataset to 72687 domains. Then, many DGA domains were generated and the same kind of filtering we performed thereby obtaining the 8056 domains.

(71) 2. Generate the token matrix. This can be done with sklearn as follow:

(72) object=CountVectorizer(analyzer=‘char’, ngram_range=(3, 5))

(73) counts_matrix=object.fit_transform(domains_list)

(74) 3. Preprocess the token matrix.

(75) a) Normalized such that the average of each component of the vector is 0.

(76) b) Scaled such as the variance of each component of the vector is 1.

(77) 4. Store X in QRAM. The preprocessed data represented by a matrix X is then stored in the software simulation. This consists into creating a suitable representation of the QRAM for the matrix X.

(78) 5. Generate and Store X_dot. Samples from the derivatives of the normalized dataset are taken, forming the second matrix X_dot. This data is stored in the second software representation of a QRAM data structure.

(79) 6. Simulate the quantum software for feature extraction. The simulation of the operation performed by the quantum circuits is performed. In this embedding, the linear-algebraic operation of quantum mechanics is simulated.

(80) 7. Train and test the classifier with the extracted feature. Now, any classical classification algorithm can be used to classify the received domain between good or malicious. This can be done again with sklearn or other machine learning toolkit.

(81) Execution is performed on a real data to prove high accuracy of classification procedure.

(82) This is an important key for claiming that a written a procedure which uses quantum computer indeed works in practice. In order to claim that the procedure will work on real quantum computers, it is interesting to show that the values extracted from the quantum procedure actually are useful to improve the classification accuracy of the classical algorithm. To do this, the quantum subroutines using a classical computer are simulated, mimicking the same linear algebraic procedure executed inside the quantum algorithm.

(83) The simulation has been done using the same tools used in “Andrev Abakumov” [Andrev Abakumov https://github.com/andrewaeva/DGA] hereby incorporated by reference: panda (a tool for handling datasets), sklearn, (a python machine learning library). This library has been used for: Simulating part of the quantum algorithm and the tomography step assuming no error on the quantum hardware. This step has been simulated using LinearDiscriminantAnalysis (for 2 components) on the dataset extracted as described. In fact, given a suitable representation of the input data, LinearDiscriminantAnalyis perform on the dataset the same mapping performed using the proposed invention in the quantum computer and uses optimization algorithm tuned for the matrix that is given as input. Running the classification procedure with the feature extracted from the quantum simulation. Again, this is done using sklearn tools.

(84) The increased accuracy obtained using the feature extracted from the simulated quantum procedure, apart from a very substantive speed up of the whole processing, is the following: Logistic Regression: 90.5% (+1.5%) Naive Bayes: 92.3% (+3%) Decision Trees: 94.0% (+2.6%)

(85) It is believed to have given evidence that with quantum computer it is possible to help to the resolution of classical problems. The performance of the quantum step depends on other parameters which are believed to be efficient for quantum algorithms: The conditioning number of a matrix is the ratio between the bigger and the smaller singular value. The runtime of the quantum procedure depends on the conditioning number of the matrix of the dataset, which is 14. This is one order of magnitude smaller than the conditioning number of other datasets studied in quantum machine learning algorithms. The runtime of the quantum procedure depends on the 11 norm of the dataset. The 1_1 norms of the rows inserted in the quantum algorithms are constant and will not increase significantly as the dataset increase.

(86) Beginning of Code

(87) Now, a part of the implementation will be given in more details through giving a part of code extracting the feature from the data and preparing the training set for the classifier.

(88) TABLE-US-00001 # extract length, entropy and perform the tokenization of the dataset set. all_domains, alexa_sfa_features, alexa_sfa_features_3, alexa_sfa_features_4, alexa_sfa_features_5 = preprocessing_data(parsed_args) # create the training set and the test set training_set, test_set, training_sfa, test_sfa= train_test_split(all_domains, alexa_sfa_features_4, test_size=0.2) # converting to a suitable representation the data training_set_as_matrix = training_set.as_matrix([‘domain’, ‘length’, ‘entropy’, ‘alexa_grams’]) # add word_grams e word_frequencies.. test_set_as_matrix = test_set.as_matrix([‘domain’, ‘length’, ‘entropy’, ‘alexa grams’]) # add word_grams e word_frequencies.. train_labels = np.array(training_set[‘class’].tolist( )) test_labels = np.array(test_set[‘class’].tolist( )) # convert the token matrix in a suitable format for the simulation d_training_sfa=training_sfa.todense( ) #y_train_slow, y_test_slow = feature_extraction (d_training_sfa, test_sfa.todense( ), train labels, parse_dargs) y_train_lda, y_test_1da = feature extraction (d_training_sfa, test sfa.todense( ), train_labels, parsed_args)

(89) Comparison of the different accuracy reached by the same classification procedure with a training set enhanced by the feature extracted from the simulation of the quantum algorithm.

(90) TABLE-US-00002 training_set_as_matrix_enhanced = np.concatenate((training_set_as_matrix[:,:−1], y_train_lda), axis=1) test_set_as_matrix_enhanced = np.concatenate((test_set_as_matrix[:,:−1], y_test_lda), axis=1) classify(training_set_as_matrix_enhanced[:,1:], test_set_as_matrix_enhanced[:,1:], train_labels, test_labels) classify(training_set_as_matrix[:,1:−1], test_set_as_matrix[:,1:−1], train_labels, test_labels)

(91) Here the function classify run the classification algorithm that was seen in the previous section. The first time it is called with the dataset extended with the new feature from the simulation of the quantum procedure.

(92) End of Code