The purpose of the work is to use an encryption algorithm based on cellular automata to develop a multi-threaded data processing system and study statistical performance indicators depending on the hardware component and input unit size, as well as develop recommendations for increasing the cryptographic strength of the method. A mathematical model of the encryption method using a oating window based on cellular automata is considered [1]. To study the speed of the processing of sensitive data, a variant of organizing the structure of the software module with an extended block of tuning parameters that determine the dimension of the matrix, the activation string of the bit neighborhood of the processed elements, the number of parallel calculations (threads) and the rule for expanding the boundary elements of the matrix has been developed. A method is proposed for generating a graphical dependence of the processing time on the initial parameters, the scope of which is possible both for processing individual les and continuous data streams of subscribers of a computer network. A cryptographic module has been developed that implements an encryption method based on cellular automata, a feature of which is a multithreaded mode of operation and dynamic control of the block of initial parameters. Recommendations on the installation of the neighborhood of the active elements of the matrix and the number of threads taking into account the architecture of the CPU are formulated. Experimental studies con rming the completeness and correctness of the proposed solutions were carried out.
The rapid development of information technology involves the continuous
improvement of tools to ensure the information security of con dential data [
In this paper, a new block processing method is proposed, based on a
cellular encryption algorithm with a oating window. The main di erence between a
cellular automaton with a oating window and a cellular automaton on a
partition [
Within the framework of the method under consideration, the task of protection against unauthorized access can be presented in the form of a sequence consisting of the following steps: con dential data is presented in the form of a binary matrix, the encryption block represents a oating window, the movement of which is determined by the input parameters and processing mode. As a rule, during processing (encryption), it is located in the upper left corner of the original matrix, the contents of this block are written out in a line in accordance with the route to bypass the neighborhood (neighboring bits). This sequence is replaced according to the transition function. The resulting cipher sequence is collapsed into a block in accordance with a given route and overwritten over the elements of the original matrix. Next, a shift occurs and the iterative process is repeated until the entire matrix is processed. When developing a software module, it is necessary to ensure that the le is read from the media or network interface, taking into account the hardware features of the automated system, to generate and process the initial matrix of a given width in accordance with the size of the oating window and the rules for expanding the matrix for boundary elements.
A feature of the proposed scheme for encrypting data streams using parallel computing based on cellular automata is the use of independent threads. With their help, there is a rational use of the computing resource of the central processor during processing on one computer or distribution of the processing process using network terminals [5{7]. Fig. 1 shows a basic variant of the interaction of the elements of the designed system. The information storage device stores both the source le and the encrypted le generated during the encryption process.
The encrypted matrix is formed in blocks, in the process of moving a oating
window and in the case of segmentation can be represented by a set of les. This
means that the nished blocks of the encrypted le are stored in random access
memory and wait for the end of the encryption process [
To clearly describe the operation of the method, we consider working with a
two-dimensional matrix. The size of the encryption block (m1; m2) can be set
arbitrarily, and the number of matrix columns is determined by the number
of blocks written in the alphabet A = f0; 1g. The number of matrix rows is
determined by the size of the initial data, and in the case of a network stream,
it depends on the interaction session of the computing subscribers network [
N2 = qm2 + 1; (1) where q is the partial quotient in the equality T = kq + r; 0 r < k; k = m1m2 is a block area, T is the length of the source text, and r is the remainder of the division.
A cellular automaton with a oating window is called a combination (formula 2):
CAo =< Zn; (N1; : : : ; Nn); A; (m1; : : : ; mn); ; L >; (2) where: Zn is a dimension of a cellular automaton(n = 1; 2; 3); (N1; : : : ; Nn) is a table size; (m1; : : : ; mn) is an encryption block size; is a transition function table; L is a bypass route of the encryption block of a cellular automaton with a oating window, moreover, the equalities N1 = m1; : : : ; Nn 1 = mn 1 and Nn = qmn + 1, where q is a partial quotient in equality T = kq + r; 0 r < k; k = m1: : : mn is a number of cells in the encryption block, is a length of the source text, r is a remainder of the division.
The source text is written sequentially in layers into the source text table. In the last layer, only r cells will be lled. The remaining cells are lled with either zeros or ones. The encryption process is as follows: the encryption block is located at the beginning of the table with the source text, the contents of this block are written out in a line in accordance with the traversal route L. This sequence is replaced in accordance with the transition function . The resulting cipher sequence is collapsed into a block in accordance with route L. The original block is replaced with the received one. The encryption block is shifted by one position in the data table and the process is repeated. The encryption process ends when the encryption unit is not able to move to a new position. During decryption, the oating window moves in the opposite direction, starting from the last column (the columns in the transition function are swapped). 5
In contrast to the cellular automaton on the partition, in which it is proposed to bypass the encryption block from the rst element and go in the order of rows and columns respectively, in the cellular automaton with a oating window, it is possible to bypass the encryption block in any sequence. Let the encryption block size be M N , then the number of bypass options for this block will be (M N )!. The table of transition functions depends on the size of the encryption block:as the block size increases, the number of options for lling the right side of the table of transition functions increases exponentially, and therefore, the task of breaking the cipher is complicated. But it must be taken into account that an increase in the encryption block is possible only when encrypting large messages. A 5 5 block size is recommended, but the use of 6 6 and 7 7 blocks will also be successful in improving the hardware component.
Consider the rule space in more detail. In the proposed program module, a neighborhood option is used that includes a central (processed) cell and 8 elements from the environment. From the point of view of evaluating cryptographic stability, only environmental elements of the treated cell are considered, since the central cell does not a ect the resistance. Thus, a neighborhood with four neighbors there are 28 = 256 positions and two options for lling each cell (zero or one), then the rules table can be lled in 2256 various ways.
To increase the cryptographic strength, we can consider neighborhoods of
the J th order, where J 2 N [
It is also worth noting that in conventional cellular encryption, the key is applied once. However, when encrypting with a oating window, the encryption block moves sequentially through the text, moving one column forward, thereby each element of the text is encrypted x times (depending on the size of the encryption block). On this basis, for the neighborhoods of Moore and Von Neumann of the J th order, the number of di erent bypass options will be (R!)x and (S!)x, respectively.
In the course of cryptanalysis, it was found that in order to increase the
stability of the method, the matrix neighborhood should be expanded along
with the rule of supplementing it based on a function that determines the state
of additional cells for boundary elements [
The developed software module is shown in Fig. 2. Here, in the upper part, a block of initial parameters is shown - the rule of matrix addition, optional log le maintenance, the bypass rule and block size, matrix dimension (by the number of blocks in a row). The left column shows the status of the encrypted blocks in accordance with the hash function. In addition to using a conversion table based on a hash function, it is possible to load a user-speci c transition guide or generate it. In order to eliminate the error of using an incorrect directory, the size of the installed block and the power of the number of transitions are compared. Experimental studies have con rmed the absence of a dependence of the processing speed on the number of blocks in the matrix row.
A search of the size options for the source blocks showed that the processing speed of the matrix is inversely proportional to the size of the block. The obtained processing statistics are shown in Table 1, here 100 percent corresponds to the longest encryption time of a le of 5 MB in size, which amounted to 23.2 seconds. The studies were carried out on a personal computer with a hardware con guration: CPU Intel i3 8100, HDD ST2000DL003, RAM 32 GB. The performance growth dynamics is justi ed by the fact that as the size of the blocks increases, their number in the le matrix decreases, and accordingly, the time for capturing, substituting, and rewriting elements decreases. It is important to take into account the fact that when using the lookup directory, processing time gains are achieved if a conversion table is available, otherwise its generation time may exceed the processing time since the time delays in its formation grow exponentially with increasing block area. To assess the dependence of the developed system performance on the number of parallel computing, the mode of enumerating the number of threads on les of various sizes was activated. In the formation of the initial matrix, blocks of 20 bits (block 4 5) were used (see Fig. 3). For clarity, the relative delay is indicated on the abscissa axis, 100 percent corresponds to the maximum processing time for a le of the speci ed size. Note that matching relative delay values for di erent data does not mean matching processing time.
From the graphs presented it follows that on the basis of experimental equipment
it is advisable to use no more than four threads (the processor has four physical
cores), since the vast majority of tests showed the highest system performance.
Using more than ve threads is not of interest since showed a decrease in
encryption speed due to the fact that there is a combination of tasks within one physical
(logical) processor and its work slows down. Thus, the dynamics of performance
depends on the architecture of the processor and the workload of the system as
a whole. It also follows from the graph that the dependence of the increase in
the speed of multi-threaded conversion depends on the le size. This is due to
the fact that the initialization and start-up of threads can take up a signi cant
share of the total processing time, which is impractical when processing les less
than 10 MB. Also note the block size as it determines the number of rewrites
of the elements of the original matrix, and in the case of a sequential algorithm,
the time of "downtime" [
To analyze the distribution of bits changed as a result of encryption, we form a matrix, which is the di erence between the original and encrypted matrix. Figure 4 shows a fragment of the resulting table containing 100 columns. The value of the matrix element will be the values f 1; 0; 1g. White cells correspond to 0 (the value has not changed), horizontal hatching corresponds to 1, vertical hatching corresponds to 1. A simpli ed visualization in the form of a surface is shown in Figure 5. For clarity, we took the distortion value modulo. Here, the di erence points rise from the main level and demonstrate the distribution of the changes made. The diagram shows fty rows corresponding to the rows of the matrix, the axis of a hundred divisions corresponds to the number of columns of the matrix (table width). Inclined faces show a uniform transition between states. A look at the graph \from below" (horizontal projection) coincides with Figure 4. From the results it follows that the processed matrix contains 50 percent of the changes at the bit level and 100 percent of the changes at the byte level, i.e. the result of processing is not similar to inversion and cannot be understood by an attacker without a reverse transformation, which involves knowledge or selection of key parameters. The obtained indicators con rm the high level of cryptographic strength of the encryption method under consideration based on cellular automata. In the course of further studies, it is planned to consider the changes made not only with the establishment of the fact of a change in the bit value, but also taking into account the boundary values.
In the initial de nition of a cellular automaton with a oating window, processing (encryption) begins with the rst block (depends on the input parameters and processing mode), then the iterative process is repeated in order until all blocks are processed. The introduction of a local rule for processing blocks will reduce the encryption time without losing cryptographic strength due to the fact that not all blocks will be processed, but only those with neighbors that correspond to certain markers. To do this, in the above de nition of a cellular automaton with a oating window, we introduce a new element: M - a set of markers (boundary values). 8
The cell of the matrix n will be considered as a block. A rule is introduced for
the local processing of blocks (matrix cells) based on markers - M. The marker
consists of a nite set of patterns P. Each pattern, in fact, is a set of values that
must be present around the cell so that its state is updated in accordance with
the , i.e. the update function works with a cell if and only if there is a
correspondence between the states of its neighbors and the pattern in M. However,
since there is no order in which each pattern P is compared with the states of
the cell's neighbors, no pattern should be a subpattern of the other. Based on
the studies presented in [
A cellular automaton with a oating window and a set of markers is called a combination (formula 3):
CAOM =< Zn; (N1; : : : ; Nn); A; (m1; : : : ; mn); ; L; M >; (3) where: Zn is a dimension of a cellular automaton(n = 1; 2; 3); (N1; : : : ; Nn) is a table size; (m1; : : : ; mn) is an encryption block size; is a transition function table; L is a bypass route of the encryption block of a cellular automaton with a oating window. M is a set of markers consisting of patterns P, all patterns P 2 M have the same shape, which is determined by the neighborhood of the marker. The update function is applied to cell n if and only if the state of its neighboring cells corresponds to to some element P 2 M . 9
In the course of the work, a mathematical model of the encryption method using a oating window based on cellular automata is considered. To study the speed of the processing of con dential data, a variant of organizing the structure of the software module was developed. A method is proposed for generating a graphical dependence of the processing time on the initial parameters, the scope of which is possible both for processing individual les and for continuous data streams of subscribers of a computer network, as well as at the level of a computing cluster that provides end-to-end encryption at the level of an external service.
A cryptographic module has been developed that implements the encryption method based on cellular automata, a feature of which is a multi-threaded mode of operation and dynamic control of the block of initial parameters. Recommendations are formulated for setting the neighborhood of the active elements of the matrix and the number of threads, taking into account the architecture of the central processor. Experimental studies have been carried out con rming the completeness and correctness of the proposed solutions. The expediency of using high-speed hard disk drives and saving the encryption results in asynchronous segmented mode with linking the result to the working thread is shown.
The proposed version of organizing a con dential information processing system in the form of a software module, taking into account the hardware features, allows optimizing the processing speed, and compliance with the recommendations for expanding the neighborhood during block conversion makes it possible to increase the cryptographic strength of the encryption algorithm based on cellular automata with a oating window. The totality of the results con rm the completeness and correctness of the proposed solutions.