RU2786617C1 - Method for integrity control and restore of one-dimensional data arrays based on complexing cryptographic methods and methods for noise-resistant coding - Google Patents

Abstract

FIELD: data array monitoring and restoring.

SUBSTANCE: invention relates to a method for monitoring and restoring the integrity of one-dimensional data arrays based on the integration of cryptographic methods and error-correcting coding methods. In the claimed solution, a one-dimensional data array M[k] is split into separate 1-dimensional structured data arrays

, provided that

while the elements

contained in them, depending on the operations performed on them, are interpreted as non-negative integers during code transformations or as binary vectors during cryptographic transformations, as a result of which a crypto-code structure is formed, the construction rules of which are determined and can be described by means of the ϕ-function, the use of which ensures the detection, localization and restoration of the integrity of x data blocks with signs of its violation without the need to introduce high redundancy.

EFFECT: invention provides the possibility of monitoring and restoring the integrity of one-dimensional data arrays.

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Description

The field of technology to which the invention belongs

The present invention relates to information technologies and can be used to control and restore the integrity of information presented in a 1-dimensional data space, continuously accumulated in data storage systems under destructive influences of an intruder and disturbances in the operating environment.

State of the art

a) Description of analogues

Known methods for monitoring the integrity of data through the use of cryptographic methods: key hashing, electronic signature means (Application for a patent of the Russian Federation No. 2012107193/08 publ. No. 2007141753/09 published 09/10/2010; RF patent application No. 2013149120/08 published 05.10.2015; RF patent application No. 2004110622/09 published 10.10.2007; RF patent application No. 2005113932/01 published 20.01. 2007; Knuth, D.E. The Art of Computer Programming Volume 3 Sorting and Search [Text] / D.E. Knut.- M.: "Mir", 1978. - 824 pp.; Menezes, A.J. Handbook of Applied Cryptography [Text] / A.J. Menezes, Paul C. van Oorschot, Scott A. Vanstone - M.: CRC Press, Inc., 1996. - 816 pp. Biham, E. A framework for iterative hash functions - HAIFA [Text ] / E. Biham, O. Dunkelman - M.: HAIFA, ePrint Archive, Report 2007/278 - 20 pp. The same [Electronic resource] - Access mode: eprint.iacr.org/2007/278. pdf (July, 2007) Wang, X. How to break MD5 and Ot her Hash Function [Text] / X.Wang, H.Yu. - M.: EUROCRYPT 2005, LNCS 3494, Springer-Verlag 2005. - C. 19-35; Bellare, M. New Proofs for NMAC and HMAC: Security without Collision-Resistance [Text] / M. Bellare. - M.: CRYPTO 2006, ePrint Archive, Report 2006/043. - 31 p.; The same [Electronic resource]. - Access mode: eprint.iacr.org/2006/043.pdf (2006)), for which two general schemes for obtaining hash codes are typical: for the whole data array and for each block of data contained in the array in question.

The disadvantages of these methods are:

- high redundancy of control information when hashing each block of data contained in the array under consideration, with their small dimension;

- the inability to detect and localize individual data blocks with signs of integrity violations when hashing a whole array of data.

There are known methods of restoring data integrity through the use of various types of redundancy (using hardware-software or software implementation of RAID (Redundant Array of Independent Disks) technology (RAID-arrays), duplication methods, redundant coding methods) (US Patent No. 7392458 publ. 24.06 2008; US Patent No. 7437658 published 10/14/2008; US Patent No. 7600176 published 10/06/2009; US Patent Application No. 20090132851 published 05/21/2009; US Patent Application No. 201101145677 6/16/2011; US Patent Application No. 20110167294 Published 07/07/2011; US Patent Application No. 20110264949 Published 10/27/2011; ] / G. Warren, Jr. - M .: "Williams", 2007. - 512 pp. Morelos-Zaragoza, R. The art of error-correcting coding. Methods, algorithms, applications [Text] / R. Morelos-Zaragoza; translation from English V. B. Afanasiev, Moscow: Technosfera, 2006, 320 p.; mming, R.V. Coding theory and information theory [Text] / R.V. Hemming; translation from English - M .: "Radio and communication", 1983. - 176 p.).

The disadvantage of these methods is:

- high redundancy.

b) Description of the closest analogue (prototype)

The closest in technical essence to the claimed invention (prototype) is a method for multi-level control and ensuring data integrity (RF Patent No. 2707940 publ. hash codes obtained using the standard procedure for implementing a hash function from a set of data in the order determined by a special procedure for selecting data blocks based on the mathematical apparatus of linear algebra (linear hash code system), while restoring the integrity of the detected and localized data block is carried out at the lower level through the use of error-correcting codes (Fig. 1). The application of a linear system of hash codes to pre-encoded data makes it possible to detect, localize and restore the integrity of a data block with signs of its violation without the need to introduce high redundancy.

The disadvantage of the known method is the inability to detect, localize and restore the integrity of information presented in a 1-dimensional data space, if the integrity of x data blocks is violated under the destructive influences of an attacker and disturbances in the operating environment.

Disclosure of invention

a) The technical result to which the invention is directed

The aim of the present invention is to develop a method for monitoring and restoring the integrity of 1-dimensional data arrays based on the integration of cryptographic methods and methods of error-correcting coding with the ability to detect, localize and restore the integrity of x data blocks with signs of its violation without the need to introduce high redundancy under the conditions of destructive influences of an attacker and perturbations of the operating environment.

b) A set of essential features

при условии, что i=1, 2, …, х,

содержащиеся в них элементы

для обеспечения возможности применения криптографических и кодовых преобразований при контроле и восстановлении их целостности в условиях деструктивных воздействий злоумышленника и возмущений среды функционирования представляются по правилам построения кодового слова, при этом блоки данных

будут интерпретироваться как целые неотрицательные числа и считаться k информационными блоками данных, для которых в количестве, достаточном для обеспечения возможности восстановления целостности отдельного 1-мерного структурированного массива данных

по правилам построения кодов, корректирующих ошибки, вычисляются r дополнительных контрольных блоков данных

полученная совокупность информационных и дополнительных контрольных блоков данных будет считаться кодовым словом (n, k)-кода, после выполнения кодовых преобразований получим массив с элементами

которые для обеспечения возможности контроля их целостности будут интерпретироваться как двоичные векторы

от которых посредством применения криптографической хэш-функции h вычисляются хэш-коды

где j=0, 1, …, η-1, при этом выбор совокупности блоков данных для хэширования будет определяться на основе математического аппарата теории систем векторов и линейных векторных пространств, после выполнения криптографических преобразований над элементами массива получим на основе комплексирования криптографических методов и методов помехоустойчивого кодирования крипто-кодовую конструкцию, правила построения которой определяются и могут быть описаны посредством ϕ-функции, при этом обеспечивающую обнаружение, локализацию и восстановление целостности х блоков данных с признаками ее нарушения без необходимости введения высокой избыточности.This goal is achieved by the fact that in the known method of monitoring and ensuring data integrity, which consists in the fact that in order to detect, localize and restore the integrity of a 1-dimensional data array, the data contained in it are presented in the form of data blocks of a fixed length m ₁ , m ₂ , …, m _n , which are an information group of n blocks, to which, according to the rules for constructing redundant codes, an additional control group of r blocks m _n+1 , …, m _n+2 , is added to correct an error, in the event of which the integrity of the data array is restored through the use of the mathematical apparatus of redundant codes, and error detection is performed on the basis of the reference system of hash codes calculated from them, the construction rules of which are determined by the mathematical apparatus of linear algebra, in the presented method, the 1-dimensional data array M[k] is divided into separate 1-dimensional structured data arrays

provided that i=1, 2, ..., x,

the elements they contain

to ensure the possibility of using cryptographic and code transformations when monitoring and restoring their integrity under the destructive influences of an intruder and disturbances in the operating environment, they are presented according to the rules for constructing a code word, while data blocks

will be interpreted as non-negative integers and considered as k information data blocks, for which in an amount sufficient to ensure the possibility of restoring the integrity of a separate 1-dimensional structured data array

according to the rules for constructing error-correcting codes, r additional control data blocks are calculated

the resulting set of information and additional control data blocks will be considered the code word of the (n, k)-code, after performing the code transformations, we will obtain an array with elements

which, in order to ensure the possibility of monitoring their integrity, will be interpreted as binary vectors

from which, by applying the cryptographic hash function h, hash codes are calculated

where j=0, 1, …, η-1, while the choice of a set of data blocks for hashing will be determined on the basis of the mathematical apparatus of the theory of systems of vectors and linear vector spaces, after performing cryptographic transformations on the elements of the array, we will obtain based on the complexing of cryptographic methods and methods of error-correcting coding, a crypto-code structure, the construction rules of which are determined and can be described by means of a ϕ-function, while ensuring the detection, localization and restoration of the integrity of x data blocks with signs of its violation without the need to introduce high redundancy.

при условии, что i=1, 2, …, х,

при этом содержащиеся в них элементы

в зависимости от выполняемых над ними операций интерпретируются как целые неотрицательные числа при кодовых преобразованиях или как двоичные векторы при криптографических преобразованиях, в результате которых образуется крипто-кодовая конструкция, правила построения которой определяются и могут быть описаны посредством ϕ-функции, полученная крипто-кодовая конструкция обеспечивает при этом обнаружение, локализацию и восстановление целостности х блоков данных с признаками ее нарушения без необходимости введения высокой избыточности. Контроль целостности блоков данных, интерпретируемых как двоичные векторы

будет осуществляться путем сравнения значений хэш-функции, вычисленных при запросе на использование защищаемых данных, и эталонных значений, что позволит в момент времени t в условиях деструктивных воздействий злоумышленника и возмущений среды функционирования определить блоки данных с признаками нарушения целостности. Новым является то, что в предлагаемом способе 1-мерный массив данных М[л] разбивается на отдельные 1-мерные структурированные массивы данных

при условии, что i=1, 2, …, х,

в результате выполнения криптографических и кодовых преобразований над элементами которых обеспечивается возможность обнаружения, локализации и восстановления целостности х блоков данных с признаками ее нарушения. Новым является то, что на основе комплексирования криптографических методов и методов помехоустойчивого кодирования образуется крипто-кодовая конструкция, правила построения которой определяются и могут быть описаны посредством ϕ-функции, которая обеспечивает обнаружение, локализацию и восстановление целостности блоков данных с признаками ее нарушения в количестве, определяемом еще при разбиении 1-мерного массива данных M[k] без необходимости введения высокой избыточности. Новым является то, что в предлагаемом способе ошибки с кратностью больше «1» подлежат обнаружению и локализации, в том числе, посредством используемого кода, корректирующего ошибки.A comparative analysis of the claimed solution with the prototype shows that the proposed method differs from the known one in that the goal is achieved by splitting the 1-dimensional data array M[k] into separate 1-dimensional structured data arrays

provided that i=1, 2, ..., x,

while the elements they contain

depending on the operations performed on them, they are interpreted as non-negative integers during code transformations or as binary vectors during cryptographic transformations, as a result of which a crypto-code construction is formed, the construction rules of which are determined and can be described by means of the ϕ-function, the resulting crypto-code construction ensures the detection, localization and restoration of the integrity of x blocks of data with signs of its violation without the need to introduce high redundancy. Integrity control of data blocks interpreted as binary vectors

will be carried out by comparing the hash function values calculated when requesting the use of protected data and the reference values, which will allow at time t under the destructive influences of an attacker and disturbances in the operating environment to determine data blocks with signs of integrity violation. What is new is that in the proposed method, the 1-dimensional data array M[l] is divided into separate 1-dimensional structured data arrays

provided that i=1, 2, ..., x,

as a result of performing cryptographic and code transformations on the elements of which, it is possible to detect, localize and restore the integrity of x data blocks with signs of its violation. What is new is that, based on the complexing of cryptographic methods and methods of error-correcting coding, a crypto-code structure is formed, the construction rules of which are determined and can be described by means of a ϕ-function, which ensures the detection, localization and restoration of the integrity of data blocks with signs of its violation in the amount, determined even when partitioning a 1-dimensional data array M[k] without the need to introduce high redundancy. What is new is that in the proposed method, errors with a multiplicity greater than "1" are subject to detection and localization, including by means of the error-correcting code used.

c) Cause-and-effect relationship between the features and the technical result Thanks to the new set of essential features, the following possibilities are realized in the method:

- monitoring and restoring the integrity of 1-dimensional data arrays with the ability to detect, localize and restore the integrity of x data blocks with signs of its violation;

- construction of a crypto-code structure, the construction rules of which are determined and can be described by means of a ϕ-function that ensures the detection, localization and restoration of the integrity of data blocks with signs of its violation in the amount determined even when splitting a 1-dimensional data array M[k] without need for high redundancy.

- detection and localization of an error with a multiplicity greater than "1" by means of the error-correcting code used.

Evidence of compliance of the claimed invention with the conditions of patentability "novelty" and "inventive step"

The analysis of the prior art made it possible to establish that there are no analogues characterized by a set of features identical to all the features of the claimed technical solution, which indicates the compliance of the claimed method with the condition of patentability "novelty".

The results of the search for known solutions in this and related fields of technology in order to identify features that match the distinguishing features of the prototype of the claimed object showed that they do not follow explicitly from the prior art. The prior art also did not reveal the fame of distinctive essential features that cause the same technical result that is achieved in the claimed method. Therefore, the claimed invention meets the condition of patentability "inventive step".

Brief description of the drawings

The claimed method is illustrated by drawings, which show:

fig. 1 is a general diagram illustrating a method for multi-level control and data integrity;

fig. 2 is a diagram of a 1-dimensional data space;

fig. 3 is a diagram illustrating the arrangement of information and control symbols in a codeword of an (n, k) code;

fig. 4 is a diagram illustrating the construction order of an (n, k) code word;

fig. 5 is a diagram illustrating the arrangement of computed hash codes in 1-dimensional space;

fig. 6 is a diagram illustrating the hashing order of codeword elements of an (n, k) code;

fig. 7 is a diagram illustrating the execution of encoding and hashing operations in 1-dimensional space;

fig. 8 is a diagram illustrating the performance of 1-dimensional cryptographic and coding transformations on elements of individual structured data arrays represented in a 1-dimensional data space;

fig. 9 is a diagram illustrating the developed method for monitoring and restoring the integrity of one-dimensional data arrays based on the integration of cryptographic methods and noise-correcting coding methods.

Implementation of the invention

The location of data blocks M _k (k=0, 1, ..., k-1) to be protected in a 1-dimensional data space can be characterized using one coordinate axis (Fig. 2).

At the same time, to ensure the possibility of using cryptographic and code transformations in monitoring and restoring the integrity of structured data arrays, the interpretation of the data blocks contained in them will be different.

The data blocks of an arbitrary structured data array will be interpreted as non-negative integers, represented, for example, in the binary number system:

where μ _g ∈ {0, 1}; g=0, 1, …, τ-1; or as elements of the extended field GF(2 ^τ ):

- фиктивная переменная; μ_g ∈ {0, 1}; g=0, 1, …, τ-1, для обеспечения возможности выполнения с ними преобразований, идентичных преобразованиям, используемым при построении кодов, корректирующих ошибки. К примеру, при выполнении операции расширения для построения кодов системы остаточных классов: модулярных кодов, модулярных полиномиальных кодов.where

- dummy variable; μ _g ∈ {0, 1}; g=0, 1, …, τ-1, to enable them to perform transformations identical to those used in the construction of error-correcting codes. For example, when performing an extension operation to construct the codes of the system of residual classes: modular codes, modular polynomial codes.

Interpreting data blocks as vectors:

where μ _g ∈ {0, 1}; g=1, 2, …, τ, makes it possible to perform transformations with them that are identical to the transformations used in various cryptoalgorithms, for example, when using the hashing function.

Therefore, depending on the type of transformations performed to control and restore the integrity of structured data arrays, various forms of representation of the data blocks contained in them are used.

To ensure the possibility of restoring the integrity of the structured data array M[k], presented in a 1-dimensional data space:

where k is the dimension of the data array, the data blocks M _k contained in it are represented according to the rules for constructing a code word.

In this case, data blocks M _k (elements of the structured data array M[k]) will be interpreted as non-negative integers and considered as information symbols (data blocks):

for which, in an amount sufficient to ensure the possibility of restoring the integrity of the structured data array, r additional control characters (data blocks) are calculated:

The resulting set of information (data blocks M _k ) and additional control (data blocks M _ρ , where ρ=k, k+1, ..., k+r-1) symbols:

will be considered a code word (n, k) - code (Fig. 3).

The calculation of additional control symbols (data blocks M _ρ ) is performed according to the rules for constructing error-correcting codes, taking into account the correction abilities required to ensure the possibility of restoring the integrity of the structured data array (Fig. 4).

The rules for constructing (n, k)-codes with a description of their parameters, in particular, the minimum code distance d _min , are presented in many well-known works (Morelos-Zaragoza, R. The art of error-correcting coding. Methods, algorithms, application [Text] / R. Morelos-Zaragoza, translated from English by V. B. Afanasyev, Moscow: Technosfera, 2006, 320 p., Hemming, R. V. Coding theory and information theory [Text] / R. V. Hemming, translated from English - M .: "Radio and communication", 1983. - 176 p.).

After performing the code transformations, the array (1) will take the form:

where the elements M _p (ρ=k, ..., n-1) of the subarray M[r] are obtained as a result of code transformations over the elements M _k (k=0, 1, ..., k-1) of the subarray M[k].

To ensure the possibility of monitoring the integrity of the (n, k)-code of the array (2) obtained during the construction of the codeword, its elements:

will be interpreted as binary vectors M _i (i=0, 1, …, n-1), from which hash codes H _j (j=0, 1, …, η-1) are calculated by applying the cryptographic hash function h.

The choice of a set of data blocks M _i for hashing will be determined on the basis of the mathematical apparatus of the theory of systems of vectors and linear vector spaces.

To do this, the vector of data blocks M ₀ , M ₁ , ..., M _n-1 is considered as a system of linearly independent vectors:

only for a non-zero set of coefficients:

where x _q ∈ {0, 1}; q=0, 1, …, n-1.

This system forms the basis:

в свою очередь, также можно рассматривать как систему линейно независимых векторов, образующих базис:Vector of data blocks with hash codes

in turn, can also be considered as a system of linearly independent vectors that form the basis:

представляется в виде двоичной матрицы, составленной из коэффициентов базиса:A hashing scheme for a collection of data blocks

represented as a binary matrix composed of the coefficients of the basis:

where η<p.

In this case, the rows of the matrix have the following properties:

- are different and linearly independent vectors;

- distance between vectors (according to Hamming) d _min ≥2;

- each vector has a weight (in the sense of Hamming) ω≥d _min ;

- the zero vector is not included in the matrix.

The generating matrix in the theory of linear codes has similar properties, which makes it possible to use the rules for constructing linear codes for hashing data.

When hashing data, we get a vector of data blocks with calculated hash codes H _j (j=n, ..., w-1):

where the symbol "→", meaning mapping, is used in this case as a special multidimensional non-commutative hashing operation.

The figure 5 shows the order of the calculated hash codes in relation to the information and additional control symbols of the code word (n, k)-code in 1-dimensional space.

The order of obtaining a vector of data blocks with calculated hash codes is explained by the following expression:

означает специальную многомерную некоммутативную операцию хэширования блоков данных, представленных двоичными векторами M_i, отмеченных единичным символом a_n-1,w-n-1=1 (если a_i=∅, то a_iM_i=∅, где «∅» - пустое множество); M_i - информационный вектор (массив

);

a_i ∈ {0,1}.where symbol

means a special multidimensional non-commutative hashing operation of data blocks represented by binary vectors M _i marked with a single symbol a _n-1,wn-1 =1 (if a _i =∅, then a _i M _i =∅, where "∅" is an empty set ); M _i - information vector (array

);

a _i ∈ {0,1}.

The hashing order of the elements of the code word (n, k)-code, interpreted as binary vectors M _i (i=0, 1, ..., n-1), is shown in figure 6.

The operations performed when hashing data are defined by the state standard (GOST 34.11-2012. Information technology. Cryptographic information protection. Hashing function. - M.: Standartinform, 2012. - 34 p.).

After performing cryptographic transformations on the elements of the array (2), we obtain a crypto-code structure represented by an array:

whose construction rules are determined and can be described by means of a ϕ-function of the following form:

where the symbol "1D" denotes that 1-dimensional cryptographic (hash function h) and code (encoding function f) transformations are performed on the elements of the structured data array M[k] represented in the 1-dimensional data space; k=0, 1, ..., k-1; ρ=k, …, n-1; j=n, …, w-1.

элементами s_l ∈ {0,1}, по одному для каждого проверочного символа (блока данных).When checking data integrity, to detect an error in the theory of linear codes, it is required to calculate the error syndrome S - row matrix

elements s _l ∈ {0,1}, one for each check symbol (data block).

будет характеризоваться несоответствием сравниваемых двоичных векторов при проверке синдрома.Integrity violation (error occurrence) of the considered data blocks with calculated hash codes

will be characterized by a mismatch of the compared binary vectors when checking the syndrome.

со значениями ранее вычисленных эталонных хэш-кодов H_j. По результатам сравнения делается вывод:To do this, the values of the hash codes calculated during the request for the use of these data are compared.

with the values of previously calculated reference hash codes H _j . Based on the results of the comparison, it is concluded:

- about the absence of signs of violation of the integrity of data blocks, with

- violation of the integrity of data blocks, when

After the detection and localization of a data block (set of data blocks) with signs of integrity violation, the integrity of structured data arrays is restored by applying the mathematical apparatus of the error-correcting codes used.

In the obtained crypto-code structure, described by the ϕ-function (3), to control and restore the integrity of the structured data array presented in the 1-dimensional data space, 1-dimensional cryptographic and code transformations are performed (Fig. 7), that is, in space with the dimension corresponding to the dimension of the data space.

In this case, the error-correcting code used in coding to restore the integrity of those already detected and localized by using the hashing function of data blocks with signs of integrity violation is sufficient to have a correcting ability equal to its detecting one.

To ensure cryptographic reliability in the control and restoration of the integrity of structured data arrays, the calculated reference hash codes H _j must be stored in a reliable environment.

In the case of constructing a crypto-code structure according to the rules determined by means of a ϕ-function of the following form:

where initially hash codes are calculated from the elements of the structured data array M[ _k ], and then additional control characters, then it is required to provide a storage environment that excludes destructive effects, also for them, since the hash function will be applied only to data blocks Mk .

The set of data blocks M _k and the hash codes calculated from them will be interpreted as non-negative integers and considered as information symbols, for which additional control symbols will be calculated in an amount sufficient to ensure the possibility of restoring the integrity of the structured data array M[k] according to the rules for constructing codes correcting errors.

Errors with a multiplicity greater than "1" are subject to detection and localization by means of the error-correcting code used. At the same time, in such crypto-code constructions, to confirm the integrity of the original structured data array with cryptographic certainty after the recovery procedure, the introduction of additional control mechanisms is required.

To ensure the possibility of detecting and localizing x data blocks with signs of integrity violation (x-fold error) by using a hash function, it is required to split the considered 1-dimensional structured data array M[k] into separate 1-dimensional structured data arrays with a lower dimension.

So, with such a partition of the considered 1-dimensional structured data array M[k] and obtaining a set of separate 1-dimensional structured data arrays:

с элементами:where

with elements:

control and restoration of their integrity will be performed by applying 1-dimensional cryptographic and code transformations (Fig. 8), carried out according to the same rules as for a separate structured data array presented in a 1-dimensional data space.

Such control of their integrity will be characterized by the possibility of detecting and localizing x blocks of data with signs of integrity violation (x-fold error).

A diagram illustrating the developed method for monitoring and restoring the integrity of one-dimensional data arrays based on the integration of cryptographic methods and noise-correcting coding methods is shown in figure 9.

Claims (1)

A method for monitoring and restoring the integrity of one-dimensional data arrays based on the integration of cryptographic methods and methods of error-correcting coding, which consists in the fact that in order to detect, localize and restore the integrity of a 1-dimensional data array, the data contained in it are presented in the form of data blocks of a fixed length m ₁ , m ₂ , …, m _n , which are an information group of n blocks, to which, according to the rules for constructing redundant codes, an additional control group r of blocks m _n+1 , …, m _n+r , is added to correct an error, in the event of which the restoration of the integrity of the array data is carried out by using the mathematical apparatus of redundant codes, and error detection is performed on the basis of the reference system of hash codes calculated from them, the construction rules of which are determined by the mathematical apparatus of linear algebra, characterized in that a 1-dimensional data array M[k] is divided into separate 1 -dimensional structures bath datasets

provided that

the elements they contain

to ensure the possibility of using cryptographic and code transformations when monitoring and restoring their integrity under the destructive influences of an intruder and disturbances in the operating environment, they are presented according to the rules for constructing a code word, while data blocks

will be interpreted as non-negative integers and considered as k information data blocks, for which in an amount sufficient to ensure the possibility of restoring the integrity of a separate 1-dimensional structured data array

according to the rules for constructing error-correcting codes, r additional control data blocks are calculated

the resulting set of information and additional control data blocks will be considered the code word of the (n, k)-code, after performing the code transformations, we will obtain an array with elements

which, in order to ensure the possibility of monitoring their integrity, will be interpreted as binary vectors

from which, by applying the cryptographic hash function h, hash codes are calculated

where j=0, 1, ..., n-1, while the choice of a set of data blocks for hashing will be determined on the basis of the mathematical apparatus of the theory of systems of vectors and linear vector spaces, after performing cryptographic transformations on the elements of the array, we will obtain based on the complexing of cryptographic methods and methods of error-correcting coding, a crypto-code construction, the construction rules of which are determined and can be described by means of a ϕ-function, while ensuring the detection, localization and restoration of the integrity of x data blocks with signs of its violation without the need to introduce high redundancy.

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