RU2771208C1 - Method for control and recovery of integrity of multidimensional data arrays - Google Patents

Abstract

FIELD: data arrays monitoring and restoring.SUBSTANCE: invention relates to a method for monitoring and restoring the integrity of multidimensional data arrays. In the method for performing integrity control, data blocks Mi (i=1, 2, …, n) are represented as fixed-length subblocks Mi,l, Mi,2, …, Mi,n, from which the reference hash codes Hi hash -functions h(Mi), the values of which are subsequently compared with the values of the hash codesof the hash functioncalculated from the checked data blockswhose subblocks are also subblocks of data blocks Mj (j=1, 2, …, n), which, in order to restore data integrity in case of its violation, are formed according to the rules similar to the rules for constructing redundant modular codes, while providing for subblocks M1,j, M2,j, …, Mn,j, which are an information group of n subblocks, designed to uniquely restore data blocks Mj in case of violation of their integrity, calculation of the control group (k - n) of subblocks Mn+1,j, Mn+2,j, …, Mk,j, additionally introduced to correct the error, in the event of which the restoration of data blocks Mj without prejudice to the uniqueness of their representation is carried out by reconfiguring the system by excluding the subblock [Mi,j] from the calculations with the error that has occurred, while the multidimensional data array of dimension k is represented as 3- dimensional data array М[k, k, k], consisting of k3 data blocks Mi,j,r (i=j=r=0, 1, …, k - 1), which, for integrity control, will be placed in an array of dimensions k+1, while filling from 0 to k-1 of its blocks, to which the hash function h is applied to detect signs of integrity violation, while the calculated hash codes Hi, j, r ( i, j, r = 0, …, k) will be placed in 3k2 free blocks of the array and will be reference values, the values of which, when requesting the use of data, are compared with the values of the hash codesof the hash functioncalculated already from the checked data blockswhen restoring the integrity of the data blocks Mi,j,r to be protected, as well as the reference hash codes Hi,j,r calculated from them will be interpreted as elements of GF(2t) and will be the least polynomial residues in basesin this case, the resulting 3-dimensional data array M[k+1, k+1, k+1] will be considered as a single superblock of the modular polynomial code, on which the expansion operation is performed by introducing n - k redundant bases, for which the corresponding 3k2(n - k) excess residues are calculated, which are additionally introduced to correct the error, in the event of which the restoration of data blocks Mi,j,r without prejudice to the uniqueness of their representation is carried out by reconfiguring the system by excluding from the calculations the data block with features integrity violations.EFFECT: ensuring data integrity control.1 cl, 10 dwg

Description

The field of technology to which the invention belongs

The present invention relates to information technology and can be used to control and restore data integrity in multidimensional storage systems based on the use of cryptographic hash functions and error control codes to protected data blocks under restrictions on the allowable resource costs.

State of the art

a) Description of analogues

Known methods of data integrity control through the use of cryptographic methods: key and keyless hashing, electronic signature means (Patent for invention RUS No. 26207030, 07.12.2015; Patent for invention RUS No. 2669144, 28.11.2017; Patent for invention RUS No. 2680033, 22.05 .2017; Patent for invention RUS No. 2680350, 02.05.2017; Patent for invention RUS No. 2680739, 11.28.2017; Patent for invention RUS No. 2686024, 25.04.2018; Knuth, D.E. The art of computer programming. Volume 3. Sorting and search / D.E. Knuth - M.: "Mir", 1978. - 824 pp.; Dichenko, S. Two-dimensional control and assurance of data integrity in information systems based on residue number system codes and cryptographic hash functions / S. Dichenko, O. Finko // Integrating Research Agendas and Devising Joint Challenges International Multidisciplinary Symposium ICT Research in Russian Federation and Europe 2018. P. 139-146 Dichenko S. A. Hybrid crypto-code method of control and restore integrity d data for secure information-analytical systems / S. Dichenko, O. Finko // Issues of cybersecurity. - 2019. - No. 6 (34). - P. 17-36), which are characterized by three generalized schemes for applying the hash function:

- with the calculation of one common hash code from to data blocks (Fig. 1);

- with the calculation of one hash code from each of the data blocks (Fig. 2);

- with the construction of a fully connected hashing network (Fig. 3).

The disadvantages of these methods are:

- for the hash function application scheme with the calculation of one common hash code from k data blocks:

- does not allow, after data integrity control, to localize a data block with integrity violation;

- for the hash function application scheme with the calculation of one hash code from each of the data blocks:

- high redundancy of control information when checking the integrity of data blocks represented by binary vectors of small dimension;

- for the hash function application scheme with the construction of a fully connected hashing network:

- high redundancy of control information when checking the integrity of data blocks represented by binary vectors of small dimension;

- in general, this model does not allow, after data integrity control, to localize a data block with integrity violation.

There are known methods for 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) (Patent for invention RUS No. 2406118, April 10, 2007; Invention patent RUS No. 2481632, May 10, 2013; Invention patent RUS No. 2513725, April 20, 2014; Invention patent RUS No. 2598991, October 10, 2016; USA Invention No. 7437658, October 14, 2008; USA Invention Patent No. 7600176, October 6, 2009; Warren, G. Bit Counting: Algorithmic Tricks for Programmers (Hacker's Delight) / G. Warren, Jr. - M .: "Williams", 2007. - 512 pp. Morelos-Zaragoza, R. The Art of Noise-Immune Coding Methods, Algorithms, Application / R. Morelos-Zaragoza, translated from English by V. B. Afanasyev - M.: Technosfera, 2006. - 320 p. ; Hemming, R.V. Coding theory and information theory / R .AT. Hemming; translation from English - M .: "Radio and communication", 1983. - 176 p.).

The disadvantages of these methods are:

- high redundancy;

- the inability to increase the corrective ability of recovery tools in the face of restrictions on the allowable resource costs.

b) Description of the closest analogue (prototype)

The closest in technical essence to the claimed invention (prototype) is a method of two-dimensional control and data integrity (Fig. 4), based on the control and restoration of data integrity, presented in the form of a two-dimensional array of data blocks of a fixed length, from the elements of the rows of which previously through application of the hash function, the reference hash codes are calculated, the values of which are subsequently compared with the values of the hash codes already calculated from the checked data blocks, when requesting their use, and the mathematical apparatus of redundant modular codes is applied to the elements of the array columns (Dichenko S.A. ., Samoilenko D.V., Finko O.A. A method for two-dimensional control and ensuring data integrity // Patent for invention RUS No. 2696425, 02.08.2019).

The disadvantage of the known method is the lack of the possibility of improving the corrective ability of recovery tools in terms of restrictions on the allowable resource costs.

Disclosure of invention

a) The technical result to which the invention is directed The purpose of the present invention is to develop a method for monitoring and restoring the integrity of multidimensional data arrays based on the application of cryptographic hash functions to protected data blocks and the mathematical apparatus of redundant modular codes with the possibility of increasing the corrective ability of recovery tools under conditions of restrictions to allowable resource costs.

b) A set of essential features

хэш-функции

вычисляемых уже от проверяемых блоков данных

подблоки которых также являются подблоками блоков данных M_j (j=1, 2, …, n), которые для восстановления целостности данных в случае ее нарушения формируются по правилам, аналогичным правилам построения избыточных модулярных кодов, обеспечивая при этом для подблоков M_1,j, M_2,j, …, M_n,j, которые являются информационной группой n подблоков, предназначенной для однозначного восстановления блоков данных M_j в случае нарушения их целостности, вычисление контрольной группы (k - n) подблоков M_n+1,j, M_n+2,j, …, M_k,j, дополнительно вводимой для коррекции ошибки, в случае возникновения которой восстановление блоков данных M_j без ущерба для однозначности их представления осуществляется посредством реконфигурации системы путем исключения из вычислений подблока [M_i,j] с возникшей ошибкой, в представленном же способе многомерный массив данных размерности к представляется в виде 3-мерного массива данных М[k, k, k], состоящего из k³ блоков данных M_i,j,r (i = j = r = 0, 1, …, k - 1), которые для контроля целостности будут размещаться в массиве размерности k+1, заполняя при этом от 0 до k - 1 его блоков, к которым для обнаружения признаков нарушения целостности применяется хэш-функция h, при этом вычисленные хэш-коды H_i,j,r (i, j, r = 0, …, k) будут размещаться в 3k² свободных блоках массива и являться эталонными, значения которых при запросе на использование данных сравниваются со значениями хэш-кодов

хэш-функции

вычисляемых уже от проверяемых блоков данных

при восстановлении целостности блоки данных M_i,j,r, подлежащие защите, а также вычисленные от них эталонные хэш-коды H_i,j,r будут интерпретироваться как элементы GF(2^t) и являться наименьшими полиномиальными вычетами по основаниям

при этом полученный 3-мерный массив данных М[k+1, k+1, k+1] будет рассматриваться как единый суперблок модулярного полиномиального кода, над которым выполняется операция расширения путем введения n - k избыточных оснований

для которых вычисляются соответствующие им 3k²(n - k) избыточных вычетов, дополнительно вводимых для коррекции ошибки, в случае возникновения которой восстановление блоков данных M_i,j,r без ущерба для однозначности их представления осуществляется посредством реконфигурации системы путем исключения из вычислений блока данных с признаками нарушения целостности.This goal is achieved by the fact that in the known method of two-dimensional control and data integrity, which consists in the fact that for the implementation of integrity control data blocks M _i (i=1, 2, ..., n) are represented as subblocks of fixed length M _i,1 , M _i,2 , …, M _i,n , from which the reference hash codes H _i of the hash function h(M _i ) are preliminarily calculated, the values of which are subsequently compared with the values of the hash codes

hash functions

computed already from the checked data blocks

whose subblocks are also subblocks of data blocks M _j (j=1, 2, …, n), which, in order to restore data integrity in case of its violation, are formed according to the rules similar to the rules for constructing redundant modular codes, while providing for subblocks M _1,j , M _2,j , …, M _n,j , which are an information group of n subblocks, designed to uniquely restore data blocks M _j in case of violation of their integrity, calculation of the control group (k - n) of subblocks M _n+1,j , M _n+2,j , …, M _k,j , additionally introduced to correct the error, in the event of which the restoration of data blocks M _j without prejudice to the uniqueness of their representation is carried out by reconfiguring the system by excluding the subblock [M _i,j ] from the calculations with an error, in the presented method, a multidimensional data array of dimension k is represented as a 3-dimensional data array M[k, k, k], consisting of k ³ data blocks M _i,j,r (i = j = r = 0 , 1, …, k - 1), which which for integrity control will be placed in an array of dimension k + 1, while filling from 0 to k - 1 of its blocks, to which the hash function h is applied to detect signs of integrity violation, while the calculated hash codes H _{i, j, r} (i, j, r = 0, …, k) will be placed in 3k ² free blocks of the array and will be reference values, the values of which are compared with the values of the hash codes when requesting to use the data

hash functions

computed already from the checked data blocks

when integrity is restored, the data blocks M _i,j,r to be protected, as well as the reference hash codes H _i,j,r calculated from them, will be interpreted as elements of GF(2 ^t ) and will be the least polynomial residues in bases

in this case, the resulting 3-dimensional data array M[k+1, k+1, k+1] will be considered as a single superblock of the modular polynomial code, on which the expansion operation is performed by introducing n - k redundant bases

for which the corresponding 3k ² (n - k) excess residues are calculated, additionally introduced to correct the error, in the event of which the restoration of data blocks M _i,j,r without prejudice to the uniqueness of their representation is carried out by reconfiguring the system by excluding the data block from the calculations with signs of integrity.

A comparative analysis of the claimed solution and the prototype shows that the proposed method differs from the known one in that the goal is achieved by presenting a multidimensional data array of dimension k in the form of a 3-dimensional data array M[k, k, k], consisting of k ³ data blocks M _i,j,r , to detect signs of violation of the integrity of which the hash function is used and 3k ² hash codes H _i,j,r are calculated, which, when integrity is restored, are interpreted as elements of GF(2 ^t ) and form a single superblock of the modular polynomial code , which allows you to increase the corrective ability of recovery tools in the face of restrictions on the allowable resource costs.

вычисляемых при запросе на использование данных, подлежащих защите, а для восстановления целостности блоков данных M_i,j,г выполнить процедуру реконфигурации системы путем исключения из вычислений блока данных с признаками нарушения целостности. Новым является то, что многомерный массив данных размерности к представляется в виде 3-мерного массива данных М[k, k, k], состоящего из k³ блоков данных M_i,j,r, которые для контроля целостности будут размещаться в массиве размерности k+1, заполняя при этом от 0 до k - 1 его блоков, при этом свободные блоки массива будут предназначаться для эталонных хэш-кодов H_i,j,r. Новым является то, что для восстановлении целостности блоки данных M_i,j,_r, подлежащие защите, а также вычисленные от них эталонные хэш-коды H_i,j,r будут интерпретироваться как элементы GF(2^t) и являться наименьшими полиномиальными вычетами по основаниям

Новым является то, что полученный 3-мерный массив данных М[k+1, k+1, k+1], содержащий блоки данных M_i,j,r и эталонные хэш-коды H_i,j,r, будет рассматриваться как единый суперблок модулярного полиномиального кода, над которым выполняется операция расширения путем введения n - k избыточных оснований, для которых вычисляются соответствующие им 3k²(n - k) избыточных вычетов, что позволяет повысить вероятность исправления возникающих ошибок, приводящих к нарушению целостности данных, подлежащих защите.The control and restoration of the integrity of k ³ data blocks M _i,j , _r will be carried out by calculating 3k ² hash codes H _i,j,r from them, which will be interpreted as elements of GF(2 ^t ) and form a single superblock of a modular polynomial code , which will allow at time t under conditions of restrictions on the allowable resource costs to detect signs of integrity violation to compare the values of the hash codes H _i,j,r with the values of the hash codes

computed when requesting the use of data to be protected, and to restore the integrity of data blocks M _{i, j, r,} perform the system reconfiguration procedure by excluding from calculations a data block with signs of integrity violation. What is new is that a multidimensional data array of dimension k is represented as a 3-dimensional data array M[k, k, k], consisting of k ³ data blocks M _i,j,r , which, for integrity control, will be placed in an array of dimension k +1, while filling from 0 to k - 1 of its blocks, while the free blocks of the array will be intended for the reference hash codes H _i,j,r. What is new is that to restore the integrity of the data blocks M _i,j , _r to be protected, as well as the reference hash codes H _i,j,r calculated from them, will be interpreted as elements of GF(2 ^t ) and will be the least polynomial residues in grounds

What is new is that the resulting 3-dimensional data array M[k+1, k+1, k+1], containing data blocks M _i,j,r and reference hash codes H _i,j,r , will be considered as a single superblock of a modular polynomial code, on which the expansion operation is performed by introducing n - k redundant bases, for which the corresponding 3k ² (n - k) redundant residues are calculated, which makes it possible to increase the probability of correcting errors that occur, leading to a violation of the integrity of the data to be protected .

c) Causal relationship between features and technical result

Thanks to a new set of essential features, the method implements the possibility of:

- integrity control of a multidimensional data array with low redundancy of control information;

- localization of data blocks with signs of integrity violation;

- restoration of the integrity of a multidimensional data array with low redundancy;

- increasing the corrective ability of recovery tools under conditions of restrictions on the allowable resource costs.

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 - a scheme for applying a hash function with the calculation of one common hash code from k data blocks;

fig. 2 is a diagram of the application of the hash function with the calculation of one hash code from each of the data blocks;

fig. 3 is a diagram of the application of the hash function with the construction of a fully connected hash network;

fig. 4 is a diagram illustrating the procedure for monitoring and restoring the integrity of data represented as a two-dimensional array of data blocks;

fig. 5 is a diagram of a 3-dimensional cube containing blocks of data M _i,j,r ;

fig. 6 - order of location in the cube dimension k=3 data blocks to be protected, and hash codes;

fig. 7 - hashing network for detection and localization of 1-fold error;

fig. 8 - hashing network for detection and localization of 2-fold errors;

fig. 9 - dependencies of the change in the probabilities P _isp.1 , P _isp.2 on the dimension k;

fig. 10 - the arrangement of redundant data blocks in accordance with the entered links in a 3-dimensional cube.

Implementation of the invention

A multidimensional data array is represented as a p-dimensional array consisting of elements M _ψ1 , …, _ψp , where the indices ψ ₁ , …, ψ _p take values from 1 to k _a ( a =1, …, p), respectively. In this case, the p-dimensional data array will contain k ₁ ×k ₂ ×…×k _p elements and will be denoted as

A multidimensional data array M[k ₁ , k ₂ , ..., k _p ] is a mathematical set with a certain structure and axiomatic rules, which allows us to consider it similarly to space, and the elements contained in it (data blocks M _ψ1 , ..., _ψp ) - like points in space. Such a space will be called the data space.

The data space will be considered a discrete metric space, since it contains points in its structure, represented by array elements isolated from each other in a certain sense. Inside the multidimensional data array M[k ₁ , k ₂ , …, k _p ] all elements (data blocks M _ψ1 , …, _ψp ) are located along abstract lines parallel to the coordinate axes at equal distances from each other.

Example 1. A 3-dimensional data array M[k ₁ , k ₂ , k ₃ ] can be represented as a 3-dimensional cube (Fig. 5) containing a coordinate system with axes: x, y, z, along which blocks are plotted data M _i,j,r (i = 0, 1, …, k ₁ - 1; j = 0, 1, …, k ₂ - 1; r = 0, 1, …, k ₃ - 1).

Let's represent a 3-dimensional data array M[k ₁ , k ₂ , k ₃ ] in the following form:

» с индексом (z) показывает порядок представления массива посредством сечений, ориентированных по оси z; стрелки «→» и «↓» с индексами (x) и (у) указывают направления, в которых возрастают соответствующие индексы у элементов массива по осям х и у.where is the arrow

» with index (z) shows the order of the array representation by means of sections oriented along the z axis; the arrows "→" and "↓" with indices (x) and (y) indicate the directions in which the corresponding indices y of the array elements along the x and y axes increase.

If all dimensions of a hypercube containing data blocks have the same values (k ₁ = k ₂ = ... = k _p ), then it will be a regular figure, and its size can be described by one number k, equal to the number of data blocks located on his rib. Such a hypercube will be called a hypercube of dimension k.

In this case, a 3-dimensional data array M[k, k, k]={M _i,j,r } of dimension k can be represented using orientation sections (z) in the following form:

where i, j, r = 0, …, k - 1.

Let's place a 3-dimensional data array (1) of dimension k in an array of dimensions k + 1, represented by a 3-dimensional cube, filling from 0 to k - 1 of its blocks.

With this arrangement, out of (k+1) ³ blocks of a 3-dimensional cube, k ³ blocks are dedicated to storing blocks of data to be protected.

The 3-dimensional data array (1) will take the form:

where "0" denotes a writable cube block.

To detect signs of violation of the integrity of multidimensional data arrays (data blocks M _{i, j} , _r (i, j, r = 0, …, k - 1)) we apply the hash function h to the elements of array (2).

Let's place the obtained reference hash codes H _i,j,r (i, j, r = 0, …, k) into the cube blocks free for writing.

The resulting 3-dimensional array containing data blocks and hash codes, using orientation sections (z), can be represented as follows:

Thus, the resulting 3-dimensional array (3) can be represented as a 3-dimensional cube containing (k + 1) ³ blocks, including:

- k ³ blocks of data M _i,j , _r (i, j, r = 0, ..., k - 1) to be protected;

- 3k ² blocks with hash codes H _i,j,r (i, j, r = 0, …, k);

- 3k + 1 free blocks to write.

At the same time, blocks with reference hash codes calculated from them are added along three axes to each block of data to be protected, which are used to detect data with signs of integrity violation.

Under the violation of the integrity of one data block, we mean the occurrence of an error in it, respectively, the violation of the integrity of q data blocks is determined by the occurrence of a q-fold error.

The detection of a data block with signs of integrity violation is performed by comparing the values of the reference hash codes previously calculated from it and the hash codes calculated when requesting its use. In case of a mismatch between the compared hash codes, a conclusion is made about the occurrence of an error and its syndrome is determined.

Under the error syndrome, we mean the binary number obtained by writing the symbol "0" for each performed check for the compliance of the values of the calculated and reference hash code and the symbol "1" if the compared values do not match.

Example 2. To control the integrity of multidimensional data arrays, let's place in a 3-dimensional cube (Fig. 6) data blocks to be protected and their corresponding hash codes.

In this case, the data blocks M _i,j,r to be protected, and the reference hash codes H _i,j,r calculated from them, are interpreted as binary vectors:

g=1, 2, …, t.where

g=1, 2, …, t.

The resulting 3-dimensional array using orientation sections (x) can be represented as follows:

in this case, each hash code is calculated from two data blocks located with it in one row or one column of the array.

Example 3. Hash codes H ₀₀₂ , H ₀₁₂ , H ₀₂₀ , H ₀₂₁ are calculated as follows:

where "||" - operation of concatenation (combination).

Let us build a hashing network (Fig. 7) to enable detection and localization of a 1-fold error.

In this case, each block of data M _i,j,r will correspond to a non-repeating set of three hash codes H _i,j,r .

Example 4. In accordance with the constructed hashing network (Fig. 7), the following hash codes correspond to data blocks M ₁₀₀ , M ₀₁₁ :

- for M ₁₀₀ : N ₁₂₀ , N ₁₀₂ , N ₂₀₀ ;

- for M ₀₁₁ : H ₀₂₁ , H ₀₁₂ , H ₂₁₁ ,

moreover, the resulting sets of hash codes for all data blocks will be non-repeating.

Let's build a table of error syndromes that lead to a violation of the integrity of the data block M _i,j , _r , in which the place of the error is determined by the presence of the symbol "1" in the corresponding columns and rows.

Example 5. Syndromes of 1-fold errors, leading to a violation of the integrity of data blocks [M ₁₀₀ ] and [M ₀₁₁ ], are presented in table 1.

The hashing network and the corresponding table of error syndromes for detecting and localizing q data blocks with signs of integrity violations are built according to similar rules.

The hash network for 2-fold error detection and localization is shown in FIG. eight.

Example 6. Syndromes of 2-fold errors leading to a violation of the integrity of data blocks [M ₁₀₀ ] and [M ₁₁₀ ], as well as [M ₀₀₁ ] and [M ₀₁₁ ], are presented in Table 2.

To restore the integrity of multidimensional data arrays, the data blocks M _i,j,r to be protected, as well as the reference hash codes H _i,j,r calculated from them, will be interpreted as elements of GF(2 ^t ):

g=t - 1, t - 2, …, 0;

- фиктивная переменная.where

g=t - 1, t - 2, …, 0;

is a dummy variable.

таким, чтоIn this case, data blocks and reference hash codes will be the smallest polynomial residues in bases

such that

представлены при помощи сечений ориентации (x);where are the bases

represented by orientation sections (x);

i ₁ , i ₂ = 0, 1, …, k; i ₁ ≠ i ₂ .

Wherein

- степень полинома

where

- polynomial degree

The resulting 3-dimensional array, represented by orientation sections (x):

will be considered as a single superblock of the modular polynomial code (MPC) according to the base system:

In accordance with the Chinese remainder theorem for polynomials represented in the form (7) and satisfying condition (4), and polynomials represented in the form (6) such that condition (5) is satisfied, the system of comparisons:

has the only solution

Let's perform the IPC expansion operation by introducing n - k redundant bases:

We obtain the corresponding excess residues:

Получим расширенный МПК в кольце многочленов:Moreover, condition (4) is satisfied, and condition (5) takes the form:

We get the extended MPC in the ring of polynomials:

Let's place the redundant data blocks in the cells of the 3-dimensional array free for writing, which can be represented by means of orientation sections (x) in the following form:

The resulting 3-dimensional array (10) can be represented as a 3-dimensional cube and contains (n+1) ³ blocks, including:

- k ³ blocks of data M _i,j,r (i, j, r = 0, ..., k - 1) to be protected;

- 3k ² blocks with hash codes H _i,j,r (i, j, r = 0, …, k);

- 3k ² (n - k) redundant data blocks, as well as free blocks for writing.

In this case, to restore the integrity of k ³ + 3k ² data blocks to be protected and the reference hash codes calculated for data integrity control, 3k ² (n - k) redundant data blocks are required.

The data to be protected, presented in the form (10), is sent to storage.

When requesting the use of data after monitoring their integrity, if an error is detected, a procedure for restoring the integrity of the data is performed.

In accordance with the rules for decoding modular codes (Akushsky I.Ya., Yuditsky D.M. Machine arithmetic in residual classes. - M .: Soviet radio, 1968. - 604 p.), the criterion for the absence of detectable errors in the extended IPC (9) is fulfillment of the inequality:

- решение системы (8) для

символ «(⋅)'» указывает на возможное нарушение целостности данных.where

- solution of system (8) for

the symbol "(⋅)'" indicates a possible violation of data integrity.

The criterion for the detected error is the fulfillment of the inequality:

выполняется путем вычисления наименьшего вычета:Block Integrity Restoration

is done by calculating the smallest residue:

повторно вычислено с учетом исключения искаженного блока данных

where

recalculated taking into account the elimination of the corrupted data block

In the developed method, in comparison with the prototype, under the restrictions imposed on the recovery tools, depending on the dimension k, the maximum number of possible q data blocks with integrity violation in the cube is determined as follows:

q=k ³ .

In this case, to restore the integrity of all corrupted data blocks, 3k ² redundant data blocks will be required. At the same time, in the prototype, the classic use of redundant IPC, which corrects q or less errors, if n - k≥2q, 2k ³ redundant data blocks are required.

The dependences of the probabilities P of _correcting the errors that occur are shown in Fig. 9, where - R _isp.1 - probability, when using the developed method, P _isp.2 - probability, when using the prototype.

искаженных блоков данных, как при классическом применении избыточного МПК, но и других блоков данных, подлежащих защите, в соответствии с введенными связями в 3-мерном кубе при восстановлении целостности многомерных массивов данных (фиг. 10).The increase in the probability of correcting errors that occur due to the use of the developed method is explained by the fact that n - k redundant data blocks are used to restore the integrity of not only

distorted data blocks, as in the classical use of redundant IPC, but also other data blocks to be protected, in accordance with the introduced links in a 3-dimensional cube when restoring the integrity of multidimensional data arrays (Fig. 10).

Claims (1)

A method for monitoring and restoring the integrity of multidimensional data arrays, which consists in the fact that for the implementation of integrity control, data blocks M _i (i=1, 2, ..., n) are represented as subblocks of fixed length M _i , _l, M _i , ₂ , ... , M _i,n , from which the reference hash codes H _i of the hash function h(M _i ) are preliminarily calculated, the values of which are subsequently compared with the values of the hash codes

hash functions

computed already from the checked data blocks

whose subblocks are also subblocks of data blocks M _j (j=1, 2, …, n), which, in order to restore data integrity in case of its violation, are formed according to the rules similar to the rules for constructing redundant modular codes, while providing for subblocks M _1,j , M ₂ ,j, …, M _n,j , which are an information group of n subblocks, designed to uniquely restore data blocks M _j in case of violation of their integrity, calculation of the control group (k - n) of subblocks M _n+1,j , M _n+2,j , …, M _k,j , additionally introduced to correct the error, in the event of which the restoration of data blocks M _j without prejudice to the uniqueness of their representation is carried out by reconfiguring the system by excluding the subblock [M _i,j ] from the calculations with an error, characterized in that the multidimensional data array of dimension k is represented as a 3-dimensional data array M[k, k, k], consisting of k ³ data blocks M _i,j,r (i=j=r=0 , 1, …, k - 1), which for co Integrity controls will be placed in an array of dimensions k + 1, while filling from 0 to k-1 of its blocks, to which the hash function h is applied to detect signs of integrity violations, while the calculated hash codes H _{i, j, r} (i , j, r = 0, …, k) will be placed in 3k ² free blocks of the array and will be reference values, the values of which are compared with the values of the hash codes when requesting to use the data

hash functions

already calculated from the data blocks being checked when

integrity restoration, the data blocks M _i,j,r to be protected, as well as the reference hash codes H _i,j,r calculated from them, will be interpreted as elements of GF(2 ^t ) and will be the least polynomial residues in bases

in this case, the resulting 3-dimensional data array M[k+1, k+1, k+1] will be considered as a single superblock of the modular polynomial code, on which the expansion operation is performed by introducing n - k redundant bases

for which the corresponding 3k ² (n - k) excess residues are calculated, additionally introduced to correct the error, in the event of which the restoration of data blocks M _i,j,r without prejudice to the uniqueness of their representation is carried out by reconfiguring the system by excluding the data block from the calculations with signs of integrity.

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