RU2808761C1 - Method for controlling data integrity based on the rules for construction of cryptographic fractal - Google Patents

Abstract

FIELD: storage systems.

SUBSTANCE: methods for monitoring data integrity in storage systems. The technical result is achieved by fragmenting the M data block into M⁽¹⁾, M⁽²⁾, M⁽³⁾ data blocks of a fixed length, each of which, in turn, is also fragmented into data blocks, to which the h hash function is applied to control integrity, and the hashing scheme is based on the rules for constructing Pascal’s triangle and is presented in the form of a triangular-shaped table, obtained for data blocks M ^(ϕ), the schemes for applying the h hash function are combined into a common scheme, which is intermediate and the M data block to be protected is designated as M^(I), when constructing two other schemes according to the same rules for other M^(II), M^(III) data blocks and combining them in the order presented for the M data block, the resulting data integrity control scheme is a scheme based on the rules for constructing a cryptographic fractal.

EFFECT: ensuring data integrity control without introducing additional control information.

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Description

Field of technology to which the invention relates

The present invention relates to information technology and can be used to control the integrity of data in storage systems through the application of cryptographic hash functions to protected data blocks under the influence of destabilizing factors.

State of the art

a) Description of analogues

There are known methods for monitoring data integrity through the use of cryptographic methods: key hashing, electronic signature means (Patent for invention RUS No. 2620730 12/07/2015; Patent for invention RUS No. 2669144 11/28/2017; Patent for invention RUS No. 2680033 05/22/2017; Patent for invention RUS No. 2680350 05/02/2017; Patent for invention RUS No. 2680739 11/28/2017; Patent for invention RUS No. 2686024 04/25/2018; Patent for invention RUS No. 2696425 05/22/2018; Patent for invention RUS No. 2707940 0 12/2/2019; Patent for invention RUS No. 2726930 07.16.2020; Patent for invention RUS No. 2758194 10.26.2021; Patent for invention RUS No. 2771146 04.27.2022; Patent for invention RUS No. 2771208 04.28.2022; Patent for invention RUS No. 2771209 2 04/08/2022; Patent for invention RUS No. 2771236 04.28.2022; Patent for invention RUS No. 2771238 04.28.2022; Patent for invention RUS No. 2771273 04.29.2022; Patent for invention RUS No. 2774099 06.15.2022; Patent for invention RUS No. 2785484 0 12/8/2022; Patent for invention RUS No. 2785800 12/13/2022; Patent for invention RUS No. 2785862 12/14/2022; Patent for invention RUS No. 2786617 12/22/2022; Patent for invention RUS No. 2793782 04/06/2023; Knut D.E. The art of computer programming. Volume 3 sorting and searching [Text] / D.E. Knut. - M.: "Mir", 1978. - 824 p.; Menezes, A.J. Handbook of Applied Cryptography [Text] / A.J. Menezes, Paul C. van Oorschot, Scott A. Vanstone. - M.: CRC Press, Inc., 1996. - 816 p.; Biham, E. A framework for iterative hash functions. - HAIFA [Text] / E. Biham, O. Dunkelman. - M.: HAIFA, ePrint Archive, Report 2007/278. - 20 s; Same [Electronic pecypc]. - Access mode: eprint.iacr.org/2007/278.pdf (July, 2007); Wang, X. How to break MD5 and Other Hash Function [Text] / X. Wang, H.Yu. - M.: EUROCRYPT 2005, LNCS 3494, Springer-Verlag 2005. - pp. 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 s; The same [Electronic resource]. Available at: eprint.iacr.org/2006/043.pdf (2006); 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; Samoylenko, D. Protection of information from imitation on the basis of crypt-code structures / D. Samoylenko, M. Eremeev, O. Finko, S. Dichenko // Advances in Intelligent Systems and Computing. 2019. No. 889. P. 317-331.; Dichenko, S.A. A conceptual model for ensuring information integrity in modern data storage systems. Computer science: problems, methodology, technologies. Collection of materials of the XIX International Scientific and Methodological Conference. Ed. D.N. Borisova. Voronezh. - 2019. -S. 697-701, for which two generalized schemes for obtaining hash codes are typical: for each subblock in a data block and for the entire data block.

The disadvantages of these methods are:

- high redundancy when monitoring the integrity of the sequence of subblocks of a small data block (when hashing each subblock in the data block);

- inability to localize corrupted subblocks in a data block (when hashing an entire data block);

- the inability to monitor data integrity without introducing additional control information commensurate with the volume of increased data when scaling storage systems.

b) Description of the closest analogue (prototype)

The closest in technical essence to the claimed invention (prototype) is a method for monitoring data integrity based on Pascal’s cryptographic triangle (Method for monitoring data integrity based on Pascal’s cryptographic triangle / S.A. Dichenko, D.V. Samoilenko, O.A. Finko / / Patent for invention RU 2730365, August 21, 2020. Application No. 2019143386 dated December 19, 2019), where data integrity is monitored by comparing hash code values calculated when requesting the use of protected data located on the lateral edges of the triangle with reference hash values -codes calculated earlier (Fig. 1). At the same time, thanks to the mechanism of cyclic calculation of hash codes located at the vertices of the triangle, the integrity of the reference hash codes themselves is monitored.

The disadvantage of this known method is the inability to monitor data integrity without introducing additional control information commensurate with the volume of increased data when scaling storage systems.

Disclosure of the Invention

a) The technical result to be achieved by the invention

The purpose of the present invention is to develop a method for monitoring data integrity based on the application of cryptographic hash functions to protected data blocks with the ability to monitor data integrity without introducing additional control information commensurate with the volume of increased data when scaling storage systems.

b) Set of essential features

This goal is achieved by the fact that in the known method of monitoring data integrity, which consists in the fact that the detection and localization of an error occurring in the subblocks m ₁ , m ₂ , ..., m _k of the data block M, located on the side edges of the triangle, is ensured by calculating the hash group -codes according to the rules for constructing Pascal’s triangle and comparing them with the reference ones, in the presented method, the data block M, presented in the form of a vector, to monitor the integrity of the data contained in it is fragmented into data blocks M ⁽¹⁾ , M ⁽²⁾ , M ^{( 3)} fixed length, each of which, in turn, is also fragmented into data blocks , where ϕ=1, 2, 3; i=1, 2, …, n; j=1, 2, to which the hash function h is applied to control integrity, and the hashing scheme is based on the rules for constructing Pascal’s triangle and is presented in the form of a triangular-shaped table, with data blocks sequentially placed on the sides of the resulting triangle , to be protected, where i=1, 2, …, n; j=1, 2, intermediate results of transformations are placed inside the triangle , where i=1, 2, …, n-1; j=1, 2, …, n-1, calculated from data blocks , subject to protection, where i=1; j=1, 2, data blocks , subject to protection, where i=2, …, n-1; j=1, 2, and blocks with values hash function h, where i=1, 2, …, n-2; j=1, 2, …, n-2, calculated at the previous level of the triangle, on the lower side of the triangle there are blocks with values hash function h, where i=n; j=1, 2, …, n, which are calculated from data blocks , subject to protection, where i=n; j=1, 2, and the results of intermediate lower-level transformations , ,..., , used to control the integrity of data blocks , where i=1, 2, …, n; j=1, 2, then obtained for data blocks M ^(ϕ) , where ϕ=1, 2, 3, schemes for applying hash function h, having triangular shapes, are combined into a general scheme in which schemes for applying hash function h for data blocks M ⁽²⁾ and M ⁽³⁾ relative to the scheme of applying the hash function h for data block M ⁽¹⁾ will be rotated counterclockwise and clockwise, respectively, from blocks with values hash function h, where i=n; j=1, 2, …, n, n+1, n+2, placed on the lower sides of the triangles, k blocks with hash function values h are calculated sequentially in a certain order, among which one or more blocks with hash function values h , applied to elements from each data block M ⁽¹⁾ , M ⁽²⁾ and M ⁽³⁾ , used to detect and localize value blocks hash function h, where i=n; j=1, 2, …, n, allowing to detect and localize data blocks , to be protected, where i=1, 2, …, n; j=1, 2, the resulting scheme for using a hash function to control the integrity of a data block M is intermediate and the data block M to be protected is denoted as M ^(I) , when constructing two other schemes according to the same rules for other data blocks M ^{( II)} , M ^(III) and combining them in the order presented for the data block M, we obtain a data integrity monitoring scheme based on the rules for constructing a cryptographic fractal - the Sierpinski triangle, which includes schemes for monitoring the integrity of data blocks M ^(I) , M ^{(II )} , M ^(III) which are intermediate for the circuit for monitoring the integrity of data blocks M' ^(I) , M' ^(II) , M' ^(III) which, in turn, will be intermediate for the circuit for monitoring the integrity of data blocks M'' ^(I) , M'' ^(II) M'' ^(III) .

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 fragmenting the data block M into data blocks M ⁽¹⁾ , M ⁽²⁾ , M ⁽³⁾ of a fixed length, each of which, in turn, is also fragmented into data blocks , where ϕ=1, 2, 3; i=1, 2, …, n; j=1, 2, to which the hash function h is applied to control integrity, and the hashing scheme is based on the rules for constructing Pascal’s triangle and is presented in the form of a table with a triangular shape, obtained for data blocks M ^(ϕ) , where ϕ =1, 2, 3, the schemes for applying the hash function h are combined into a common scheme in which the schemes for applying the hash function h for data blocks M ⁽²⁾ and M ⁽³⁾ relative to the scheme for applying the hash function h for the data block will be rotated counterclockwise and clockwise, respectively, which allows you to detect and localize data blocks with signs of integrity violations under the influence of destabilizing factors using common hash function values.

The integrity of the data block M will be monitored by comparing the values of the hash function h, calculated when requesting the use of protected data, and the reference values, which will allow at time t, under the influence of destabilizing factors, to determine data blocks with signs of integrity violation. What is new is that in the proposed method, the data block M is fragmented into data blocks M ⁽¹⁾ , M ⁽²⁾ , M ⁽³⁾ of a fixed length, each of which, in turn, is also fragmented into data blocks , where ϕ=1, 2, 3; i=1, 2, …, n; j=1, 2, to which the hash function h is applied to control integrity, and the hashing scheme is based on the rules for constructing Pascal’s triangle and is presented in the form of a table with a triangular shape, obtained for data blocks M ^(ϕ) , where ϕ =1, 2, 3, the schemes for applying the hash function h are combined into a common scheme. What is new is that the resulting scheme for using a hash function to control the integrity of a data block M is intermediate and the data block M to be protected is designated as M ^(I) , when constructing two other schemes according to the same rules for other data blocks M ^{(II )} , M ^(III) and combining them in the order presented for the data block M, we obtain a data integrity monitoring scheme based on the rules for constructing a cryptographic fractal - the Sierpinski triangle, which includes schemes for monitoring the integrity of data blocks M ^(I) , M ^(II) , M ^(III) , which are intermediate for the data block integrity monitoring circuit M' ^(I) , M' ^(II) , M' ^(III) which, in turn, will be intermediate for the data block integrity monitoring circuit M'' ^(I) , M'' ^(II) , M'' ^(III) .

c) Cause-and-effect relationship between characteristics and technical result

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

- detection of a data block with signs of integrity violation under the influence of destabilizing factors;

- localization of a detected data block with signs of integrity violation;

- monitoring data integrity without introducing additional control information commensurate with the volume of increased data when scaling storage systems.

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

The analysis of the level of technology 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 that the claimed method complies with the patentability condition of “novelty”.

The results of a search for known solutions in this and related fields of technology in order to identify features that coincide with the features of the claimed object that are distinctive from the prototype, showed that they do not follow explicitly from the prior art. The prior art also does not reveal the knowledge of distinctive essential features that determine the same technical result that was achieved in the claimed method. Therefore, the claimed invention meets the patentability requirement of “inventive step”.

Brief description of drawings

The claimed method is illustrated by drawings, which show:

fig. 1 - scheme for using a hash function based on the rules for constructing Pascal’s triangle;

fig. 2 - diagram of applying the hash function h to data blocks M ^(ϕ) to be protected;

fig. 3 - general scheme for applying the hash function h to data blocks M ⁽¹⁾ , M ⁽²⁾ , M ⁽³⁾ to be protected;

fig. 4 is a diagram illustrating the procedure for obtaining blocks with values H ^(ϕ) at the first step of applying the hash function h;

fig. 5 is a diagram illustrating the procedure for obtaining blocks with values H ^(ϕ) in the second step of applying the hash function h;

fig. 6 is a diagram illustrating the procedure for obtaining blocks with values H ^(ϕ) at the third step of applying the hash function h;

fig. 7 is a diagram illustrating the procedure for obtaining blocks with values H ^(ϕ) at the fourth step of applying the hash function h;

fig. 8 is a diagram illustrating the procedure for obtaining blocks with values H ^(ϕ) at the fifth step of applying the hash function h;

fig. 9 is a general view of a hashing network for a scheme for applying hash function h;

fig. 10 - diagram of applying hash function h to data blocks M ⁽¹⁾ to be protected (with n=6);

fig. 11 - hashing network for the scheme for applying hash function h (with n=6);

fig. 12 is a diagram of the use of a hash function h to control the integrity of a data block M;

fig. 13 - scheme for monitoring data integrity based on the rules for constructing a cryptographic fractal - the Sierpinski triangle.

Carrying out the invention

By analogy with the standard (GOST R 53111-2008. Stability of the functioning of a public communication network. Requirements and verification methods. - M.: Standartinform, 2009. - 15 p.), destabilizing factors are understood as impacts on the data storage system (DSS), source which is a physical or technological process of an internal or external nature in relation to the storage system, leading to the failure of its elements. At the same time, the implementation of threats to information security can be carried out as a result of both the destructive effects of an attacker and disturbances in the operating environment of the storage systems in question. Objects of influence can be information (data), software and hardware for processing and storing information (automated workstations, servers, etc.), software (system and application software, virtualization systems, etc.), machine storage media containing both protected information and authentication information, information security tools, etc.

Under the influence of destabilizing factors when storing information, it is possible that it may be distorted and/or destroyed, that is, its integrity may be violated. Violation of the integrity of data arrays, in turn, will be characterized by the appearance of an error in data blocks, that is, a discrepancy between the data sent for storage and the data when requesting their use.

Data block M to be protected, represented as a vector:

where μ _g ∈ {0,1} (g=1, 2, …, τ), to monitor the integrity of the data contained in it, it is fragmented into data blocks of a fixed length:

where "||" denotes the concatenation (union) operation.

Each of the received data blocks M ^(ϕ) (ϕ=1, 2, 3), in turn, is also fragmented into data blocks (i=1, 2, …,n; j=1, 2), to which the hash function h is applied to control data integrity. Scheme for applying hash function h to received data blocks is based on the rules for constructing Pascal’s triangle (Uspensky V.A., Pascal’s Triangle / V.A. Uspensky. - M.: Nauka, 1979. - 48 p.) and is presented in the form of a table having a triangular shape (Fig. 2).

Data blocks are placed sequentially along the sides of the resulting triangle. (i=1, 2, …, n; j=1, 2), to be protected, inside the triangle - intermediate results of transformations (blocks with values (i=1, 2, …, n-1; j=1, 2, …, n-1) hash functions h), calculated from:

- data blocks (i=1; j=1, 2) to be protected:

- data blocks (i=2, …, n-1; j=1, 2) to be protected, and blocks with values (i=1, 2, …, n-2; j=1, 2, …, n-2) hash function h, calculated at the previous level of the triangle, for example:

- blocks with values (i=1, 2, …, n-2; j=1, 2, …, n-2) hash function h, calculated at the previous level of the triangle, for example:

on the bottom side of the triangle - blocks with values (i=n; j=1, 2, …, n) hash functions h, which are calculated from data blocks (i=n; j=1, 2) to be protected, and the results of intermediate lower-level transformations:

Blocks with values (i=n; j=1, 2, …, n, n+1, n+2) will subsequently be used to monitor the integrity of data blocks (i=1, 2, …, n; j=1, 2).

Next, the schemes for applying the hash function h, having triangular shapes, obtained for data blocks M ^(ϕ) (ϕ = 1, 2, 3) are combined into a general scheme (Fig. 3), in which the schemes for applying the hash function h for data blocks M ⁽²⁾ and M ⁽³⁾ with respect to the hash function h for data block M ⁽¹⁾ will be rotated counterclockwise and clockwise, respectively.

From blocks with values (i=n; j=1, 2, …, n, n+1, n+2) hash functions h placed on the lower sides of the triangles, k blocks with hash function h values are calculated sequentially in a certain order, among which - one or more (depending on the value of n) blocks with the values of the hash function h applied to elements from each data block M ⁽¹⁾ , M ⁽²⁾ and M ⁽³⁾ .

Example 1

For data blocks M ^(ϕ) (ϕ=1, 2, 3), we will construct schemes for using the hash function h.

With n=6 on the bottom side of each triangle we get blocks with values ,..., hash functions h. We sequentially calculate the hash function h values from them.

At the first step, by applying the hash function h, we obtain blocks with the values , And :

and place them as shown in Fig. 4.

In the second step, by applying the hash function h, we obtain blocks with the values , , , , And

and place them as shown in Fig. 5.

In the third step, by applying the hash function h, we obtain blocks with the values , , , , , , , , , , And

and place them as shown in Fig. 6.

In the fourth step, by applying the hash function h, we obtain blocks with the values , , , , And

and place them as shown in Fig. 7.

At the fifth step we get a block with the value hash function h applied to elements from each data block M ⁽¹⁾ , M ⁽²⁾ and M ⁽³⁾ :

and place it as shown in Fig. 8.

Thus, the kth block with the value hash function h that is applied to elements from each data block M ^(ϕ) is common to all data blocks (i=1, 2, …, n; j=1, 2), subject to protection.

The superscript ϕ of the computed blocks with values H ^(ϕ) of hash function h is determined by the superscripts of the blocks with values to which hash function h is applied.

Example 2

Block with value hash function h has a superscript of “1”, since to calculate it, the hash function h is applied to blocks with values And , having a superscript "1".

Block with value hash function h has a superscript equal to “1, 2”, since to calculate it, hash function h is applied to blocks with values And , having superscripts “1” and “2”.

Thus, the superscripts of blocks with values H ^(ϕ) of the hash function h indicate the elements of which data blocks M ^(ϕ) (ϕ = 1, 2, 3) to be protected are involved in their calculation.

One or more (depending on the value of n) blocks with values H ^(1,2,3) of the hash function h are defining elements of the schemes for applying the hash function h to all data blocks M ⁽¹⁾ , M ⁽²⁾ and M ⁽³⁾ subject to protection. At the same time, monitoring the integrity of data blocks (i=1, 2, …, n; j=1, 2) to be protected is carried out by comparing the values H ^(1,2,3) of the hash function h, calculated when requesting the use of protected data, with their reference values , previously calculated and stored in a reliable environment.

When monitoring data integrity, in the event of a discrepancy between the calculated and reference values H ^(1,2,3) of the hash function h, a decision is made to violate the integrity of the data block M to be protected.

Example 3 (source data taken from Example 1. A case is considered in which the integrity of one data block may be violated ).

To detect and localize a block of data (i=1, 2, …, n; j=1, 2) with signs of integrity violation, the following actions are performed:

- calculated and reference values are compared , , , , And , to whose blocks the hash function h was applied to obtain a block with the value ;

- among the compared values, a value is determined that does not correspond to the reference value, for example, this value . Consequently, a decision is made that the data block with signs of integrity violation is located in the data blocks or M ⁽³⁾ ;

- calculated and reference values are compared , , , to whose blocks the hash function h was applied to obtain a block with the value ;

- among the compared values, a value is determined that does not correspond to the reference value, for example, this value . Consequently, a decision is made that the data block with signs of integrity violation is located in the data block M ⁽¹⁾ or M ⁽³⁾ ;

- calculated and reference values are compared , , to whose blocks the hash function h was applied to obtain a block with the value ;

- among the compared values, a value is determined that does not correspond to the reference value, for example, this value . Consequently, a decision is made that the data block with signs of integrity violation is located in the data block M ⁽¹⁾ or M ⁽³⁾ ;

- calculated and reference values are compared , , to whose blocks the hash function h was applied to obtain a block with the value ;

- among the compared values, values that do not correspond to the reference ones are determined, for example, these are the values , . Consequently, a decision is made that the data block with signs of integrity violation is located in the data block M ⁽¹⁾ or M ⁽³⁾ ;

- calculated and reference values are compared , , to whose blocks the hash function h was applied to obtain a block with the value ;

- among the compared values, a value is determined that does not correspond to the reference value, for example, this value .

Thus, a decision is made that a data block with signs of integrity violation is located in the data block M ⁽¹⁾ , since values that do not correspond to the reference ones are determined, contained in blocks with values And .

To detect and localize a block of data (i=1, 2, …, n; j=1, 2) with signs of integrity violation after detection and localization of blocks with values (i=n; j=1, 2, …, n, n+1, n+2), which do not correspond to the reference ones, a hashing network is built.

Hash network for a scheme for applying a hash function h to blocks of data , based on the rules for constructing Pascal's triangle (Fig. 2), is presented in Fig. 9.

Example 4: For a data block (i=1, 2, …, n; j=1, 2), with n=6, the scheme for applying the hash function, based on the rules for constructing Pascal’s triangle, is presented in Fig. 10.

The hashing network for the hash function application scheme (FIG. 10) is shown in FIG. eleven.

Based on the hashing network (Fig. 11), we compile Table 1, where “[⋅]” denotes the detected and localized data block (i=1, 2, …, n; j=1, 2).

In accordance with the values of integrity violation syndromes presented in Table 1, a decision is made that a data integrity violation occurred in the data block , since the calculated values And do not correspond to the reference ones.

The resulting scheme for using a hash function to control the integrity of a data block M is presented in Fig. 12.

The scheme for using a hash function to control the integrity of a data block M, shown in FIG. 12 is intermediate. The data block M to be protected is designated as M ^(I) , two other schemes are built according to the same rules for the other data blocks M ^(II) and M ^(III) and combined in the order presented for the data block M. We obtain an integrity monitoring scheme data based on the rules for constructing a cryptographic fractal, in particular, the Sierpinski triangle.

In fig. Figure 13 shows a data integrity monitoring scheme based on the rules for constructing the Sierpinski triangle, which includes data block integrity monitoring schemes M ^(I) , M ^(II) , M ^(III) , which are intermediate for the data block integrity monitoring scheme M' ^(I) , M' ^(II) , M' ^(III) , which, in turn, will be intermediate for the circuit for monitoring the integrity of data blocks M'' ^(I) , M'' ^(II) , M'' ^(III) and so on Further.

Thus, the presented scheme (Fig. 13) will have the property of self-similarity (based on the rules for constructing the Sierpinski triangle, which is a geometric fractal) and, as a consequence, its use when scaling data storage systems will allow monitoring their integrity without introducing additional control information, commensurate with the volume of data being increased.

Claims (1)

A method for monitoring data integrity based on the rules for constructing a cryptographic fractal, which consists in the fact that detection and localization of an error occurring in subblocks m ₁ , m ₂ , ..., m _k of the data block M located on the side edges of the triangle is ensured by calculating a group of hash codes according to the rules for constructing Pascal’s triangle and comparing them with the reference ones, characterized in that the data block M, presented in the form of a vector, is fragmented into data blocks M ⁽¹⁾ , M ⁽²⁾ , M ⁽³⁾ to monitor the integrity of the data contained in it fixed length, each of which, in turn, is also fragmented into data blocks , where ϕ=1, 2, 3; i=1, 2, …, n; j=1, 2, to which the hash function h is applied to control integrity, and the hashing scheme is based on the rules for constructing Pascal’s triangle and is presented in the form of a triangular-shaped table, with data blocks sequentially placed on the sides of the resulting triangle , to be protected, where i=1, 2, …, n; j=1, 2, intermediate results of transformations are placed inside the triangle , where i=1, 2, …, n-1; j=1, 2, …, n-1, calculated from data blocks , subject to protection, where i=1; j=1, 2, data blocks , subject to protection, where i=2, …, n-1; j=1, 2, and blocks with values hash function h, where i=1, 2, …, n-2; j=1, 2, …, n-2, calculated at the previous level of the triangle, on the lower side of the triangle there are blocks with values hash function h, where i=n; j=1, 2, …, n, which are calculated from data blocks , subject to protection, where i=n; j=1, 2, and the results of intermediate lower-level transformations , ,..., , used to control the integrity of data blocks , where i=1, 2, …, n; j=1, 2, then obtained for data blocks M ^(ϕ) , where ϕ=1, 2, 3, schemes for applying hash function h, having triangular shapes, are combined into a general scheme in which schemes for applying hash function h for data blocks M ⁽²⁾ and M ⁽³⁾ relative to the scheme of applying the hash function h for data block M ⁽¹⁾ will be rotated counterclockwise and clockwise, respectively, from blocks with values hash function h, where i=n; j=1, 2, …, n, n+1, n+2, placed on the lower sides of the triangles, k blocks with hash function values h are calculated sequentially in a certain order, among which one or more blocks with hash function values h , applied to elements from each data block M ⁽¹⁾ , M ⁽²⁾ and M ⁽³⁾ , used to detect and localize value blocks hash function h, where i=n; j=1, 2, …, n, allowing to detect and localize data blocks , to be protected, where i=1, 2, …, n; j=1, 2, the resulting scheme for using a hash function to control the integrity of a data block M is intermediate and the data block M to be protected is designated as M ^(I) , when constructing two other schemes according to the same rules for other data blocks M ^{( II)} , M ^(III) and combining them in the order presented for the data block M, we obtain a data integrity monitoring scheme based on the rules for constructing a cryptographic fractal - the Sierpinski triangle, which includes schemes for monitoring the integrity of data blocks M ^(I) , M ^{(II )} , M ^(III) , which are intermediate for the circuit for monitoring the integrity of data blocks M' ^(I) , M' ^(II) , M' ^(III) , which, in turn, will be intermediate for the circuit for monitoring the integrity of data blocks M '' ^(I) , M'' ^(II) , M'' ^(III) .