CN106921485A - Encrypting and decrypting method based on matrix operation - Google Patents

Encrypting and decrypting method based on matrix operation Download PDF

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Publication number
CN106921485A
CN106921485A CN201510983032.2A CN201510983032A CN106921485A CN 106921485 A CN106921485 A CN 106921485A CN 201510983032 A CN201510983032 A CN 201510983032A CN 106921485 A CN106921485 A CN 106921485A
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China
Prior art keywords
matrix
data
basic
transformation matrix
transformation
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CN201510983032.2A
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Chinese (zh)
Inventor
张勋
朱延超
刘小东
张珊珊
谢宇
周宇驰
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Aisino Corp
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Aisino Corp
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Priority to CN201510983032.2A priority Critical patent/CN106921485A/en
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0618Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
    • H04L9/0631Substitution permutation network [SPN], i.e. cipher composed of a number of stages or rounds each involving linear and nonlinear transformations, e.g. AES algorithms
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0618Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation

Abstract

The present invention relates to a kind of encrypting and decrypting method based on matrix operation, ripe algorithm is coordinated to go out a new scrambled matrix by certain rule construct using confidential information to be added, confidential information to be added is converted into ciphertext data by this scrambled matrix, by ciphertext data and original data transmissions to ciphertext recipient, ciphertext recipient constructs decryption matrix using the cleartext information for receiving using same rule, by ciphertext data deciphering, decryption information is compared with cleartext information again, such as contrast consistent, then using the information.The security that method of the present invention can not only be transmitted with guarantee information, and energy effective detection goes out whether information is tampered.

Description

Encrypting and decrypting method based on matrix operation
Technical field
The present invention relates to the technical field of the encryption and decryption of data, a kind of encrypting and decrypting method based on matrix operation is referred in particular to.
Background technology
With the arrival of information age, information security causes people and more and more payes attention to, and what security of the data in transmitting procedure also became people discusses topic warmly.The DEA for most starting all is to use simple Shift Method, and information to be encrypted is replaced with some other incoherent information, and certain this replacement has certain rule, thereby may be ensured that decrypting end is smoothly decrypted.But with advances in technology, it has been found that information is encrypted with Shift Method merely, attacker has probably grasped the rule replaced by a large amount of accumulation, so as to be solved from ciphertext data in plain text, steals secret information.Therefore current AES thought is then concentrated and has been changed to be converted using certain, i.e., carry out calculation process to be-encrypted data using certain operation rule, it is lost true colours, it is impossible to be restored in plain text by substantial amounts of accumulation analysis again.Even if so being obtained by attacker in transmitting procedure by the encryption information of conversion process cannot also decode out the cleartext information implied in ciphertext data, so as to ensure that the security of message transmitting procedure.
It is existing that the method for calculation process carried out to be-encrypted data by operation rule, the encryption to be-encrypted data is realized using matrix operation, Chinese invention patent such as Publication No. CN102314580A discloses the encryption method that a kind of support based on vector sum matrix operation is calculated, and comprises the following steps:Step one:Vector is converted raw data into, and is encrypted by scrambled matrix, so as to obtain an outsourcing vector for encryption;Step 2:Calculating parameter is converted into vector, and is encrypted by scrambled matrix, so as to obtain a calculating parameter vector for encryption;Step 3:Outsourcing vector sum calculating parameter vector to encrypting carry out scalar product, add, subtract, multiplication, so as to the result of calculation encrypted;Step 4:User obtains the plaintext of result of calculation by scrambled matrix and the computing of the result of calculation of encryption.Although the above method is a kind of encipherment scheme with security in data encryption or the computing of encryption data all the time; serve the effect of protection privacy of user; but whether methods described is unable to be tampered in detection data transmitting procedure, therefore it cannot be guaranteed that the security of message transmitting procedure.
The content of the invention
Therefore, the technical problems to be solved by the invention be overcome the problem that whether cannot be tampered in detection data transmitting procedure in the prior art so as to provide it is a kind of can be with the encrypting and decrypting method based on matrix operation of guarantee information transmitting procedure security.
In order to solve the above technical problems, a kind of encrypting and decrypting method based on matrix operation of the invention, its step is as follows:Step S1:Data transfer enters line translation using initial data to basic matrix, the basic matrix is transformed into transformation matrix, judge whether the transformation matrix is invertible matrix, if the initial data is converted into ciphertext data by the transformation matrix, the data transfer sends to data receiver the ciphertext data and the initial data in the lump;Step S2:Data receiver enters line translation according to the cleartext information for receiving to the basic matrix, and the basic matrix is transformed into transformation matrix, and obtains the inverse matrix of transformation matrix, and the ciphertext data that then will be received parse cleartext information according to the inverse matrix;Step S3:The cleartext information that the cleartext information that will be parsed is received with the data receiver is made comparisons, if comparative result is consistent, is judged to that the ciphertext data are not tampered with;If comparative result is inconsistent, it is judged to that the ciphertext data are tampered.
In one embodiment of the invention, the basic matrix is arranged by data transfer and data receiver.
In one embodiment of the invention, the basic matrix is invertible matrix.
In one embodiment of the invention, in the step S1, line translation is entered to the basic matrix with reference to initial data and is comprised the following steps that:First, if basic matrix is n rank matrixes, the initial data is converted into the original matrix data of m*n;Then the diagonal entry of the basic matrix is replaced respectively using the first row element of original matrix data, so that the basic matrix is once transformed into transformation matrix, wherein:The m and n are positive integer, and the m rounds up for X/n's, and the X is the data amount check in initial data.
In one embodiment of the invention, in the step S1 and S2, judge whether the transformation matrix is that the method for invertible matrix is:Whether the determinant for judging the transformation matrix is zero, if not zero, then the transformation matrix is invertible matrix;If zero, then continue to convert the basic matrix, until obtaining reversible transformation matrix.
In one embodiment of the invention, the method for the continuation conversion basic matrix is:The cornerwise element of the basic matrix is replaced successively using each element of the next line of original matrix data, and whether the determinant of the formed transformation matrix of judgement is zero after one element of every replacement, if not zero, stop replacing, obtain reversible transformation matrix;If zero, continue to replace next element, until the determinant of the transformation matrix for being formed is not zero.
Above-mentioned technical proposal of the invention has advantages below compared to existing technology:
Initial data is converted into ciphertext data by data transfer of the present invention by constructing scrambled matrix, data receiver parses cleartext information by decrypting matrix again, and whether the cleartext information that will be parsed makes comparisons genuine and believable such that it is able to judge the cleartext information for parsing with the cleartext information that the data receiver is received.
Brief description of the drawings
In order that present disclosure is more likely to be clearly understood, below according to specific embodiment of the invention and with reference to accompanying drawing, the present invention is further detailed explanation, wherein
Fig. 1 is the flow chart of the method for the invention.
Specific embodiment
As shown in figure 1, the present embodiment provides a kind of encrypting and decrypting method based on matrix operation, its step is as follows:Step S1:Data transfer enters line translation using initial data to basic matrix, the basic matrix is transformed into transformation matrix, judge whether the transformation matrix is invertible matrix, if the initial data is converted into ciphertext data by the transformation matrix, the data transfer sends to data receiver the ciphertext data and the initial data in the lump;Step S2:Data receiver enters line translation according to the cleartext information for receiving to the basic matrix, and the basic matrix is transformed into transformation matrix, and obtains the inverse matrix of transformation matrix, and the ciphertext data that then will be received parse cleartext information according to the inverse matrix;Step S3:The cleartext information that the cleartext information that will be parsed is received with the data receiver is made comparisons, if comparative result is consistent, is judged to that the ciphertext data are not tampered with;If comparative result is inconsistent, it is judged to that the ciphertext data are tampered.
A kind of encrypting and decrypting method based on matrix operation described in the present embodiment, in the step S1, data transfer enters line translation using initial data to the basic matrix, the basic matrix is transformed into transformation matrix, judge whether the transformation matrix is invertible matrix, if the initial data is converted into ciphertext data by the transformation matrix, because the encryption to initial data is not simple replacement, but the looks of initial data are changed by matrix operation, therefore attacker cannot by the surface data of ciphertext analyze corresponding information come;Furthermore, the data transfer sends to data receiver the ciphertext data and the initial data in the lump, the raw information to be transmitted is efficiently utilized during the step S1 tectonic transition matrixes, because the raw information of transmission is different from every time, so construct plus dematrix is also differed, cause the regular reduction of ciphertext data, effectively overcome attacker and show that rule solves the problem of plaintext after a large amount of accumulation transmission data.In the step S2, data receiver enters line translation according to the cleartext information for receiving to the basic matrix, the basic matrix is transformed into transformation matrix, and obtain the inverse matrix of transformation matrix, then the ciphertext data that will be received parse cleartext information according to the inverse matrix, the cleartext information for receiving is efficiently utilized during the step S2 tectonic transition matrixes, data receiver is conducive to be decrypted ciphertext data, due to not can determine that whether data have been tampered in data transmission procedure, so the plaintext that data receiver is received is it cannot be guaranteed that be exactly initial data, therefore further checking is needed;In the step S3, the cleartext information that the cleartext information that will be parsed is received with the data receiver is made comparisons, if comparative result is consistent, is judged to that the ciphertext data are not tampered with;If comparative result is inconsistent, it is judged to that the ciphertext data are tampered, whether such effective detection goes out in data transmission procedure to be tampered, and further ensures the authenticity of data.
In the step S1, data transfer enters line translation using initial data to the basic matrix, and the basic matrix is transformed into transformation matrix, and the transformation matrix is equivalent to scrambled matrix.The initial data is many by the method that the transformation matrix is converted into ciphertext data, such as the mode that initial data is multiplied with the transformation matrix can be obtained ciphertext data, if initial data is represented with A, transformation matrix is represented with B, ciphertext data represent with C, then the A*B=C.
The data transfer need to build an identical basic matrix with the data receiver, the basic matrix is the matrix of data transfer and data receiver agreement, so as to be conducive to the decryption of data receiver, the security of data transfer is effectively ensured, the leakage problem that data may occur in transmitting procedure is solved, while effectively prevent its problem that may be maliciously distorted in transmitting procedure;The basic matrix is invertible matrix, it is ensured that after the basic matrix is transformed into transformation matrix, and the transformation matrix is also invertible matrix, so as to be conducive to data receiver to be parsed in plain text according to the inverse matrix and ciphertext data of the transformation matrix.
How using initial data line translation to be entered to the basic matrix the following detailed description of in the step S1, the basic matrix is transformed into transformation matrix:First, if basic matrix is n rank matrixes, the initial data is converted into the matrix of m*n, wherein the m and n are positive integer, the m rounds up for X/n's, and the X is the data amount check in initial data.Specifically, if there being X data in initial data, if X is removed in remainder zero is obtained after n, then the X is removed and is set to m in obtaining business after n, if X is removed be not zero in obtaining remainder after n, the X removed in obtaining being set to m after business plus 1 after n.As there being 100 data in initial data, and basic matrix is 5 rank matrixes, then 100 to remove the business after 5 be 20, and remainder is zero, then data 20 are set into m, and now the initial data can just be converted into the matrix of 20*5.If there being 100 data in initial data, and basic matrix be 6 rank matrixes, then 100 remove after 6 business be 16, remainder is 4, then data 17 are set into m, and now the initial data can just be converted into the matrix of 17*6.For the initial data for being transformed into matrix, if data deficiencies, can be with zero padding;Then the diagonal entry of the basic matrix is replaced respectively using the first row element of original matrix data, specifically, diagonal entry a11, a22 ... ann of the basic matrix are substituted for a11, a12 ... a1n of initial data respectively, will the diagonal entry a11 of the basic matrix be substituted for the a11 of initial data, the diagonal entry a22 of the basic matrix is substituted for the a12 of initial data, successively sequentially, the diagonal entry ann of the basic matrix is substituted for the a1n of initial data, so that the basic matrix is once transformed into transformation matrix.
The present invention can be parsed in plain text jointly due to the inverse matrix using the transformation matrix and ciphertext data, therefore the transformation matrix also must be invertible matrix, therefore need to judge whether the transformation matrix is invertible matrix, and to ensure that matrix is invertible matrix, then determinant of a matrix value is not zero, and specifically, whether the determinant for judging the transformation matrix is zero, if not zero, then the transformation matrix is invertible matrix;If zero, then continue to convert the basic matrix, until obtaining reversible transformation matrix.If the determinant of the transformation matrix after once changing is zero, need to continue to convert the basic matrix, the method for continuing to convert the basic matrix is:The cornerwise element of the basic matrix is replaced successively using each element of the next line of original matrix data, and whether the determinant of the formed transformation matrix of judgement is zero after one element of every replacement, if not zero, stop replacing, obtain reversible transformation matrix;If zero, continue to replace next element, until the determinant of the transformation matrix for being formed is not zero.Specifically, cornerwise first element of basic matrix is replaced using first element of the second row of original matrix data.Specifically, cornerwise first element a11 of the basic matrix is substituted for the data of the second row first row a12 in initial data, make the basic matrix diauxic shift into transformation matrix, whether the determinant for now also needing to judge the transformation matrix after diauxic shift is zero, if be not zero, the transformation matrix after diauxic shift is exactly final transformation matrix;If zero, then order replaces cornerwise second element of basic matrix using second element of the second row of original matrix data, will cornerwise second element a22 of the basic matrix be substituted for the data of the second row secondary series a22 in initial data, whether the determinant for continuing to verify the transformation matrix after three transformations is zero, untill the determinant for obtaining transformation matrix is not equal to zero, so that it is determined that going out final transformation matrix.
In the step S2, the cleartext information that the data receiver will be received enters line translation to the basic matrix, and the basic matrix is transformed into transformation matrix, and obtains the inverse matrix of transformation matrix, and now the inverse matrix is exactly the decryption matrix of construction.
The data receiver enters data transfer in the regular and step S1 of line translation to the basic matrix according to the cleartext information for receiving and enters the regular identical of line translation to the basic matrix using initial data, so as to ensure the uniformity of matrix after conversion, it is to avoid the leakage problems that data may occur in transmitting procedure.Specifically, can quick, smoothly be decrypted in view of the data receiver, the data transfer and the data receiver can in advance arrange the rule of conversion to the basic matrix, the data receiver according to the data transfer identical building mode, the basic matrix is transformed into transformation matrix, corresponding plaintext can be parsed by the inverse matrix of the transformation matrix and the ciphertext data for receiving.Specifically, if initial data is represented with A, transformation matrix is represented with B, and ciphertext data are represented with C, then the A*B=C;The method of so data receiver parsing data is:, wherein be exactly the inverse matrix of transformation matrices, so as to just ciphertext data can be parsed in the form of plaintext according to the inverse matrix.
In the step S3, the cleartext information that the cleartext information that will be parsed is received with the data receiver is made comparisons, if comparison result is consistent, then it is assumed that the cleartext information for parsing is genuine and believable, is further illustrated in data transmission procedure and is suffered malicious attack;If comparison is inconsistent, then can be determined that data have been tampered with after the possibility for excluding algorithmic error, then it is assumed that information transfer is wrong, and the cleartext information for parsing is insincere, not can use, it is necessary to reacquire data.
To sum up, technical scheme of the present invention has advantages below:
1. the encrypting and decrypting method based on matrix operation of the present invention, in the step S1, data transfer enters line translation using initial data to the basic matrix, the basic matrix is transformed into transformation matrix, the initial data is converted into ciphertext data by the transformation matrix, due to the encryption to initial data be not it is simple replace, but the looks of initial data are changed by matrix operation, thus attacker cannot by the surface data of ciphertext analyze corresponding information come;Furthermore, the data transfer sends to data receiver the ciphertext data and the initial data in the lump, the raw information to be transmitted is efficiently utilized during the step S1 tectonic transition matrixes, because the raw information of transmission is different from every time, so construct plus dematrix is also differed, cause the regular reduction of ciphertext data, effectively overcome attacker and show that rule solves the problem of plaintext after a large amount of accumulation transmission data.In the step S2, data receiver enters line translation according to the cleartext information for receiving to the basic matrix, and the basic matrix is transformed into transformation matrix, and obtains the inverse matrix of transformation matrix, and cleartext information is parsed in conjunction with the ciphertext data;In the step S3, whether the cleartext information that will be parsed makes comparisons genuine and believable such that it is able to judge the cleartext information for parsing with the cleartext information that the data receiver is received, if after data deciphering, the cleartext information that data receiver is received is consistent with the cleartext information for parsing, illustrate that the clear data for receiving is real, data in data transmission procedure so can be gone out with effective detection to be not tampered with, so as to ensure that the authenticity of data.
2. a kind of encrypting and decrypting method based on matrix operation of the present invention, the data transfer need to build an identical basic matrix with the data receiver, the basic matrix is the matrix of data transfer and data receiver agreement, so as to be conducive to the decryption of data receiver, the security of basic matrix has been effectively ensured, the leakage problem that data may occur in transmitting procedure is avoided, its problem that may be maliciously distorted in transmitting procedure is simultaneously effective overcome;The basic matrix is invertible matrix, it is ensured that after the basic matrix is transformed into transformation matrix, and the transformation matrix is also invertible matrix, so as to be conducive to data receiver to be parsed in plain text according to the inverse matrix and ciphertext data of the transformation matrix.
Obviously, above-described embodiment is only intended to clearly illustrate example, not to the restriction of implementation method.For those of ordinary skill in the field, the change of other multi-forms can also be made on the basis of the above description or is changed.There is no need and unable to be exhaustive to all of implementation method.And the obvious change thus extended out or among changing still in the protection domain of the invention.

Claims (6)

1. a kind of encrypting and decrypting method based on matrix operation, its step is as follows:
Step S1:Data transfer enters line translation using initial data to basic matrix, the basic matrix is transformed into transformation matrix, judge whether the transformation matrix is invertible matrix, if the initial data is converted into ciphertext data by the transformation matrix, the data transfer sends to data receiver the ciphertext data and the initial data in the lump;
Step S2:Data receiver enters line translation according to the cleartext information for receiving to the basic matrix, and the basic matrix is transformed into transformation matrix, and obtains the inverse matrix of transformation matrix, and the ciphertext data that then will be received parse cleartext information according to the inverse matrix;
Step S3:The cleartext information that the cleartext information that will be parsed is received with the data receiver is made comparisons, if comparative result is consistent, is judged to that the ciphertext data are not tampered with;If comparative result is inconsistent, it is judged to that the ciphertext data are tampered.
2. the encrypting and decrypting method based on matrix operation according to claim 1, it is characterised in that:The basic matrix is arranged by data transfer and data receiver.
3. the encrypting and decrypting method based on matrix operation according to claim 1 and 2, it is characterised in that:The basic matrix is invertible matrix.
4. the encrypting and decrypting method based on matrix operation according to claim 1, it is characterised in that:In the step S1, line translation is entered to the basic matrix using initial data and is comprised the following steps that:First, if basic matrix is n rank matrixes, the initial data is converted into the original matrix data of m*n;Then the diagonal entry of the basic matrix is replaced respectively using the first row element of original matrix data, so that the basic matrix is once transformed into transformation matrix, wherein:The m and n are positive integer, and the m rounds up for X/n's, and the X is the data amount check in initial data.
5. the encrypting and decrypting method based on matrix operation according to claim 1, it is characterised in that:In the step S1 and S2, judge whether the transformation matrix is that the method for invertible matrix is:Whether the determinant for judging the transformation matrix is zero, if not zero, then the transformation matrix is invertible matrix;If zero, then continue to convert the basic matrix, until obtaining reversible transformation matrix.
6. the encrypting and decrypting method based on matrix operation according to claim 5, it is characterised in that:The method for continuing to convert the basic matrix is:The cornerwise element of the basic matrix is replaced successively using each element of the next line of original matrix data, and whether the determinant of the formed transformation matrix of judgement is zero after one element of every replacement, if not zero, stop replacing, obtain reversible transformation matrix;If zero, continue to replace next element, until the determinant of the transformation matrix for being formed is not zero.
CN201510983032.2A 2015-12-24 2015-12-24 Encrypting and decrypting method based on matrix operation Pending CN106921485A (en)

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CN116032624A (en) * 2022-12-30 2023-04-28 北京长鹰恒容电磁科技有限公司 Data transmission method based on fusion encryption

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CN108831186A (en) * 2018-06-25 2018-11-16 深圳市嘉泊智慧城市运营管理有限公司 Large-scale synthesis parking yard information management platform
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CN111130755A (en) * 2019-12-30 2020-05-08 世纪恒通科技股份有限公司 Matrix double encryption method based on signature
WO2022012162A1 (en) * 2020-07-15 2022-01-20 平安国际智慧城市科技股份有限公司 Matrix operation-based data encryption method and apparatus, electronic device, and storage medium
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CN114710324A (en) * 2022-03-16 2022-07-05 深圳市风云实业有限公司 Cross-network tunnel message transmission method based on cipher book replacement encryption and decryption
CN114710324B (en) * 2022-03-16 2024-02-13 深圳市风云实业有限公司 Cross-network tunnel message transmission method based on cipher-key replacement encryption and decryption
CN116032624A (en) * 2022-12-30 2023-04-28 北京长鹰恒容电磁科技有限公司 Data transmission method based on fusion encryption

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Application publication date: 20170704