数字签名方法、签名信息的验证方法、相关装置及电子设备

Digital signature method, signature information verification method, related device and electronic equipment

文档序号：7977 发布日期：2021-09-17 浏览：37次中文

1. A digital signature method is applied to a first electronic device and comprises the following steps:

acquiring a file to be transmitted, a private key used by the first electronic device for digital signature and first compressed data, wherein the first compressed data is obtained by compressing a first symmetric tensor which is randomly generated, the order of the first symmetric tensor is greater than 2, and the private key comprises a first reversible matrix;

generating first target data based on the first compressed data and a randomly generated second reversible matrix, wherein the first target data is: a second symmetric tensor that is isomorphic with the first symmetric tensor, or second compressed data of the second symmetric tensor;

performing digital signature on the file to be sent based on the first target data to obtain a first character string;

and based on the first character string, performing matrix multiplication processing on the inverse matrix of the first reversible matrix and the second reversible matrix to generate signature information of the first electronic device for the file to be sent.

2. The method of claim 1, further comprising:

generating third compressed data of a third symmetric tensor isomorphic with the first symmetric tensor based on the first reversible matrix and the first compressed data;

generating a public key including the first compressed data and the third compressed data, the public key corresponding to the private key;

and publishing the public key.

3. The method of claim 1, wherein the first symmetry tensor comprises the first compressed data, and the generating first target data based on the first compressed data and a randomly generated second invertible matrix comprises:

acquiring other data except the first compressed data in the first symmetric tensor based on the first compressed data;

and performing matrix multiplication processing on the second reversible matrix and the first symmetrical tensor to obtain first target data based on the first compressed data and the other data.

4. A method for verifying signature information, which is applied to a second electronic device, comprises the following steps:

acquiring a file to be transmitted, signature information of the file to be transmitted and a public key used by the second electronic device for verifying the signature information, wherein the public key corresponds to a private key associated with the signature information and comprises first compressed data of a first symmetric tensor and third compressed data of a third symmetric tensor;

performing matrix multiplication processing on the signature information and the first symmetric tensor and the third symmetric tensor based on the first compressed data and the third compressed data to generate second target data, wherein the second target data is a fourth symmetric tensor or fourth compressed data of the fourth symmetric tensor;

performing digital signature on the file to be sent based on the second target data to obtain a second character string;

verifying the signature information based on the second string;

the type of the second target data corresponds to the type of first target data, the first target data is a second symmetric tensor isomorphic with the first symmetric tensor or second compressed data of the second symmetric tensor, and the first target data is used for digitally signing the file to be sent.

5. The method of claim 4, wherein the signature information includes P strings, P being a positive integer greater than 1, the verifying the signature information based on the second string comprising:

segmenting the second character string to obtain M character strings, wherein P is equal to M;

determining that the signature information is verified successfully under the condition that the P character strings are the same as the M character strings one by one; or, determining that the signature information verification fails when a first target character string in the P character strings is different from a second target character string in the M character strings;

the position of the first target character string in the P character strings corresponds to the position of the second target character string in the M character strings, and the first target character string is any one of the P character strings.

6. A digital signature device, which is applied to a first electronic device, comprises:

the first acquisition module is used for acquiring a file to be transmitted, a private key for digital signature of the first electronic device and first compressed data, wherein the first compressed data is obtained by compressing a first symmetric tensor which is randomly generated, the order of the first symmetric tensor is greater than 2, and the private key comprises a first reversible matrix;

a first generating module, configured to generate first target data based on the first compressed data and a randomly generated second invertible matrix, where the first target data is: a second symmetric tensor that is isomorphic with the first symmetric tensor, or second compressed data of the second symmetric tensor;

the first digital signature module is used for carrying out digital signature on the file to be sent based on the first target data to obtain a first character string;

and the first multiplication processing module is used for performing matrix multiplication processing on the inverse matrix of the first reversible matrix and the second reversible matrix based on the first character string so as to generate signature information of the first electronic device for the file to be sent.

7. The apparatus of claim 6, further comprising:

a second generating module configured to generate third compressed data of a third symmetric tensor that is isomorphic with the first symmetric tensor, based on the first reversible matrix and the first compressed data;

a third generating module, configured to generate a public key including the first compressed data and the third compressed data, where the public key corresponds to the private key;

and the publishing module is used for publishing the public key.

8. The apparatus of claim 6, wherein the first generating module is specifically configured to:

acquiring other data except the first compressed data in the first symmetric tensor based on the first compressed data; and performing matrix multiplication processing on the second reversible matrix and the first symmetrical tensor to obtain first target data based on the first compressed data and the other data.

9. An apparatus for verifying signature information, the apparatus being applied to a second electronic device, comprising:

the second obtaining module is used for obtaining a file to be sent, signature information of the file to be sent and a public key used by the second electronic device for verifying the signature information, wherein the public key corresponds to a private key associated with the signature information, and comprises first compressed data of a first symmetry tensor and third compressed data of a third symmetry tensor;

a second multiplication processing module, configured to perform matrix multiplication processing on the signature information and the first symmetric tensor and the third symmetric tensor based on the first compressed data and the third compressed data to generate second target data, where the second target data is a fourth symmetric tensor or fourth compressed data of the fourth symmetric tensor;

the second digital signature module is used for carrying out digital signature on the file to be sent based on the second target data to obtain a second character string;

a verification module for verifying the signature information based on the second character string;

10. The apparatus according to claim 9, wherein the signature information includes P character strings, P being a positive integer greater than 1, and the verification module is specifically configured to:

segmenting the second character string to obtain M character strings, wherein P is equal to M;

11. An electronic device, comprising:

at least one processor; and

a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,

the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-3 or to perform the method of any one of claims 4-5.

12. A non-transitory computer readable storage medium having stored thereon computer instructions for causing the computer to perform the method of any one of claims 1-3 or to perform the method of any one of claims 4-5.

13. A computer program product comprising a computer program which, when executed by a processor, implements the method of any of claims 1-3 or performs the method of any of claims 4-5.

Background

The digital signature is a basic task of public key cryptography, and the public key cryptography means that a cryptographic scheme comprises a public key and a private key, and the public key can be published, so that two users can carry out encryption and decryption and identity authentication on the premise of not establishing communication. The goal of digital signatures, in turn, is to authenticate the sender of the document, thereby ensuring that the sender of the document is authentic, which is of fundamental importance in e-commerce and internet protocols.

At present, in internet communication, a commonly used digital signature scheme is based on the difficulty of large number decomposition and discrete logarithm, such as an asymmetric encryption algorithm based on diffie-hellman key exchange.

Disclosure of Invention

The disclosure provides a digital signature method, a signature information verification method, a related device and electronic equipment.

According to a first aspect of the present disclosure, there is provided a digital signature method, applied to a first electronic device, including:

performing digital signature on the file to be sent based on the first target data to obtain a first character string;

According to a second aspect of the present disclosure, there is provided a method for verifying signature information, the method being applied to a second electronic device, including:

performing digital signature on the file to be sent based on the second target data to obtain a second character string;

verifying the signature information based on the second string;

According to a third aspect of the present disclosure, there is provided a digital signature apparatus, which is applied to a first electronic device, including:

the first digital signature module is used for carrying out digital signature on the file to be sent based on the first target data to obtain a first character string;

According to a fourth aspect of the present disclosure, there is provided an apparatus for verifying signature information, the apparatus being applied to a second electronic device, including:

the second digital signature module is used for carrying out digital signature on the file to be sent based on the second target data to obtain a second character string;

a verification module for verifying the signature information based on the second character string;

According to a fifth aspect of the present disclosure, there is provided an electronic device comprising:

at least one processor; and

a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,

the memory stores instructions executable by the at least one processor to enable the at least one processor to perform any one of the methods of the first aspect or to perform any one of the methods of the second aspect.

According to a sixth aspect of the present disclosure, there is provided a non-transitory computer readable storage medium storing computer instructions for causing a computer to perform any one of the methods of the first aspect or to perform any one of the methods of the second aspect.

According to a seventh aspect of the present disclosure, there is provided a computer program product comprising a computer program which, when executed by a processor, implements any of the methods of the first aspect or performs any of the methods of the second aspect.

The technology disclosed by the invention solves the problem of low security of the digital signature, and improves the security of the digital signature.

It should be understood that the statements in this section do not necessarily identify key or critical features of the embodiments of the present disclosure, nor do they limit the scope of the present disclosure. Other features of the present disclosure will become apparent from the following description.

Drawings

The drawings are included to provide a better understanding of the present solution and are not to be construed as limiting the present disclosure. Wherein:

fig. 1 is a schematic flow chart of a digital signature method according to a first embodiment of the present disclosure;

fig. 2 is a flowchart illustrating a method of verifying signature information according to a second embodiment of the present disclosure;

fig. 3 is a schematic structural diagram of a digital signature apparatus according to a third embodiment of the present disclosure;

fig. 4 is a schematic configuration diagram of a signature information verification apparatus according to a fourth embodiment of the present disclosure;

FIG. 5 is a schematic block diagram of an example electronic device used to implement embodiments of the present disclosure.

Detailed Description

Exemplary embodiments of the present disclosure are described below with reference to the accompanying drawings, in which various details of the embodiments of the disclosure are included to assist understanding, and which are to be considered as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the present disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.

First embodiment

As shown in fig. 1, the present disclosure provides a digital signature method, which is applied to a first electronic device, and includes the following steps:

step S101: the file to be sent, a private key used by the first electronic device for digital signature and first compressed data are obtained, the first compressed data are obtained by compression based on a first symmetric tensor which is randomly generated, the order of the first symmetric tensor is greater than 2, and the private key comprises a first reversible matrix.

In the embodiment, the digital signature method relates to the technical field of quantum computing, in particular to the field of information security in quantum computing, and can be widely applied to a plurality of scenes such as electronic commerce, identity verification, software distribution and the like.

For example, in an authentication application scenario, party a needs to send a file to party b, and party b needs to verify that the file was indeed sent by party a and not others. At this time, party A can digitally sign the file, and party B can verify that the sender of the file is party A after receiving the file and the corresponding signature information and obtaining the public key of the public broadcast of party A.

For another example, in an application scenario of software distribution, the obtained software may be subjected to publisher authentication, so as to determine the source of the software.

In practical use, the digital signature method according to the embodiment of the present disclosure may be executed by the digital signature apparatus according to the embodiment of the present disclosure. The digital signature device of the embodiment of the present disclosure may be configured in any first electronic device to execute the digital signature method of the embodiment of the present disclosure. The first electronic device may be a server or a terminal, and is not limited specifically here.

The first electronic device serves as a communication sender and can communicate with other electronic devices to send files. In order to enable the other electronic devices to verify that the received file was indeed sent by the first electronic device and to verify the authenticity of the sender, the first electronic device may digitally sign the file to be sent using digital signature techniques, before sending the file.

The file to be sent refers to a file which needs to be sent to other electronic devices by the first electronic device, and the type of the file can be a text, a compressed packet, audio and video and the like.

The private key may be pre-stored for the first electronic device, and is used to encrypt and digitally sign a file to be sent of the first electronic device. The private key may correspond to a public key, a combination of the private key and the public key may be referred to as a key pair, and the public key is usually disclosed to other electronic devices by the other electronic devices, so that the other electronic devices may decrypt and sign the signature information of the first electronic device using the public key.

As a task in public key cryptography, digital signature schemes require the difficulty of being based on some algorithmic problem to guarantee the security of digital signatures. With the development of quantum computers, the algorithm problem on which the existing digital signature scheme is based may not be difficult for the quantum computers in general, i.e. the algorithm problem on which the scheme is based may not be able to resist quantum attacks, and therefore, the security of the digital signature is threatened.

Among them, the above-mentioned difficulty is a delicate concept. First, unlike what is generally considered worst-case, what is needed here is a difficulty in the average sense, i.e., there is no effective algorithm for most of the inputs. Secondly, since not all difficult algorithms correspond to the proper digital signature protocol, the corresponding protocol needs to be designed based on the problem. Finally, the usability of this problem in the context of post-quantum cryptography, such as the problem of large number decomposition, has to be explored also from the point of view of quantum algorithm design, which is difficult from the point of view of classical computers, but easy from the point of view of quantum computing.

From the viewpoint of computational complexity, the tensor isomorphic problem can be considered as a more difficult problem in isomorphic type problems, and the tensor isomorphic problem can be described as follows.

Let p be a prime number, gf (p) denotes the modulo p domain, and GL (n, p) denotes the set of invertible matrices of size n × n over gf (p). The multi-order matrix over gf (p) may be referred to as a tensor, where the order of the tensor is typically greater than 2.

Taking the tensor as a third-order matrix as an example, the tensor can be referred to as an n × n × n matrix, which has n × n × n components, and n can be referred to as the dimension of the tensor. Let A be one tensor, with A ═ a_ijk) Another tensor is denoted by B, with B ═ B_ijk) The data of each order is n in length, that is, the index i, j and k of the tensor can take 1 to n respectively, which is represented by i, j, k epsilon {1,2_ijk,b_ijkE GF (p) is respectively two tensors of the ith sheet, the jth line and the kth column, and the tensors (a) can be formed by the arrangement of the elements_ijk) And (b)_ijk). The tensor isomorphism problem is to solve whether an invertible matrix exists, and the invertible matrix is obtained by using C ═ C_ij) E GL (n, p) such that a is (C, C) ° B. That is, the tensor isomorphic problem is to determine whether two tensors are isomorphic tensors, and to solve an invertible matrix in which the two tensors are transformed into each other when the two tensors are isomorphic tensors.

Here, "°" in the formula (C, C) ° B means that the three matrices are multiplied from the three directions of the tensor, respectively, that is, the three matrices can be simultaneously multiplied in the three directions of the tensor, and the three matrices can be the same reversible matrix C. The result of the multiplication is also a tensor, which can be represented by the B' tableWherein, B' ═ B_i'_jk) And b is_i'_jkIs a number of the corresponding positions of the subscripts in the tensor B',

and the symmetric tensor isomorphic problem continues the definition of the tensor isomorphic problem, unlike the tensor isomorphic problem, the isomorphic tensor is a symmetric tensor, that is, in (C, C) ° B, both tensor a and tensor B are symmetric tensors, and the symmetric tensor is defined as: setting a quantity A which satisfies a_ijk＝a_ikj＝a_jik＝a_jki＝a_kij＝a_kji。

From the quantum computation angle, due to the difficulty in solving the tensor isomorphic problem, the security of the digital signature designed by adopting the tensor isomorphic problem in the quantum algorithm angle provides guarantee. When the two problems are solved by adopting algorithms such as a Grubesynebar base and the like respectively, on one hand, the data symmetry and the relation of the symmetrical tensors are better relative to other tensors, on the other hand, whether the two symmetrical tensors are isomorphic tensors or not is solved due to the problem of attacking the precision of the algorithm, and on the condition that the two symmetrical tensors are isomorphic tensors, a reversible matrix of mutual transformation of the two symmetrical tensors is solved, and the convergence speed of the isomorphic problems of the symmetrical tensors is slower relative to the isomorphic problems of the tensors in operation.

This shows that the digital signature is designed based on the algorithm problem by using the symmetric tensor isomorphic problem, and the digital signature is more secure than the digital signature designed by using the tensor isomorphic problem. Therefore, in the embodiment of the present disclosure, the algorithm problem based on may adopt a symmetric tensor isomorphic problem, and the design of the digital signature may be performed by using the difficulty in solving the angles of most computers (including quantum computers) by using the symmetric tensor isomorphic problem.

It should be noted that, in the case that the symmetric tensor is the higher-order matrix, the isomorphic problem of the symmetric tensor can be further generalized to the symmetric tensor that is the higher-order matrix, that is, the isomorphic problem of the symmetric tensor of the higher-order matrix can be based onThe isomorphic problem of the symmetric tensor of the third-order matrix is analogized. For example, for two symmetric tensors that are fourth-order matrices, a ═ can be used for each of the two symmetric tensors_ijkl) And B ═ B_ijkl) The symmetric tensor isomorphic problem refers to the presence or absence of the invertible matrix C, such that a is (C, C) ° B.

On the premise of the isomorphic problem of the symmetric tensors, even if two symmetric tensors are known to be isomorphic tensors, the reversible matrix transformed between the two symmetric tensors is difficult to solve, so that in order to ensure the security of the digital signature, the private key of the first electronic device for the digital signature can be set to be in a matrix form, so as to ensure the difficulty of breaking the private key.

Specifically, the private key may include a first reversible matrix, and the public key may be set to a compressed form of the symmetric tensor, and the public key is published. Therefore, if other electronic devices need to forge the signature information of the first electronic device for the file to be sent, the private key needs to be obtained by cracking according to the public key, which is equivalent to that the other electronic devices need to solve the isomorphic problem of the symmetric tensor. Due to the difficulty in solving the isomorphic problem of the symmetric tensor, the private key of the first electronic device is difficult to crack by other electronic devices according to the public key, and thus the signatures of the first electronic device are difficult to forge by the other electronic devices, so that the security of the digital signatures can be ensured.

In practical application, an identity authentication protocol can be constructed by adopting a zero-knowledge interaction protocol of a classical graph isomorphism problem based on a symmetric tensor isomorphism problem. Depending on the security required, the protocol may be run through several rounds with multiple symmetric tensors generated in each round. Based on the identity authentication protocol, a digital signature scheme can be constructed by using a classic identity recognition protocol Fiat-Shamir conversion process.

Depending on the major parameters in the protocol (e.g., n is the dimension of the symmetric tensor, p is the size of the field, r is the number of rounds, and t is the number of symmetric tensors generated in each round), and the understanding of the best algorithm runtime for the isomorphic problem of symmetric tensors, an appropriate choice of parameters can be made to achieve the desired security of the digital signature, e.g., to achieve 128-bit or 256-bit security.

The file to be sent can be acquired in various ways, for example, the file to be sent can be acquired from a file stored in advance, and for example, the file to be sent can be actively generated.

The private key may be generated in advance by the first electronic device and stored in the database, or may be set in advance by a developer and stored in the database, which is not specifically limited herein.

The private key is, for example, pre-generated by a first electronic device and stored in a database, and the first electronic device may randomly generate at least one first reversible matrix, for example, randomly generate t-1 first reversible matrices, and use C_iE GL (n, p), i e {1, 2., t-1}, where t can be set according to the actual situation, and t is greater than or equal to 2. The private key of the first electronic device may include a plurality of reversible matrices, each of which may be C₀,C₁,...,C_t-1Wherein, C₀Is an identity matrix of size n.

The first compressed data may be compressed data of a first symmetric tensor, and taking design of a digital signature scheme by using a isomorphic problem of a symmetric tensor of a third-order matrix as an example, when constructing a private key and a public key of the first electronic device, a first symmetric tensor may be randomly generated, and a may be used₀Representing a first symmetric tensor A₀＝(a_ijk)，i,j,k∈{1,2,...,n}，a_ijkE gf (p), the first symmetric tensor may be isomorphic as an initial symmetric tensor, which may be part of a public key. Wherein, the data in the first symmetric tensor has a symmetric relation a_ijk＝a_ikj＝a_jik＝a_jki＝a_kij＝a_kji。

The first symmetric tensor can be compressed to obtain first compressed data, wherein the data volume in the first compressed data is smaller than the data volume in the first symmetric tensor. That is, compressing the first symmetric tensor means removing part or all of redundant data in the first symmetric tensor to obtain first compressed data, and the first symmetric tensor can be accurately restored based on the first compressed data.

In an alternative embodiment, due to the symmetry of the first symmetry tensor, a satisfying i ≦ j ≦ k may be assigned_ijkIs eliminated, or a satisfying i > j or j > k is eliminated_ijkThe values of (A) are removed, namely half of the data with the symmetrical relation is reserved, and the other half of the data can be obtained according to the symmetrical relation.

For example, when reserving a_ijkWhen the data (i is more than or equal to j is less than or equal to k), calling a if necessary_jkiJki may be reordered to ijk based on a_ijk＝a_jkiI.e. a can be derived from the first compressed data_jkiThe value of (c). For example, if i is 1, j is 2, and k is 3, call a is required₂₃₁Can be reordered based on a₁₂₃＝a₂₃₁I.e. a can be derived from the first compressed data₂₃₁The value of (c).

The whole of the first compressed data may be referred to as a compressed representation of the first symmetric tensor, and a specific data structure may be used to store the compressed representation of the first symmetric tensor, such as a key value-content value data structure, where key is used to store the subscript of the data, i.e., ijk, and value is used to store the value corresponding to the subscript, so that it is possible to avoid repeatedly storing the values that should be the same, and thus the storage space of the first electronic device may be greatly reduced.

Step S102: generating first target data based on the first compressed data and a randomly generated second reversible matrix, wherein the first target data is: a second symmetric tensor that is isomorphic with the first symmetric tensor, or second compressed data of the second symmetric tensor.

For i e { 1.,. r }, r } which may be a positive integer, the first electronic device may randomly generate at least one second invertible matrix, which may be represented by D_iAnd epsilon GL (n, p). That is, the first target data may be generated based on the second invertible matrix generated at random and the first compressed data.

The first target data may be at least one second symmetric tensor that is isomorphic with the first symmetric tensor, or may be second compressed data of the at least one second symmetric tensor, where each second symmetric tensor may correspond to one second compressed data.

Specifically, the formula of the structure can be B_i＝(D_i,D_i,D_i)°A₀I ∈ {1,..., r }, where the second symmetric tensor is B_i. The other data in the first symmetric tensor can be constructed based on the first compressed data, the first symmetric tensor can be constructed by the first compressed data and the other data, then the second reversible matrix and the first symmetric tensor can be subjected to matrix multiplication to obtain the second symmetric tensor, or the second compressed data of the second symmetric tensor, namely, only part of data of the second symmetric tensor is calculated, for example, only b satisfying that i is less than or equal to j is less than or equal to k is calculated_ijkThe amount of calculation can be reduced, and the processing speed of the digital signature is improved.

The second reversible matrix and the first symmetric tensor can also be subjected to matrix multiplication, and under the condition that other data in the first symmetric tensor need to be called, corresponding data can be obtained from the first compressed data and substituted and calculated based on the symmetric relation between the other data and the first compressed data, and finally the second symmetric tensor or second compressed data of the second symmetric tensor is obtained.

Step S103: and performing digital signature on the file to be sent based on the first target data to obtain a first character string.

The file to be sent (denoted by M) may be digitally signed using a hash function (denoted by H), specifically, the file to be sent M and the first target data may be used as a character string to be connected in series, and then, the character string after being connected in series is subjected to hash operation to obtain the first character string.

In the case that the first target data is the second symmetric tensor, the file M to be transmitted and the second symmetric tensor B can be transmitted₁，…，B_rThe strings are concatenated, and then the concatenated string is hashed to obtain a first string, which is then processed by H (M | B)₁|...B_r) Is expressed as MB₁|...B_rRepresenting the file M to be transmitted and a second symmetric tensor B₁，…，B_rAs a string concatenation. Wherein, the file M to be sent and the second symmetrical tensor B are₁，…，B_rThe hash operation is performed after the serial connection of the character strings, so that the data volume can be increased, and the safety of the first character string generated by the hash function can be improved.

Under the condition that the first target data is the second compressed data, the file M to be sent and the second compressed data can be used as character strings to be connected in series, and then the character strings after being connected in series are subjected to hash operation to obtain the first character string. The file M to be sent and the second compressed data are used as character strings to be connected in series and then subjected to Hash operation, and the calculation speed is high.

The first string may be a binary string, i.e. 01 string, and its length may be r × s, and the parameter s is also a parameter of the authentication protocol, and satisfies t ═ 2 with the parameter t^s. And H is a hash function whose input may be a string of arbitrary length, and whose output is r × s in length and outputs a 01 string.

Step S104: and based on the first character string, performing matrix multiplication processing on the inverse matrix of the first reversible matrix and the second reversible matrix to generate signature information of the first electronic device for the file to be sent.

Signature information of the first electronic device for the file to be sent can be generated based on the first character string, the first reversible matrix and the second reversible matrix. The signature information may include a first character string and a target matrix generated by the first character string, the first invertible matrix and the second invertible matrix, and in an optional embodiment, the signature information may include a plurality of character strings into which the first character string is divided and a target matrix generated by the plurality of character strings, the first invertible matrix and the second invertible matrix.

The step S104 specifically includes:

segmenting the first character string to obtain P character strings, wherein P is a positive integer greater than 1;

based on the P character strings, matrix multiplication processing is carried out on the inverse matrix of the first reversible matrix and the second reversible matrix to obtain a target matrix;

wherein the signature information comprises the P character strings and the target matrix.

Specifically, the first character string may be segmented to obtain a plurality of character strings, for example, r 01 character strings with a length of s may be obtained, and the r character strings may be respectively represented by f₁,...,f_rThis means that r is greater than 1.

A target matrix may be generated based on the P character strings, the first invertible matrix, and the second invertible matrix, and specifically, for i ∈ { 1.,. r }, a subscript f may be obtained from the first invertible matrix_iThe first reversible matrix of (1), after which the first electronic device may employ the formulaAnd calculating an object matrix. Wherein E is_iIs an object matrix, which may be plural in number,denotes the f-th of the private key_iThe inverse of the first invertible matrix, e.g. when the 01 string f_iWhen it is 1, thenIs a first invertible matrix C in the private key₁I.e. the target matrix may be based on a second invertible matrix D_iWith the first invertible matrix in the private keyThe inverse matrix of (2) is obtained by matrix multiplication.

Finally, based on the r character strings and a plurality of target matrices, determining signature information of the first electronic device for the file to be sent, where the signature information is (f)₁,...,f_r,E₁,...,E_r)。

If another electronic device, such as a third electronic device, wishes to impersonate the first electronic device, it is desirable toThe third electronic device cannot generate the target matrix based on the private key, namely cannot adopt a formula because the third electronic device does not have the private keyGenerating an object matrix E₁,...,E_rAnd solving a symmetric tensor isomorphism problem is needed to crack the private key, so that the private key of the first electronic device is difficult to be taken by the third electronic device.

In addition, the direct attack method of the third electronic device on the protocol can be attributed to the following problems: it is desirable to find a way to generate multiple 01 strings, using g₁,...,g_rE {0, 1.,. t-1} representation, such that in the calculationAfter i ∈ { 1.. multidot., r }, H (M | B) is calculated₁|...B_r) Obtained f₁,...,f_rSatisfy, for all i ∈ { 1.,. r }, there is f_i＝g_i. And the probability of success of such an attack does not significantly exceed 1/2, depending on the nature of the hash function^rs。

Therefore, based on the above two points, it is very difficult for the third electronic device to forge the signature information of the first electronic device.

Further, the combination of parameters in the protocol can be set as follows to achieve a security of 128 bits, as shown in table 1 below.

Table 1 some parameter combinations to achieve 128bit security

	n	p	r	s	Public key length (Bytes)	Signature Length (Bytes)
							Combination 1	9	8191	128	1	536	16864
Combination 2	9	8191	16	8	68639	2122
							Combination 3	9	8191	21	6	17160	2780

In this way, by using the randomly generated second reversible matrix and the public-private key to generate the signature, it is very difficult for other electronic devices to forge the reversible matrix between them, i.e. forge the private key, through an knowable public key (the public key may be a compressed representation of a plurality of symmetrical tensors or a plurality of symmetrical tensors) without knowing the private key, so that it is very difficult to forge the digital signature, and the security of the digital signature can be improved.

In this embodiment, a private key of the first electronic device is set to be in a form of a reversible matrix, and first target data is constructed through a second reversible matrix and an initial symmetry tensor which are randomly generated, where the first target data is a second symmetry tensor isomorphic with the initial symmetry tensor or second compressed data of the second symmetry tensor, and the file to be sent is digitally signed by using a hash function based on the first target data. Therefore, if other electronic devices need to forge the signature information of the first electronic device for the file to be sent, the private key needs to be obtained by cracking according to the public key, which is equivalent to that the other electronic devices need to solve the isomorphic problem of the symmetric tensor. Due to the difficulty in solving the isomorphic problem of the symmetric tensor, the private key of the first electronic device is difficult to crack by other electronic devices according to the public key, and thus the signatures of the first electronic device are difficult to forge by the other electronic devices, so that the security of the digital signatures can be ensured.

And when the two problems are solved by adopting algorithms such as a Grubvenbase algorithm and the like, on one hand, the data symmetry and the relationship of the symmetrical tensors are better relative to other tensors, on the other hand, whether the two symmetrical tensors are isomorphic tensors or not is solved due to the problem of attacking algorithm precision, and on the condition that the two symmetrical tensors are isomorphic tensors, a reversible matrix of mutual transformation of the two symmetrical tensors is solved, and the convergence speed of the isomorphic tensors of the symmetrical tensors is slower relative to the isomorphic problems of the tensors in operation. Therefore, the digital signature is designed by adopting the symmetric tensor isomorphic problem in the algorithm problem, and the digital signature is higher in safety compared with the digital signature designed by adopting the tensor isomorphic problem.

Table 2 is a cracking time table for attacking different digital signature schemes by adopting a Ginberg, the digital signature schemes are based on algorithms of a symmetrical tensor isomorphic problem and a tensor isomorphic problem respectively, wherein N/A in the Table 2 indicates that cracking cannot be carried out. As shown in table 2 below, under different parameters in the protocol, the difficulty is higher in solving the symmetric tensor isomorphic problem relative to the tensor isomorphic problem. Moreover, the digital signature scheme is designed by adopting the isomorphic problem of the symmetrical tensor, and only the compression expression of one symmetrical tensor needs to be stored in a finite fieldAnd the domain element greatly reduces the length of the public key.

Table 2 cracking time table for different digital signature schemes using the roboran base attack

Parameters in protocol	(n＝4，p＝5)	(n＝5，p＝5)
			Tensor isomorphic problem	0.076s	94.448s
Isomorphic problem of symmetric tensor	N/A	N/A

In addition, the digital signature scheme may be implemented based on a programming language Python prototype, and the runtime table of each scheme is shown in table 3 below.

TABLE 3 runtime tables for various scenarios

As can be seen from table 3 above, this scheme provides a significant improvement in run time over other schemes.

Optionally, the method further includes:

generating third compressed data of a third symmetric tensor isomorphic with the first symmetric tensor based on the first reversible matrix and the first compressed data;

generating a public key including the first compressed data and the third compressed data, the public key corresponding to the private key;

and publishing the public key.

The embodiment is a process of generating a public key based on a private key, and in order to enable other electronic devices to perform identity verification on a sender of a file to be sent, namely the first electronic device, under the condition that the signature information and the file to be sent are received by the first electronic device, the public key corresponding to the private key needs to be published.

The private key of the first electronic device comprises a first invertible matrix C_iE GL (n, p), i e {1, 2.., t-1} and an identity matrix C of size n₀Third compressed data of a third symmetric tensor isomorphic to the first symmetric tensor can be generated based on the first reversible matrix and the first compressed data, and the public key can include the first compressed data and the third compressed data.

Specifically, formula A may be employed based on the first invertible matrix and the first compressed data_i＝(C_i,C_i,C_i)°A₀I e {1, t-1}, generating third compressed data of a third symmetric tensor isomorphic to the first symmetric tensor, the third symmetric tensor can be represented by A_iI ∈ { 1.,. t-1 }. The manner of generating the third compressed data is similar to the manner of generating the second compressed data, and is not described herein again.

Then, the generated public key may be published, and accordingly, the public key of the first electronic device may be obtained by other electronic devices.

In this embodiment, third compressed data of a third symmetry tensor that is isomorphic with the initial symmetry tensor is constructed by the private key and the first compressed data, and the first compressed data and the third compressed data are published as a public key of the first electronic device. Therefore, the public key is set to be in a form of compressed data of the isomorphic symmetry tensor, other electronic equipment can only perform signature breaking on signature information of the first electronic equipment based on the public key published by the first electronic equipment to verify the identity of the first electronic equipment, and the isomorphic symmetry tensor corresponding to the public key is difficult to break a reversible matrix, namely a private key, between the isomorphic symmetry tensors, which is equivalent to solving the isomorphic problem of the symmetry tensor, so that the safety of the digital signature can be improved, and the attack of a quantum computer can be effectively resisted.

Moreover, by setting the public key as a compressed representation of the symmetric tensor, the length of the public key can be reduced, and thus the amount of data interaction between the electronic devices can be reduced.

Optionally, the first symmetry tensor includes the first compressed data, and the generating of the first target data based on the first compressed data and the randomly generated second invertible matrix includes:

acquiring other data except the first compressed data in the first symmetric tensor based on the first compressed data;

and performing matrix multiplication processing on the second reversible matrix and the first symmetrical tensor to obtain first target data based on the first compressed data and the other data.

In the present embodiment, when calculating the symmetric tensor isomorphic with the first symmetric tensor or the compressed representation of the symmetric tensor, the first symmetric tensor may be restored based on the first compressed data, and then the reversible matrix and the first symmetric tensor may be subjected to matrix multiplication to obtain the symmetric tensor isomorphic with the first symmetric tensor or the compressed representation of the symmetric tensor.

Thus, on the one hand, the data storage amount of the first electronic device can be reduced, and on the other hand, the data calculation amount can be reduced.

Second embodiment

As shown in fig. 2, the present disclosure provides a method for verifying signature information, which is applied to a second electronic device, and includes the following steps:

step S201: acquiring a file to be transmitted, signature information of the file to be transmitted and a public key used by the second electronic device for verifying the signature information, wherein the public key corresponds to a private key associated with the signature information and comprises first compressed data of a first symmetric tensor and third compressed data of a third symmetric tensor;

step S202: performing matrix multiplication processing on the signature information and the first symmetric tensor and the third symmetric tensor based on the first compressed data and the third compressed data to generate second target data, wherein the second target data is a fourth symmetric tensor or fourth compressed data of the fourth symmetric tensor;

step S203: performing digital signature on the file to be sent based on the second target data to obtain a second character string;

step S204: verifying the signature information based on the second string;

In this embodiment, the second electronic device is an electronic device that receives a file to be sent, the first electronic device may send the file to be sent and signature information of the file to be sent to the second electronic device, and accordingly, the second electronic device may receive the file to be sent and the signature information of the file to be sent.

And the first electronic device publishes the public key for verifying the identity of the file to be sent and the signature information of the file to be sent before sending the file to be sent, and correspondingly, the second electronic device can obtain the public key published by the first electronic device.

The public key corresponds to the private key associated with the signature information, that is, the public key and the private key for generating the signature information are a key pair, and the public key may include third compressed data of a third symmetry tensor and first compressed data of an initial symmetry tensor randomly generated by the first electronic device.

The target matrix in the signature information may be matrix-multiplied by the first symmetric tensor and the third symmetric tensor based on the first compressed data and the third compressed data to generate second target data, where the second target data is at least one fourth symmetric tensor or fourth compressed data of the at least one fourth symmetric tensor, and the fourth symmetric tensor may be B_i' means.

Specifically, for i e { 1.,. r }, the second electronic device may employ a formulaFourth compressed data of at least one fourth symmetric tensor or fourth symmetric tensor is generated. When in useThe first symmetric tensor is obtained, and the rest is the third symmetric tensor.

Then, based on the second target data, a hash function is adopted to perform digital signature on the file to be sent, so as to obtain a second character string. Specifically, the file M to be sent and the second target data may be used as a character string to be connected in series, and then, the character string after being connected in series is subjected to hash operation to obtain a second character string.

When the second target data is a fourth symmetrical tensor, the file M to be transmitted and the fourth symmetrical tensor B can be transmitted₁'，…，B_r' concatenate as a string, then hash the concatenated string to obtain a second string, and use H (M | B)₁'|...|B_r') is used. Wherein M | B₁'|...|B_r' represents the file M to be transmitted and the fourth symmetrical tensor B₁'，…，B_r' As string concatenation, the second string can also be a binary string, i.e. 01 stringIts length may also be r × s.

The type of the second target data may correspond to the type of the first target data, that is, when the first target data is in the form of a symmetric tensor, the second target data should also be in the form of a symmetric tensor, and when the first target data is in the compressed representation of a symmetric tensor, the second target data should also be in the compressed representation of a symmetric tensor, so that consistency of digital signature and signature verification by using a hash function can be ensured.

Finally, the signature information may be verified based on the second character string, and in a case that the second character string is the same as the character string in the signature information, the signature information is successfully verified, that is, it is determined that the file to be transmitted is indeed transmitted by the first electronic device. And in the case that the second character string is not identical to the character string in the signature information, the signature information fails to be verified, that is, the file to be sent is determined to be sent by other electronic equipment instead of the first electronic equipment. Wherein, the second character string is not identical with the character string in the signature information, which means that at least one character string is not identical.

In the embodiment, second target data is generated by compression representation and signature information based on a symmetric tensor in a public key, and a hash function is adopted to digitally sign a file to be sent based on the second target data to obtain a second character string; and verifying the signature information based on the second string. Therefore, the second electronic device can verify the signature information very conveniently to verify the identity of the sender of the file to be sent based on the public key and the received file to be sent and the received signature information of the file to be sent under the condition of acquiring the public key published by the first electronic device.

Optionally, the signature information includes P character strings, where P is a positive integer greater than 1, and step S204 specifically includes:

segmenting the second character string to obtain M character strings, wherein P is equal to M;

In this embodiment, the second character string may be segmented to obtain a plurality of character strings, for example, r 01 character strings with a length of s may be obtained, and the r character strings may be respectively represented by f₁',...,f_r' means.

For i ∈ { 1.,. r }, if f exists in all_i＝f_i', the verification of the signature information is successful, otherwise, the verification of the signature information is failed.

In this embodiment, the second character string is segmented to obtain a plurality of character strings, and the plurality of character strings are compared with the plurality of character strings in the signature information one by one, so that the signature information is successfully verified under the condition that the character strings are the same, and the signature information is unsuccessfully verified under the condition that any character string is different, so that the signature information can be conveniently verified.

Third embodiment

As shown in fig. 3, the present disclosure provides a digital signature apparatus 300, which is applied to a first electronic device, and includes:

a first obtaining module 301, configured to obtain a file to be sent, a private key used by the first electronic device for digital signature, and first compressed data, where the first compressed data is obtained by compressing a first symmetric tensor generated randomly, an order of the first symmetric tensor is greater than 2, and the private key includes a first reversible matrix;

a first generating module 302, configured to generate first target data based on the first compressed data and a randomly generated second invertible matrix, where the first target data is: a second symmetric tensor that is isomorphic with the first symmetric tensor, or second compressed data of the second symmetric tensor;

a first digital signature module 303, configured to digitally sign the file to be sent based on the first target data to obtain a first character string;

a first multiplication processing module 304, configured to perform matrix multiplication processing on the inverse matrix of the first invertible matrix and the second invertible matrix based on the first character string, so as to generate signature information of the first electronic device for the file to be sent.

Optionally, the apparatus further comprises:

a third generating module, configured to generate a public key including the first compressed data and the third compressed data, where the public key corresponds to the private key;

and the publishing module is used for publishing the public key.

Optionally, the first generating module 302 is specifically configured to:

The digital signature apparatus 300 provided in the present disclosure can implement each process implemented by the digital signature method embodiment, and can achieve the same beneficial effects, and for avoiding repetition, the details are not repeated here.

Fourth embodiment

As shown in fig. 4, the present disclosure provides an apparatus 400 for verifying signature information, the apparatus being applied to a second electronic device, and including:

a second obtaining module 401, configured to obtain a file to be sent, signature information of the file to be sent, and a public key used by the second electronic device to verify the signature information, where the public key corresponds to a private key associated with the signature information, and the public key includes first compressed data of a first symmetry tensor and third compressed data of a third symmetry tensor;

a second multiplication processing module 402, configured to perform matrix multiplication processing on the signature information and the first symmetric tensor and the third symmetric tensor based on the first compressed data and the third compressed data to generate second target data, where the second target data is a fourth symmetric tensor or fourth compressed data of the fourth symmetric tensor;

a second digital signature module 403, configured to digitally sign the file to be sent based on the second target data to obtain a second character string;

a verification module 404, configured to verify the signature information based on the second character string;

Optionally, the signature information includes P character strings, where P is a positive integer greater than 1, and the verifying module 404 is specifically configured to:

segmenting the second character string to obtain M character strings, wherein P is equal to M;

The signature information verification apparatus 400 provided by the present disclosure can implement each process implemented by the signature information verification method embodiment, and can achieve the same beneficial effects, and for avoiding repetition, the details are not repeated here.

In the technical scheme of the disclosure, the acquisition, storage, application and the like of the personal information of the related user all accord with the regulations of related laws and regulations, and do not violate the good customs of the public order.

The present disclosure also provides an electronic device, a readable storage medium, and a computer program product according to embodiments of the present disclosure.

FIG. 5 illustrates a schematic block diagram of an example electronic device 500 that can be used to implement embodiments of the present disclosure. Electronic devices are intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The electronic device may also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions, are meant to be examples only, and are not meant to limit implementations of the disclosure described and/or claimed herein.

As shown in fig. 5, the apparatus 500 comprises a computing unit 501 which may perform various appropriate actions and processes in accordance with a computer program stored in a Read Only Memory (ROM)502 or a computer program loaded from a storage unit 508 into a Random Access Memory (RAM) 503. In the RAM 503, various programs and data required for the operation of the device 500 can also be stored. The calculation unit 501, the ROM 502, and the RAM 503 are connected to each other by a bus 504. An input/output (I/O) interface 505 is also connected to bus 504.

A number of components in the device 500 are connected to the I/O interface 505, including: an input unit 506 such as a keyboard, a mouse, or the like; an output unit 507 such as various types of displays, speakers, and the like; a storage unit 508, such as a magnetic disk, optical disk, or the like; and a communication unit 509 such as a network card, modem, wireless communication transceiver, etc. The communication unit 509 allows the device 500 to exchange information/data with other devices through a computer network such as the internet and/or various telecommunication networks.

The computing unit 501 may be a variety of general-purpose and/or special-purpose processing components having processing and computing capabilities. Some examples of the computing unit 501 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various dedicated Artificial Intelligence (AI) computing chips, various computing units running machine learning model algorithms, a Digital Signal Processor (DSP), and any suitable processor, controller, microcontroller, and so forth. The calculation unit 501 executes the respective methods and processes described above, such as the digital signature method or the verification method of signature information. For example, in some embodiments, the digital signature method or the verification method of the signature information may be implemented as a computer software program tangibly embodied in a machine-readable medium, such as the storage unit 508. In some embodiments, part or all of the computer program may be loaded and/or installed onto the device 500 via the ROM 502 and/or the communication unit 509. When the computer program is loaded into the RAM 503 and executed by the computing unit 501, one or more steps of the above-described digital signature method or verification method of signature information may be performed. Alternatively, in other embodiments, the computing unit 501 may be configured to perform the digital signature method or the verification method of the signature information by any other suitable means (e.g., by means of firmware).

Various implementations of the systems and techniques described here above may be implemented in digital electronic circuitry, integrated circuitry, Field Programmable Gate Arrays (FPGAs), Application Specific Integrated Circuits (ASICs), Application Specific Standard Products (ASSPs), system on a chip (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and/or combinations thereof. These various embodiments may include: implemented in one or more computer programs that are executable and/or interpretable on a programmable system including at least one programmable processor, which may be special or general purpose, receiving data and instructions from, and transmitting data and instructions to, a storage system, at least one input device, and at least one output device.

Program code for implementing the methods of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the program codes, when executed by the processor or controller, cause the functions/operations specified in the flowchart and/or block diagram to be performed. The program code may execute entirely on the machine, partly on the machine, as a stand-alone software package partly on the machine and partly on a remote machine or entirely on the remote machine or server.

In the context of this disclosure, a machine-readable medium may be a tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

To provide for interaction with a user, the systems and techniques described here can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and a pointing device (e.g., a mouse or a trackball) by which a user can provide input to the computer. Other kinds of devices may also be used to provide for interaction with a user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form, including acoustic, speech, or tactile input.

The systems and techniques described here can be implemented in a computing system that includes a back-end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: local Area Networks (LANs), Wide Area Networks (WANs), and the Internet.

The computer system may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server may be a cloud server, a server of a distributed system, or a server with a combined blockchain.

It should be understood that various forms of the flows shown above may be used, with steps reordered, added, or deleted. For example, the steps described in the present disclosure may be executed in parallel or sequentially or in different orders, and are not limited herein as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved.

The above detailed description should not be construed as limiting the scope of the disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions may be made in accordance with design requirements and other factors. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present disclosure should be included in the scope of protection of the present disclosure.

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