CN113158176B - Public key analysis method, device, equipment and storage medium based on SM2 signature - Google Patents
Public key analysis method, device, equipment and storage medium based on SM2 signature Download PDFInfo
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- CN113158176B CN113158176B CN202110611489.6A CN202110611489A CN113158176B CN 113158176 B CN113158176 B CN 113158176B CN 202110611489 A CN202110611489 A CN 202110611489A CN 113158176 B CN113158176 B CN 113158176B
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/30—Authentication, i.e. establishing the identity or authorisation of security principals
- G06F21/45—Structures or tools for the administration of authentication
- G06F21/46—Structures or tools for the administration of authentication by designing passwords or checking the strength of passwords
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- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/60—Protecting data
- G06F21/64—Protecting data integrity, e.g. using checksums, certificates or signatures
Abstract
The invention discloses a public key analysis method, a device, equipment and a storage medium based on SM2 signature, wherein the method comprises the following steps: inputting standard SM2 signature value (r ', s '), message M ' executed with digital signature, and hash value of signer
Distinguishable identification of signer
And elliptic curve system parameters including elliptic curve equation parameters a, b and base point G = (x) G ，y G ) And the order n of the base point; s2: converting the data types of r 'and s' into integers
Calculating
Converting the data type of e' into an integer; s3: the public key of the signer is resolved by converting the compressed point to a point on an elliptic curve. The invention realizes public key resolution of SM2 signature with execution efficiency basically equivalent to that of the traditional method under the condition of not changing SM2 signature algorithm and not reducing the security of SM2 signature algorithm.
Description
Technical Field
The invention belongs to the field of information security, and particularly relates to a public key analysis method, device, equipment and storage medium based on SM2 signature.
Background
Cryptologists NealKoblitz and Victor Miller, in 1985, proposed the idea of Elliptic Curve Cryptography (ECC) respectively, making it a powerful tool for constructing public key cryptosystems. The SM2 algorithm specified in the national standard GB/T32918 'information security technology SM2 elliptic curve public key cryptographic algorithm' is a specific ECC cryptographic algorithm, and mainly comprises a digital signature algorithm, a key exchange protocol and a public key encryption algorithm. GB/T32918.2 stipulates the digital signature algorithm of SM2 elliptic curve public key cryptographic algorithm, including digital signature generation algorithm and verification algorithm and corresponding flow, can satisfy the safety requirements of identity authentication and data integrity, information source authenticity in various cryptographic applications. The digital signature algorithm generates a digital signature on data by a signer and verifies the authenticity of the signature by a verifier. Each signer has a public key and a private key, wherein the private key is used to generate the signature and the verifier verifies the signature with the public key of the signer. Before the generation process of the signature and the verification process of the signature, a cipher hash function is respectively used for compressing the distinguishable identification ID of the signature user, partial elliptic curve system parameters, the public key hash value of the signature user and the message to be signed to obtain the hash value of the user.
In many fields such as cloud computing, big data, internet of things, mobile internet, industrial control systems, block chains and the like, SM2 is used for data signature to ensure data authenticity and integrity, and in order to verify the correctness of the signature, a public key needs to be verified, and the public key is used for executing an SM2 signature verification function. In order to solve the problem of how to acquire a public key under the conditions that the public key is not timely sent or the data of the public key is abnormal and the like, an SM2 signature recovery public key method (Wanyao, Rahao, Linli, a method for recovering the public key based on SM2 signature [ P ]. Karman island: CN111066285A, 2020-04-24.) is provided for the Wangzhao of Aliaba and the like for the subsequent execution of an SM2 signature verification function, and an SM2 signature recovery public key scheme (Wangzhao, Jiang Meng, Baijian, subsun) is provided for the application scenes of a block chain such as Wangzhao of China Nean and the like (Wangzhao, Jiang, Lang, and Li, a method for recovering the public key and the address based on SM2 signature [ P ]. Sichuan province: CN112152814A, 2020-12-29) in the block chain. Both of these solutions solve the problem of recovering the public key from the SM2 signature.
Although these two schemes can recover the public key, there are the following problems.
(1) Both of these schemes completely change the signature algorithm of SM 2: the input parameters, output results and execution flow of the SM2 signature algorithm are changed.
(2) These two schemes are incompatible with existing SM2 signature and signature verification algorithms: on the one hand, the standard SM2 signature value cannot recover the public key using these two schemes, and on the other hand, the signature value calculated by these two algorithms cannot be recognized by the standard SM2 signature verification algorithm.
(3) Both of these solutions result in the SM2 software and hardware implementation modules having to be modified, especially not for hardware implementation.
(4) These two schemes may risk reducing the security of the signature of the SM2 algorithm: an additional output parameter v is introduced from within the SM2 signature algorithm, which would reduce the security of the SM2 signature algorithm, neither of which gives an explicit security analysis evaluation.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a public key analysis method, a device, equipment and a storage medium based on SM2 signature, which realize public key analysis of SM2 signature with execution efficiency basically equivalent to that of the traditional method under the condition of not changing SM2 signature algorithm and not reducing the security of SM2 signature algorithm.
The purpose of the invention is realized by the following technical scheme:
the symbols, abbreviations or notations used in the present invention are as follows:
a and B: two users of the SM2 public key cryptosystem, a being the signer and B being the verification signer.
q: finite field F q The number of elements in (c).
F q : a finite field containing q elements.
a，b：F q The elements in (1), which define F q An elliptic curve E above.
E（F q ）：F q A set of all rational points of the upper elliptic curve E.
O: the infinity point (or zero point) on the elliptic curve E is the unit cell of the elliptic curve addition group.
G: the order n of a base point of the elliptic curve is prime.
#E（F q ）：E（F q ) The number of points on, called elliptic curve E (F) q ) The order of (a).
n: the order of the base point G.
[k] P: the point k times the point P on the elliptic curve.
d A ，d B : private keys of user a and user B, respectively.
P A ，P B : public keys for user a and user B, respectively.
Hash (): a cryptographic hash function.
ID A ，ID B : user A is respectively of length entlen A Bit distinguishable identification ID A And user B has a length ofentlen B Bit distinguishable identification ID B 。
ENTL A ，ENTL B : respectively, a discernible identity ID of user a A Bit length of (entlen) A Converted two bytes ENTL A And a discemable identification ID of user B B Bit length of (entlen) B Converted two bytes ENTL B 。
Z A ，Z B : respectively hash values for user a/user B. With the hash value Z of user A A For example, the coordinates x of the elliptic curve equation parameters a, b, G are first scaled according to the algorithm given in sections 4.2.5 and 4.2.4 of GB/T32918.1 G 、y G And P A Coordinate x of A 、y A Is converted into a bit string and then recalculated
。
mod n: modulo n arithmetic. For example, 23mod7= 2.
x | | y: and splicing x and y, wherein x and y are bit strings or byte strings.
The public key analysis method based on SM2 signature comprises the following steps:
s1: inputting standard SM2 signature value (r ', s '), message M ' executed with digital signature, and hash value of signer
Distinguishable identification of signer
And elliptic curve system parameters including elliptic curve equation parameters a, b and base point G = (x) G ，y G ) And the order n of the base point;
s2: converting the data types of r 'and s' into integers
Calculating
Converting the data type of e' into an integer;
s3: resolving the public key of the signer by converting the compressed point into a point on the elliptic curve;
wherein the content of the first and second substances,
is the concatenation of x and y, wherein x and y are bit strings or byte strings,
is a cryptographic hash function with a message digest length of v bits.
Further, the method also comprises an input parameter checking step: examination of
And
if the two are not true, returning an error; where n is the order of the base point G.
Further, when an intermediate temporary variable is used, step S3 specifically includes:
s311: computing
，
；
S312: bit setting
Compressing the point
Conversion to a point on the SM2 elliptic curve
；
S313: put n e =0，n e An error number counter;
s314: computing public keys
Wherein [ k ]]P: the point k times the point P on the elliptic curve.
Further, the method also comprises a public key correctness checking step:
a, b and x G 、y G 、
、
Converting the data type of the data into a byte string;
computing
；
Examination of
If yes, return to
；
Otherwise, calculate n e = n e +1, check n e If not more than 1 is true, if true, Q is set = -Q, and step S314 is executed.
Further, when two intermediate temporary variables are used, step S3 specifically includes:
s321: computing
，
，
；
S322: bit setting
To compress the point
Conversion to a point on the SM2 elliptic curve
；
S323: n is arranged e =0，n e An error number counter;
s324: computing public keys
(ii) a Wherein the content of the first and second substances,
，
；
wherein, [ k ] P: the point k times the point P on the elliptic curve.
Further, the method also comprises a public key correctness checking step:
a, b and x G 、y G 、
、
Converting the data type of the data into a byte string;
computing
；
Examination of
If yes, return to
；
Otherwise, calculate n e = n e +1, check n e If it is not more than 1, set R 1 =-R 1 Step S324 is executed;
wherein, [ k ] P: the point k times the point P on the elliptic curve.
Further, the method also comprises a public key correctness checking step:
a, b and x G 、y G 、
、
Converting the data type of the data into a byte string;
computing
；
Examination of
If yes, return to
；
Otherwise, calculate n e = n e +1, check n e If it is not more than 1, set R 1 =-R 1 Step S324 is performed.
On the other hand, the invention also provides a public key analysis device based on SM2 signature, which comprises:
the parameter input module is used for inputting parameters required by analyzing the public key;
the data conversion module is used for converting data types;
and the public key analysis module is used for converting the compression point into a point on the elliptic curve to analyze the public key of the signer.
Further, the system also comprises a parameter checking module and a public key checking module; wherein, the first and the second end of the pipe are connected with each other,
the parameter checking module is used for checking whether the input parameters are wrong;
and the public key verifying module is used for verifying the correctness of the public key according to the hash value of the signer.
In another aspect, the present invention further provides a computer device, which includes a processor and a memory, where the memory stores a computer program, and the computer program is loaded and executed by the processor to implement any one of the above public key parsing methods based on SM2 signature.
In another aspect, the present invention further provides a computer-readable storage medium, in which a computer program is stored, the computer program being loaded and executed by a processor to implement any one of the above public key parsing methods based on SM2 signature.
The invention has the beneficial effects that:
the defects of the traditional scheme are overcome, and the signature algorithm of the SM2 is changed. The invention does not make any changes to the SM2 signature algorithm.
The defects of the traditional scheme are overcome, and the traditional SM2 signature algorithm and signature verification algorithm are incompatible. The invention uses the signature value of the standard SM2 signature algorithm, thus being completely compatible with the existing SM2 signature algorithm and the existing SM2 signature verification algorithm.
The defects of the traditional scheme are overcome, and the SM2 software and hardware implementation modules need to be changed. The invention uses the signature value of the standard SM2 signature algorithm, so that the SM2 software and hardware implementation modules do not need to be modified.
The method solves the defects of the traditional scheme, and probably has the risk of reducing the signature security of the SM2 algorithm. The signature value of the standard SM2 signature algorithm is used in the invention, and the SM2 signature algorithm is not changed, so that the security of the SM2 signature algorithm is not influenced in any negative way.
The performance efficiency of the present invention is comparable to that of the conventional scheme, since the performance efficiency of multiple points ([ k ] P) is the slowest and differs by several orders of magnitude in SM2 and related schemes compared to the hash operation, point addition, integer operation, etc. involved, the performance efficiency of the scheme is usually evaluated in terms of the number of times the multiple points are performed. The two schemes of the invention and the traditional scheme both need to execute the multi-point operation for 2 times, so the execution efficiency of the invention is equivalent to that of the two schemes of the traditional scheme.
Drawings
Fig. 1 is a flow chart of a public key parsing method based on SM2 signature according to embodiment 1 of the present invention;
fig. 2 is a flowchart of a public key parsing method based on SM2 signature according to embodiment 2 of the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
It should be noted that, in order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described below, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments.
Thus, the following detailed description of the embodiments of the present invention is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
First, the symbols, abbreviations and signs used in the present embodiment will be explained.
A and B: two users of the SM2 public key cryptosystem, a being the signer and B being the verification signer.
q: finite field F q The number of elements in (c).
F q : a finite field containing q elements.
a，b：F q The elements in (1), which define F q An elliptic curve E above.
E（F q ）：F q A set of all rational points of the upper elliptic curve E.
O: the infinity point (or zero point) on the elliptic curve E is the unit cell of the elliptic curve addition group.
G: the order n of a base point of the elliptic curve is prime.
#E（F q ）：E（F q ) The number of points on, called elliptic curve E (F) q ) The order of (a).
n: the order of the base point G.
[k] P: the point k times the point P on the elliptic curve.
d A ，d B : private keys of user a and user B, respectively.
P A ，P B : public keys for user a and user B, respectively.
Hash (): a cryptographic hash function.
ID A ，ID B : user A is respectively of length entlen A Bit distinguishable identification ID A And user B is entlen in length B Bit distinguishable identification ID B 。
ENTL A ，ENTL B : respectively, a discernible identity ID of user a A Bit length of (entlen) A Converted two bytes ENTL A And a discemable identification ID of user B B Bit length of (entlen) B Converted two bytes ENTL B 。
Z A ，Z B : respectively hash values for user a/user B. With the hash value Z of user A A For example, the coordinates x of the elliptic curve equation parameters a, b, G are first scaled according to the algorithm given in sections 4.2.5 and 4.2.4 of GB/T32918.1 G 、y G And P A Coordinate x of A 、y A Is converted into a bit string and then recalculated
。
mod n: modulo n arithmetic. For example, 23mod7= 2.
x | | y: and splicing x and y, wherein x and y are bit strings or byte strings.
As shown in fig. 1, it is a flow chart of a public key parsing method based on SM2 signature provided in this embodiment, and the method specifically includes the following steps:
s1: inputting standard SM2 signature value (r ', s '), message M ' executed with digital signature, and hash value of signer
Distinguishable identification of signer
And elliptic curve system parameters including elliptic curve equation parameters a, b and base point G = (x) G ，y G ) And the order n of the base point, checking the input parameters and calculating the hash value calculation.
S1-1: converting the data types of r 'and s' into integers according to the specification of the data type conversion of section 4.2 of SM2 standard GB/T32918.1, and checking
And
whether both are true. If one fails to becomeImmediately, an "error" is returned.
S1-2: device for placing
Calculating
According to the specification of section 4.2 data type conversion of the SM2 standard GB/T32918.1, the data type conversion method is to
Converts to integers.
S2A: the public key of the signer is parsed.
S2A-1: computing
，
；t 1 Is an intermediate temporary variable;
S2A-2: bit setting
Compression point defined by the SM2 standard
Conversion to a point on the SM2 elliptic curve
Preferably, the specific implementation mode can adopt the A.5 scheme of GB/T32918.1;
S2A-3: put n e =0，n e The error number counter is initialized to 0 and is used for verifying the correctness of the subsequent public key;
S2A-4: computing public keys
Wherein [ k ]]P: k times the point P on the elliptic curve;
s3: the correctness of the public key is checked using the hash value of the signer.
S3-1: a, b, x according to the specification of the 4.2 th data type conversion of the SM2 standard GB/T32918.1 G 、y G 、
、
Is converted into a string of bytes. Computing
；
S3-2: examination of
If yes, return to
(ii) a Otherwise (
False), calculate n e = n e +1, check n e If the result is not more than 1, setting Q = -Q, and jumping to the step S2A-4; otherwise (n) e Not ≦ 1) returns an "error".
Compressing point
Conversion to a point on the SM2 elliptic curve
Two points are actually obtained
The public key parsing method based on SM2 signature provided by the embodiment realizes public key parsing of SM2 signature with execution efficiency basically equivalent to that of the conventional method under the condition of not changing SM2 signature algorithm and not reducing the security of SM2 signature algorithm.
Example 2
The symbols, abbreviations and signs used in this example are the same as those in example 1, and are not described herein again.
As shown in fig. 2, it is a flow chart of the public key parsing method based on SM2 signature provided in this embodiment, and the method specifically includes the following steps:
s1: the input standard SM2 signature value (r ', s '), the message M ' on which the digital signature is performed, the hash value of the signer
Distinguishable identification of signer
And elliptic curve system parameters including elliptic curve equation parameters a, b and base point G = (x) G ，y G ) And the order n of the base point, checking the input parameters and calculating the hash value calculation.
S1-1: converting the data types of r 'and s' into integers according to the specification of the 4.2 th section data type conversion of SM2 standard GB/T32918.1, and checking
And
whether both are true. If one fails, an error is returned.
S1-2: device for placing
Calculating
According to the specification of section 4.2 data type conversion of the SM2 standard GB/T32918.1, the data type conversion method is to
The data type of (c) is converted into an integer.
S2B: the public key of the signer is parsed.
S2B-1: computing
，
，
；t 1 、t 2 Is an intermediate temporary variable;
S2B-2: bit setting
Compression point defined by the SM2 standard
Conversion to a point on the SM2 elliptic curve
Preferably, the specific implementation mode can adopt the A.5 scheme of GB/T32918.1;
S2B-3: put n e =0，n e The error number counter is initialized to 0 for verifying the correctness of the public key subsequently; computing
，
；
S2B-4: computing
；
S3: the correctness of the public key is checked using the hash value of the signer.
S3-1: a, b, x according to the specification of the 4.2 th data type conversion of the SM2 standard GB/T32918.1 G 、y G 、
、
Is converted into a string of bytes. Computing
；
S3-2: examination of
If yes, return to
(ii) a Otherwise (
False), calculate n e = n e +1, check n e Whether or not 1 is true, if true, put R 1 =-R 1 Jumping to step S2B-4; otherwise (n) e Not ≦ 1) returns an "error".
Compressing point
Conversion to a point on the SM2 elliptic curve
Actually, two will be obtainedDot
Since operations other than the multi-point operation take extremely short time compared to the multi-point operation, the number of times of the multi-point operation is counted:
in example 1, (S1 + S2A + S3) as per the flow, S2A-1 to S2A-4 are performed once; if S3-2 appears
Is not true and n e When the value is less than or equal to 1, the control device jumps back to S2A-4 to execute S2A-4 again. The probability is 1/2.
In example 2, (S1 + S2B + S3) as per the flow, S2B-1 to S2B-4 are performed once; if S3-2 appears
Is false and n e When the value is less than or equal to 1, the control device jumps back to S2B-4 to execute S2B-4 again. The probability is 1/2.
From the above, in embodiment 1, the multi-point operation (e.g., [ s ] G) is performed:
(1) S2A-4 when executed for the first time: 2 times;
(2) when the equation does not jump back to S2A-4: 0.5 x 2 times; totaling: 3 times.
In embodiment 2, the multi-point operation (e.g., [ s ] G) performs:
(1) S2A-3 and S2A-4 performed for the first time: 2 times;
(2) when the equation does not jump back to S2B-4: 0 time; totaling: 2 times.
As described above, in embodiment 2, the operation time is shorter than that in embodiment 1, and the SM2 public key can be analyzed more efficiently.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (7)
1. The public key analysis method based on SM2 signature is characterized by comprising the following steps:
s1: inputting standard SM2 signature value (r ', s '), message M ' executed with digital signature, and hash value of signer
Distinguishable identification of signer
And elliptic curve system parameters including elliptic curve equation parameters a, b and base point G = (x) G ，y G ) And the order n of the base point; examination of
And
if the two are not true, returning an error; wherein n is the order of the base point G;
s2: converting the data types of r 'and s' into integers
Calculating
Converting the data type of e' into an integer;
s3: converting the compression point into a point on an elliptic curve through an intermediate temporary variable to analyze the public key of the signer;
when an intermediate temporary variable is used, step S3 specifically includes:
s311: computing
，
；
S312: bit setting
Compressing the point
Conversion to a point on the SM2 elliptic curve
；
S313: put n e =0，n e An error number counter;
a, b and x G 、y G 、
、
Converting the data type of the data into a byte string;
computing
；
Examination of
If yes, return to
；
Otherwise, calculate n e = n e +1, check n e If not more than 1 is true, if so, Q is set to be Q = -Q, and the step S314 is executed;
s314: computing public keys
Wherein [ k ]]P: k times the point P on the elliptic curve;
wherein the content of the first and second substances,
is the concatenation of x and y, wherein x and y are bit strings or byte strings,
is a cryptographic hash function with a message digest length of v bits.
2. The method for public key resolution based on SM2 signature as claimed in claim 1, wherein when two intermediate temporary variables are used, step S3 specifically includes:
s321: computing
，
，
；
S322: bit setting
Compressing the point
Conversion to a point on the SM2 elliptic curve
；
S323: put n e =0，n e An error number counter;
s324: computing public keys
(ii) a Wherein the content of the first and second substances,
，
；
wherein, [ k ] P: the point k times the point P on the elliptic curve.
3. The public key parsing method based on SM2 signature as claimed in claim 2, wherein the method further comprises a public key correctness checking step of:
a, b and x G 、y G 、
、
Converting the data type of the data into a byte string;
computing
；
Examination of
If yes, return to
；
Otherwise, calculate n e = n e +1, check n e Whether or not less than 1If true, put R 1 =-R 1 Step S324 is performed.
4. An SM2 signature-based public key parsing apparatus for implementing the SM2 signature-based public key parsing method as claimed in claim 1, the apparatus comprising:
the parameter input module is used for inputting parameters required by analyzing the public key;
the data conversion module is used for converting data types;
and the public key analysis module is used for converting the compression point into a point on the elliptic curve to analyze the public key of the signer.
5. The public key parsing apparatus based on SM2 signature as recited in claim 4, further comprising a parameter verification module and a public key verification module; wherein the content of the first and second substances,
the parameter checking module is used for checking whether the input parameters are wrong;
and the public key verifying module is used for verifying the correctness of the public key according to the hash value of the signer.
6. A computer device, characterized in that the computer device comprises a processor and a memory, in which a computer program is stored, which is loaded and executed by the processor to implement the public key parsing method based on SM2 signature according to any of claims 1 to 3.
7. A computer-readable storage medium, in which a computer program is stored, which is loaded and executed by a processor to implement the SM2 signature-based public key parsing method according to any one of claims 1 to 3.
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