CN115174057A - Online and offline signature generation method and system based on SM2 signature - Google Patents

Abstract

The invention discloses an online and offline signature generation method and system based on SM2 signature, the scheme utilizes color change Long Haxi to hash a message, and then the operation is carried out to obtain a final signature. The offline stage signs the chameleon hash value, and the online stage enables the chameleon hash of the message m to be the same as the offline stage value, so that the SM2 signature can support the online and offline function. The invention has the advantages of high safety, perfect function and the like, and can ensure that the SM2 signature has the function of online and offline signature. The method can be applied to light-weight signature scenes, such as environments of mobile phones, portable computers and the like.

Description

An online and offline signature generation method and system based on SM2 signature

technical field

The invention belongs to the technical field of information security, in particular to an online and offline signature generation method and system based on SM2 signature.

Background technique

Digital signature is an important cryptographic scheme, which generates digital signature of message by some cryptographic operation instead of writing signature or seal. In these schemes, each user will generate a (private) signing key and a (public) verification key. The user signs the message with the private signing key, and anyone can use the signer's public verification key to authenticate the signer and verify the message. A signature scheme is considered secure if any attacker who knows the user's public key but not the user's private key cannot forge the signature on a new message.

SM2 is an elliptic curve public key cryptography algorithm promulgated by the State Cryptography Administration in December 2010 (see "SM2 Elliptic Curve Public Key Cryptography Algorithm" specification). SM2 mainly includes three parts: signature algorithm, key exchange algorithm, and encryption algorithm. Based on this algorithm, digital signature, key exchange and data encryption can be realized.

This patent designs an online and offline signature generation method and system based on SM2 signature. This scheme uses the chameleon hash to hash the message, and then operates to obtain the final signature. In the offline phase, the chameleon hash value is signed, and in the online phase, the chameleon hash of the message m is the same as the value in the offline phase, so that the SM2 signature can support the online and offline functions.

SUMMARY OF THE INVENTION

The above-mentioned technical problems of the present invention are mainly solved by the following technical solutions:

An online and offline signature generation method based on SM2 signature, which is characterized in that an online signature or an offline signature is obtained based on system parameters, user private key, trapdoor key, and message, and specifically, a trapdoor hash function is used to perform a given message. Hash, and then use the given signature scheme to sign the hash value; using the chameleon hash, the offline phase signs the chameleon hash value, and the online phase makes the chameleon hash of the message m the same as the value in the offline phase.

In the above method, when signing in the offline phase, the system parameter PP, the private key d of the user A, the trapdoor key t, and the message m are given;

计算(x_e，y_e)＝e＝w·G；选取

计算(x₁，y₁)＝k·G，计算r＝(x_e+x₁)mod q；s＝((1+d)^-1·(k-r·d))mod q；User A randomly selects

Calculate (x _e , y _e )=e=w·G; choose

Calculate (x ₁ , y ₁ )=k·G, calculate r=(x _e +x ₁ )mod q; s=((1+d) ⁻¹ ·(kr·d))mod q;

output offline signature value for message m

In the above method, when signing in the online phase, the system parameter PP, the private key d of the user A, the trapdoor key t, and the message m are given;

User A calculates

Output the final signature value σ=(r, s, c) for message m.

In the above method, before the online signature or the offline signature, system initialization and key generation are performed, wherein the system initialization is based on the security parameters, and the system parameters are generated, specifically:

生成椭圆曲线方程y²＝x³+ax+b mod p，满足方程的点构成一个阿贝尔群

Given a security parameter 1 ⁿ , choose a finite field

Generate the elliptic curve equation y ² =x ³ +ax+b mod p, the points satisfying the equation form an abelian group

其阶为q；Pick a generator at random

Its order is q;

output system parameters

In the above method, when the key is generated,

计算公钥P_A＝d·G；Given the system parameter PP, user A randomly selects

Calculate the public key P _A =d·G;

计算T＝t·G；Output public-private key pair (P _A , d); randomly selected

Calculate T = t · G;

Output the public hash key T of the chameleon hash, the trapdoor key t.

In the above method, after online signature or offline signature, signature verification is performed, specifically

如果不成立，则验证不通过；Given system parameters PP, message m, signature value σ=(r, s, c), the verifier verifies

If it does not hold, the verification fails;

Calculate (x _e , y _e )=e=H(m)·G+c·T in turn; (x ₁ , y ₁ )=s·G+(r+s)·PA ; R ₌ (x _e +x ₁ ) modq;

Verify whether the equation R=r is established, if so, it is a legal signature; otherwise, the verification fails.

A system, characterized in that the system is configured to be able to obtain an online signature or an offline signature based on system parameters, user private keys, trapdoor keys, messages, and in particular to hash a given message using a trapdoor hash function , and then use the given signature scheme to sign the hash value; using the chameleon hash, the offline phase signs the chameleon hash value, and the online phase makes the chameleon hash of the message m the same as the value in the offline phase.

Therefore, the present invention has the following advantages: the existing online and offline signature algorithms are mainly designed based on international algorithms, and there is no online and offline signature algorithm based on my country's commercial cryptographic standards. The present invention has the advantages of high security, perfect functions, etc. Signature has the function of online and offline signature. It can be used in lightweight signature scenarios, such as mobile phones, portable computers and other environments.

Description of drawings

Accompanying drawing 1 is the method flow chart of the present invention;

Accompanying drawing 2 is the signature generation and verification flow chart of the present invention;

Detailed ways

The technical solutions of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

Example:

The parameters involved in the present invention are defined as follows:

n: Security parameter length.

a, b: Elliptic curve parameters.

PP: System parameter.

阶为素数q的椭圆曲线群，元素为椭圆曲线上的点。

The group of elliptic curves whose order is a prime number q, and the elements are points on the elliptic curve.

包含p个元素的素域。循环群

的一个生成元。

A prime field containing p elements. Cyclic group

a generator of .

的元素个数。p: finite field

the number of elements.

的阶。q: cyclic group

step.

由整数1，2，...，q-1组成的整数集合。

The set of integers consisting of the integers 1, 2, ..., q-1.

P _A : User A's public key.

T: Public hash key.

d: User A's private key.

t: Trapdoor key.

mod q: Modulo q operation.

H: cryptographic hash function,

m: message value.

w, k: intermediate variables, which are random numbers.

(r, s): Offline signature value.

(r, s, c): The final signature value.

FIG. 1 is a flow chart of a method implemented in the present invention. The method includes the following steps:

S1: Generate system parameters based on security parameters.

S2: The user selects a random number and generates a public-private key pair, a public hash key, and a trapdoor key.

S3: Obtain online signature or offline signature based on system parameters, user private key, trapdoor key, and message.

S4: Verify the signature based on system parameters, messages, and signature values.

For the purpose of the present invention, the present invention proposes an online and offline signature generation method and system based on SM2 signature, and the specific description is given below.

The specific program process is as follows:

1) System initialization: Given a safety parameter 1 ⁿ , perform the following steps:

生成椭圆曲线方程y²＝x³+ax+b mod p，满足方程的点构成一个阿贝尔群

a) choose a finite field

Generate the elliptic curve equation y ² =x ³ +ax+b mod p, the points satisfying the equation form an abelian group

其阶为q。b) randomly select a generator

Its order is q.

c) Output system parameters

2) Key generation: Given the system parameter PP, a user A performs the following steps:

计算公钥P_A＝d·G。a) randomly selected

Calculate the public key P _A =d·G.

b) Output the public-private key pair (P _A , d).

计算T＝t·G。c) randomly selected

Calculate T=t·G.

d) Output the public hash key T of the chameleon hash, the trapdoor key t.

Signature: Given system parameters PP, user A's private key d, trapdoor key t, and message m, as shown in Figure 2, user A performs the following steps:

Offline stage:

计算(x_e，y_e)＝e＝w·G。e) randomly selected

Calculate (x _e , y _e )=e=w·G.

计算(x₁，y₁)＝k·G，f) randomly selected

Calculate (x ₁ , y ₁ )=k·G,

g) Calculate r=(x _e +x ₁ ) mod q.

h) Calculate s=((1+d) ⁻¹ ·(kr·d))mod q.

i) output the offline signature value for message m

Online stage:

a) Calculate

b) Output the final signature value σ=(r, s, c) for message m.

3) Verification: Given system parameters PP, message m, and signature value σ=(r, s, c), as shown in Figure 2, the verifier performs the following steps:

如果不成立，则验证不通过。a) Verify

If it does not hold, the verification fails.

b) Calculate (x _e , y _e )=e=H(m)·G+c·T.

c) Calculate (x ₁ , y ₁ )=s· _G +(r+s)·PA .

d) Calculate R=(x _e +x ₁ ) mod q.

e) Verify whether the equation R=r is established, if so, it is a legal signature; otherwise, the verification fails.

The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which the present invention pertains can make various modifications or additions to the described specific embodiments or substitute in similar manners, but will not deviate from the spirit of the present invention or go beyond the definitions of the appended claims range.

Claims (7)

1. An online and offline signature generation method based on SM2 signature is characterized in that an online signature or an offline signature is acquired based on system parameters, a user private key, a trapdoor key and a message, specifically, a given message is hashed by using a trapdoor hash function, and then a hash value is signed by using a given signature scheme; and signing the chameleon hash value by using the chameleon Long Haxi in the off-line stage, wherein the chameleon hash value of the message m is the same as the value of the off-line stage in the on-line stage.

2. The method for generating the online and offline signature based on the SM2 signature as claimed in claim 1, wherein during the offline stage signature, a system parameter PP, a private key d of a user a, a trapdoor key t, and a message m are given;

user A random selection

Calculating (x) _e ，y _e ) = e = w · G; selecting

Calculating (x) ₁ ，y ₁ )＝k·G，

Calculation of r = (x) _e +x ₁ )mod q；s＝((1+d) ^-1 ·(k-r·d))mod q；

Outputting offline signature value for message m

3. The method for generating the online and offline signature based on the SM2 signature as claimed in claim 1, wherein during the online stage signature, a system parameter PP, a private key d of a user a, a trapdoor key t, and a message m are given;

user A computing

The final signature value σ = (r, s, c) on the message m is output.

4. The method for generating online and offline signatures based on SM2 signature as claimed in claim 1, wherein the system initialization and key generation are performed before the online signature or the offline signature, wherein the system initialization is based on security parameters to generate system parameters, specifically, system parameters

Given a safety parameter 1 ⁿ Selecting a finite field

Generating an elliptic Curve equation y ² ＝x ³ + ax + b mod p, the points satisfying the equation forming an Abel group

Randomly selecting a generator

The order is q;

outputting system parameters

5. The SM2 signature-based online and offline signature generation method of claim 4, wherein when the key is generated,

given system parameters PP, user A randomly selects

Computing the public key P _A ＝d·G；

Outputting public and private key pair (P) _A D); random selection

Calculating T = T · G;

and outputting the chameleon hashed public hash key T and the trapdoor key T.

6. The SM2 signature-based online and offline signature generation method as claimed in claim 1, wherein signature verification is performed after online signature or offline signature, specifically, signature verification is performed

Given the system parameter PP, the message m, the signature value σ = (r, s, c), the verifier verifies

If not, the verification is not passed;

calculating (x) in sequence _e ，y _e )＝e＝H(m)·G+c·T；(x ₁ ，y ₁ )＝s·G+(r+s)·P _A ；R＝(x _e +x ₁ )mod q；

Verifying whether the equation R = R is true, and if so, determining that the equation R = R is a legal signature; otherwise, the verification is not passed.

7. A system configured to enable on-line or off-line signature acquisition based on system parameters, a user private key, a trapdoor key, and a message, in particular, hashing a given message using a trapdoor hash function, and then signing the hash value using a given signature scheme; and signing the chameleon hash value by using the chameleon Long Haxi in the off-line stage, wherein the chameleon hash value of the message m is the same as the value of the off-line stage in the on-line stage.

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