CN115550007A - Signcryption method and system with equivalence test function based on heterogeneous system - Google Patents

Abstract

The invention discloses a signcryption method and a signcryption system with an equivalent test function based on a heterogeneous system, wherein system parameters are initialized; CLC-based key generation and PKI-based key generation; generating a trap value td; a sending end of the CLC environment obtains signcryption text by utilizing a private key, identity information and a public key of a receiver through Hash operation and XOR operation; the receiving end of the PKI environment performs decryption by Hash operation and XOR operation according to the signcryption ciphertext, the public key of the sending end and the private key of the receiver; performing equivalence test by taking an authorization trap door and a ciphertext of a sending end based on a CLC environment and a receiving end based on a PKI environment as input, and respectively returning test results to the sending end and the receiving end by a server; if the keywords are tested to be equal, the plaintext of the two users is indicated to be equal, otherwise, the plaintext is not equal. The method has high calculation efficiency, can be applied to data retrieval, realizes the integrity, confidentiality and authentication among wireless sensor networks, and meets the requirements of safety and privacy.

Description

A signcryption method and system with equivalence testing function based on heterogeneous system

technical field

The invention belongs to the field of secure communication, in particular to a signcryption method and system based on a heterogeneous system with an equivalence test function.

Background technique

Due to time and space constraints, data storage and processing becomes a concern. Fortunately, the concept of cloud computing is considered to be an advantageous method to support the above-mentioned services without resource constraints. In this cloud-assisted environment, cloud servers provide a platform to process outsourced data collected by smart devices, greatly improving efficiency. As a result of these high-impact processing capabilities, a series of architectures based on cloud-assisted environments WBANS has emerged.

Although there are many benefits of using WBANS, the storage and transmission data in the system may lack security protection, resulting in various security issues, such as privacy leakage. Therefore, the concept of encryption is considered to overcome this weakness. However, the retrieval methods used for plaintext cannot be used for ciphertext. In order to obtain specific information from a large number of ciphertexts, directly using the solution of downloading and then decrypting not only reduces the efficiency, but also brings the risk of data leakage. In this way, through encryption, the availability of information is greatly reduced. In 2002, Zheng introduced the concept of signcryption, which allows encryption and signing to occur simultaneously in one logical step compared to previous methods, an approach known as "sign first, then encrypt". Using this scheme, the overhead is also reduced a lot. Since then, a lot of research has been done on the signcryption mechanisms used in various cryptosystems. Subsequently, in 2004, Boneh et al. proposed the concept of public key encryption with keyword search, which allows searching for corresponding encrypted data using keywords without decryption. Although this primitive can ensure that the cloud server performs matching operations on different ciphertexts, there is a problem that cannot be ignored, that is, the search function only supports encryption of sensitive data using the same public key. To solve this problem, in 2010, Yang et al. proposed the public key encryption with equivalence test (PKEET) scheme. In this case, the cloud server can perform an equivalence test on different ciphertexts encrypted with different public keys.

Regarding the open nature of the WBANS transmission channel, the PKEET-based scheme still has defects such as forgery or deletion between sensors and smart devices. Ensuring data integrity, authentication and confidentiality is critical. Inspired by this, in 2019, Wang et al. introduced a public key signcryption scheme (PKS-DET) with specified equivalence tests on ciphertexts. Encryption and signature operations can be performed at the same time, which greatly improves the computational efficiency and meets the previous requirements. However, their scheme is only suitable for a single system, not for complex heterogeneous systems. Furthermore, Sun and Li proposed a heterogeneous signcryption solution that allows messages to be transferred between users of PKI and CLC systems. In addition, heterogeneous schemes for the interactions between these systems are gradually being proposed. Ting et al. proposed a heterogeneous online/offline signcryption scheme that allows secure transmission of messages from sensor nodes in an IBC system to internet hosts in a PKI system. Saeed et al. constructed a new heterogeneous online/offline signcryption scheme for building secure channels for the Internet of Things. In 2020, Xiong et al. introduced the heterogeneous signcryption scheme in PKI into CLC. In 2021, Ali et al. proposed a heterogeneous signcryption scheme from CLC to PKI. Existing signcryption protocols with equivalence tests face the obstacle that they are only applicable to a single cryptosystem, but not to complex heterogeneous WBANS environments. In order to effectively solve these problems, the present invention proposes an equivalence test scheme in which the sending end belongs to an environment without a certificate, and the receiving end belongs to an environment based on public key infrastructure.

Contents of the invention

Purpose of the invention: the purpose of the present invention is to design a kind of signcryption method and system with equivalence test function and system based on heterogeneous system. The sending end is under the CLC cryptographic system, and the receiving end is under the PKI cryptographic system. Secure communication under the system.

Technical solution: The present invention proposes a heterogeneous system-based signcryption method with an equivalence test function, which specifically includes the following steps:

(1) Heterogeneous system parameter initialization; The heterogeneous system parameters include threshold value module, signcryption module based on CLC environment, decryption signcryption module based on PKI environment, equivalence test module and trusted third-party module Set system parameters;

(2) The sending end of the CLC environment submits the identity information ID _s to the key generation center. The key generation center generates a part of the private key D _s according to the system parameters and the identity information ID _s and sends it to the user. The user randomly selects a secret value x _s , set the complete private key and public key according to the secret value x _s and the partial private key D _s ;

计算对应的公钥PK_r，公钥与CA颁发的证书绑定，输出公钥PK_r和私钥SK_r；(3) The receiving end of the PKI environment randomly selects the private key β ₁ ,

Calculate the corresponding public key PK _r , bind the public key to the certificate issued by the CA, and output the public key PK _r and private key SK _r ;

(4) The receiving end of the PKI environment obtains the trapdoor value td _r =SK _{r according to the private key SK r ;}

(5) The sending end of the CLC environment performs signcryption according to the system parameters, the identity ID _s and private key S _s of the sending end, and the public key PK _r of the receiving end, and obtains the sign-encrypted ciphertext σ and sends it to the receiving end;

(6) The receiving end of the PKI environment outputs a message M or rejects the ciphertext according to the system parameters, the public key PK _s , the sign-encrypted ciphertext σ, the identity ID _s of the sending end and the private key of the receiving end;

(7) Perform an equivalence test according to the ciphertext σ _s and trapdoor td _s at the sending end and the ciphertext and trapdoor td _r at the receiving end to check whether the ciphertext encrypted with different public keys contains the same message M.

Further, the implementation process of the step (1) is as follows:

为一个双线性映射；定义四个安全的哈希函数

KGC随机选择一个主密钥

计算P_pub＝sP，

KGC公开系统参数{G₁，G₂，P，e，P_pub，，H₁，H₂，H₃，H₄}，保密主密钥s；定义一个函数E，接收端的公钥PK_α；如果PK_γ＝PK_α，且E(PK_r)＝1，该方案是签密方案；然而当PK_γ＝PK_α，且E(PK_r)＝0时，该方案是公钥加密方案。Given a security parameter k, let _G1 and G2 be _two cyclic multiplicative groups, the two groups have the same order p, q is a prime number, and P is the generator of _G1 ;

is a bilinear map; define four secure hash functions

KGC randomly selects a master key

Calculate _Ppub = sP,

KGC public system parameters {G ₁ , G ₂ , P, e, P _pub ,, H ₁ , H ₂ , H ₃ , H ₄ }, secret master key s; define a function E, public key PK _α of the receiver; If PK _γ =PK _α , and E(PK _r )=1, the scheme is a signcryption scheme; however, when PK _γ =PK _α , and E(PK _r )=0, the scheme is a public key encryption scheme.

Further, the implementation process of the step (2) is as follows:

发送给用户；According to system parameters and identity information ID _s , calculate part of the private key

sent to the user;

公钥PK_s＝x_s(H₁(ID_s)+P_pub)。Randomly select a secret value x _s and calculate the full private key based on the partial private key D _s

Public key PK _s =x _s (H ₁ (ID _s )+P _pub ).

Further, the implementation process of the step (3) is as follows:

计算对应的公钥PK_r＝(PK₁，PK₂)＝(β₁P，β₂P)、私钥

Randomly select the private key β ₁ ,

Calculate the corresponding public key PK _r = (PK ₁ , PK ₂ ) = (β ₁ P, β ₂ P), private key

Further, the step (5) includes the following steps:

(51) Select random numbers x ₁ , x ₂ , and calculate blinded values r ₁ , r ₂ according to the Diffie-Hellman difficulty problem;

(52) Use random numbers x ₁ , x ₂ , message M, ID _s of the sender, public key PK _s of the sender, and public keys PK ₁ and PK ₂ of the receiver to obtain the hash value h, thereby obtaining the signature value C ₁ ;

(53) Use mixed signcryption to calculate C ₂ , C ₃ , and at the same time obtain C ₄ , C ₅ through XOR operation, so as to obtain signcrypted ciphertext σ=(C ₁ , C ₂ , C ₃ , C ₄ , C ₅ );

(54) Send the signcrypted ciphertext σ=(C ₁ , C ₂ , C ₃ , C ₄ , C ₅ ) and ID _s to the receiving end.

Further, the step (6) includes the following steps:

计算得到盲化值r₁，r₂；(61) According to system parameters, public key PK _s , signciphered ciphertext σ=(C ₁ , C ₂ , C ₃ , C ₄ , C ₅ ), identity ID _s of the sender and private key of the receiver

Calculate the blinding values r ₁ , r ₂ ;

如果是，输出M，否则输出⊥；如果E(PK_r)＝1，检验

并且仅当盲化值r₁＝e(C₁，PK_s+H₂(PK_s)(H₁PK_s)P+P_pub)t^-h，如果是输出M；否则输出“⊥”。(62) Obtain M||x ₂ through XOR operation, so as to obtain the hash value h; if E(PK _r )=0, check

If yes, output M, otherwise output ⊥; if E(PK _r )=1, check

And only when the blinded value r ₁ =e(C ₁ , PK _s +H ₂ (PK _s )(H ₁ PK _s )P+P _pub )t ^-h , if yes output M; otherwise output "⊥".

Further, the step (7) includes the following steps:

检验等式

是否相等，如果是，消息M_s＝M_r其中，

分别为发送端和接收端带有关键字的盲化值。According to the sender's ciphertext σ _s = (C _1,s , C _2,s , C _3,s , C _4,s , C _5,s ), the trapdoor td _s , and the receiver's ciphertext σ _r =(C _{1, r} , C _{2, r} , C _{3, r} , C _{4, r} , C _{5, r} ), trapdoor td _r , calculate blinded value r _{2, s} , r _{2, r} ; calculate keywords

Check the equation

Are they equal, if yes, the message M _s =M _r where,

are the blinded values with keywords at the sender and receiver, respectively.

Based on the same inventive concept, the present invention also provides a signcryption system based on a heterogeneous system with an equivalence test function, including a memory, a processor, and a computer program stored on the memory and operable on the processor. When the computer program is loaded into the processor, the above-mentioned signcryption method with equivalence testing function based on the heterogeneous system is implemented.

Beneficial effect: Compared with the prior art, the beneficial effect of the present invention is that the theoretical basis and technical guarantee are provided for the signcryption communication between the sending end belonging to the CLC environment and the receiving end belonging to the PKI environment; Users of the environment are provided with end-to-end confidentiality, integrity, authentication and non-repudiation services.

Description of drawings

Fig. 1 is a flow chart of the present invention;

Fig. 2 is the flow chart of sign encryption of the present invention;

Fig. 3 is the flow chart of deciphering of the present invention;

Fig. 4 is a flow chart of the equivalent test of the present invention.

detailed description

The present invention will be described in further detail below in conjunction with the accompanying drawings.

The invention proposes a heterogeneous system-based signcryption method with equivalence test function, and designs a heterogeneous system-based signcryption protocol (HSCIP-ET) with equivalence test function. The sensors used in the CLC system are responsible for collecting the user's data and performing sign encryption using the public key of the Service Management Center (MC) present in the PKI system. In addition, MC also uploads the trapdoor to the cloud server. When an AP in the CLC system wants to retrieve a message with a signcryption keyword, the cloud server can perform an equivalence test on different ciphertexts and return the result to the requesting user. As shown in Figure 1, it specifically includes the following steps:

Step 1: Heterogeneous system parameter initialization; heterogeneous system parameters include the threshold value module, the signcryption module based on the CLC environment, the decryption signcryption module based on the PKI environment, the equivalent test module and the trusted third-party module that need to be set System parameters.

为一个双线性映射。定义四个安全的哈希函数

KGC随机选择一个主密钥

计算P_pub＝sP，

KGC公开系统参数{G₁，G₂，P，e，P_pub，H₁，H₂，H₃，H₄}，保密主密钥s。定义一个函数E，接收者的公钥PK_α。如果PK_γ＝PK_α，且E(PK_r)＝1，该方案是签密方案；然而当PK_γ＝PK_α，且E(PK_r)＝0时，该方案是公钥加密方案。Given a security parameter k, let _G1 and G2 be _two cyclic multiplicative groups, the two groups have the same order p, q is a prime number, and P is the generator of _G1 .

is a bilinear map. Define four secure hash functions

KGC randomly selects a master key

Calculate _Ppub = sP,

KGC publicizes system parameters {G ₁ , G ₂ , P, e, P _pub , H ₁ , H ₂ , H ₃ , H ₄ }, and keeps secret master key s. Define a function E, receiver's public key PK _α . If PK _γ =PK _α , and E(PK _r )=1, the scheme is a signcryption scheme; however, when PK _γ =PK _α , and E(PK _r )=0, the scheme is a public key encryption scheme.

The parameter description mainly used in this invention implementation process is as shown in table 1:

Table 1 parameter description

Step 2: Generate a key for the CLC environment.

和公钥PK_s＝x_s(H₁(ID_s)+P_pub)。The sending end of the certificateless environment (CLC) submits the identity information ID _s to the key generation center, and the key generation center generates a part of the private key D _s according to the system parameters and the identity information ID _s and sends it to the user. The user randomly selects a secret value x _s , set the full private key according to the secret value and partial private key D _s

and public key PK _s =x _s (H ₁ (ID _s )+P _pub ).

计算对应的公钥PK_r，公钥与CA颁发的证书绑定，输出公钥PK_r＝(PK₁，PK₂)＝(β₁P，β₂P)、私钥

Step 3: The receiving end of the PKI environment randomly selects the private key β ₁ ,

Calculate the corresponding public key PK _r , the public key is bound to the certificate issued by the CA, and the output public key PK _r = (PK ₁ , PK ₂ ) = (β ₁ P, β ₂ P), private key

Step 4: According to the private key SK _r , generate trapdoor value td _r =SK _r .

接收端的公钥PK_r＝(PK₁，PK₂)＝(β₁P，β₂P)，进行签密，得到签密密文σ并发送给接收端。如图2所示，具体步骤如下：Step 5: According to the system parameters, ID _s and private key of the sender, the sender

The public key PK _r =(PK ₁ , PK ₂ )=(β ₁ P, β ₂ P) of the receiving end is signed encrypted to obtain the sign encrypted ciphertext σ and sent to the receiving end. As shown in Figure 2, the specific steps are as follows:

Select random numbers x ₁ , x ₂ , and calculate blinded values r ₁ , r ₂ according to the Diffie-Hellman difficulty problem; use random numbers x ₁ , x ₂ , message M, identity ID _s of the sender, and public key PK of the sender _s , the public key PK ₁ and PK ₂ of the receiving end, get the hash value:

h=H ₂ (M, r ₁ , r ₂ , ID _s , PK _s , PK ₁ , PK ₂ )

and thus get the signed value:

C ₁ =E(PK _r )(x ₁ +h)S _s ,;

C ₂ , C ₃ are obtained by hybrid signcryption calculation:

C ₂ =x ₁ PK ₁

C ₃ =x ₂ PK ₂

At the same time, C ₄ and C ₅ are obtained through XOR operation:

Thus, the signciphered ciphertext σ=(C ₁ , C ₂ , C ₃ , C ₄ , C ₅ ) and identity ID _s are obtained.

输出消息M或拒绝该密文，具体如图3所示。Step 6: The receiving end of the PKI environment is based on the system parameters, the public key PK _s , the sign-encrypted ciphertext σ=(C ₁ , C ₂ , C ₃ , C ₄ , C ₅ ), the identity ID _s of the sending end and the private key of the receiving end

Output message M or reject the ciphertext, as shown in Figure 3.

计算得到盲化值r₁，r₂：According to system parameters, public key PK _s , sign-encrypted ciphertext σ=(C ₁ , C ₂ , C ₃ , C ₄ , C ₅ ), identity ID _s of the sender and private key of the receiver

Calculate the blinding values r ₁ , r ₂ :

r ₁ =e(C ₂ ,SK ₁ )

r ₂ =e(C ₃ ,SK ₂ ).

从而得到哈希值h＝H₂(M，r₁，r₂，ID_s，PK_s，PK₁，PK₂)。如果E(PK_r)＝0，检验

如果是，输出M，否则输出“⊥”；如果E(PK_r)＝1，检验

并且仅当r₁＝e(C₁，PK_s+H₂(PK_s)(H₁PK_s)P+P_pub)t^-h，如果是输出M；否则输出“⊥”。Obtained by XOR operation

Thus, the hash value h=H ₂ (M, r ₁ , r ₂ , ID _s , PK _s , PK ₁ , PK ₂ ) is obtained. If E(PK _r )=0, test

If yes, output M, otherwise output "⊥"; if E(PK _r )=1, check

And only when r ₁ =e(C ₁ , PK _s +H ₂ (PK _s )(H ₁ PK _s )P+P _pub )t ^-h , output M if it is; otherwise output "⊥".

Step 7: According to the ciphertext σ _s of the sender = (C _{1, s} , C _{2, s} , C _{3, s} , C _{4, s} , C _{5, s} ), the trapdoor td _s , and the ciphertext σ _r of the receiver =(C _{1, r} , C _{2, r} , C _{3, r} , C _{4, r} , C _{5, r} ), the trapdoor td _r conducts an equivalence test to check whether the ciphertext encrypted with different public keys contains the same The message M, as shown in Figure 4, the specific steps are as follows:

1) Calculate the blinding value r _2,s =e(C _3,s ,SK _2,s );

2) Calculate the blinding value r _2,r = e(C _3,s ,SK _2,r );

3) Calculate keywords

4) Calculate keywords

是否相等，如果是，则M_s＝M_r；其中，r_2，s，r_2，r分别为发送端和接收端的盲化值，X_s，X_r分别为发送端和接收端的关键字，

分别为发送端和接收端带有关键字的盲化值。5) Check the equation

Whether they are equal, if yes, then M _s =M _r ; wherein, r _{2, s} , r _{2, r} are the blinding values of the sending end and the receiving end respectively, X _s , X _r are the keywords of the sending end and the receiving end respectively,

are the blinded values with keywords at the sender and receiver, respectively.

Based on the same inventive concept, the present invention also provides a signcryption system based on a heterogeneous system with an equivalence test function, including a memory, a processor, and a computer program stored on the memory and operable on the processor, wherein the computer When the program is loaded into the processor, the above-mentioned signcryption method with equivalence testing function based on the heterogeneous system is implemented.

The invention not only realizes the function of equivalent test to determine whether two ciphertexts contain the same message, but also maintains the integrity, authentication and confidentiality of data at the same time. The invention allows the sending end to be in the CLC cryptographic system and the receiving end to be in the PKI cryptographic system to carry out safe communication. Compared with existing related schemes, this scheme has lower computational cost and communication overhead. Under the assumption of calculating the q-bilinear pairing inverse Diffie-Hellman difficulty in the random oracle model, the present invention is indistinguishable under adaptively chosen ciphertext attacks, and under the assumption of calculating the Diffie-Hellman difficulty, can Combating Adaptive Chosen Message Attacks.

Claims (8)

1. a kind of signcryption method with equivalence test function based on heterogeneous system, is characterized in that, comprises the following steps: (1) Heterogeneous system parameter initialization; The heterogeneous system parameters include threshold value module, signcryption module based on CLC environment, decryption signcryption module based on PKI environment, equivalence test module and trusted third-party module Set system parameters; (2) The sending end of the CLC environment submits the identity information ID _s to the key generation center. The key generation center generates a part of the private key D _s according to the system parameters and the identity information ID _s and sends it to the user. The user randomly selects a secret value x _s , set the complete private key and public key according to the secret value x _s and the partial private key D _s ; (3) The receiving end of the PKI environment randomly selects the private key

Calculate the corresponding public key PK _r , bind the public key to the certificate issued by the CA, and output the public key PK _r and private key SK _r ; (4) The receiving end of the PKI environment obtains the trapdoor value td _r =SK _{r according to the private key SK r ;} (5) The sending end of the CLC environment performs signcryption according to the system parameters, the identity ID _s and private key S _s of the sending end, and the public key PK _r of the receiving end, and obtains the sign-encrypted ciphertext σ and sends it to the receiving end; (6) The receiving end of the PKI environment outputs a message M or rejects the ciphertext according to the system parameters, the public key PK _s , the sign-encrypted ciphertext σ, the identity ID _s of the sending end and the private key of the receiving end; (7) Perform an equivalence test according to the ciphertext σ _s and trapdoor td _s at the sending end and the ciphertext and trapdoor td _r at the receiving end to check whether the ciphertext encrypted with different public keys contains the same message M. 2. a kind of signcryption method with equivalence test function based on heterogeneous system according to claim 1, is characterized in that, described step (1) realization process is as follows: Given a security parameter k, let _G1 and G2 be _two cyclic multiplicative groups, the two groups have the same order p, q is a prime number, and P is the generator of _G1 ;

G ₁ ×G ₁ →G ₂ is a bilinear map; define four secure hash functions H ₁ :

H ₂ :

_H3 :

H ₄ : G ₂ → {0, 1} ^* ; KGC randomly selects a master key

Calculate _Ppub = sP,

KGC public system parameters {G ₁ , G ₂ , P, e, P _pub ,, H ₁ , H ₂ , H ₃ , H ₄ }, secret master key s; define a function E, public key PK _α of the receiver; If PK _γ =PK _α , and E(PK _r )=1, the scheme is a signcryption scheme; however, when PK _γ =PK _α , and E(PK _r )=0, the scheme is a public key encryption scheme. 3. a kind of signcryption method with equivalence test function based on heterogeneous system according to claim 1, is characterized in that, described step (2) realization process is as follows: According to system parameters and identity information ID _s , calculate part of the private key

sent to the user; Randomly select a secret value x _s and calculate the full private key based on the partial private key D _s

Public key PK _s =x _s (H ₁ (ID _s )+P _pub ). 4. a kind of signcryption method with equivalence test function based on heterogeneous system according to claim 1, is characterized in that, described step (3) realization process is as follows: random private key

Calculate the corresponding public key PK _r = (PK ₁ , PK ₂ ) = (β ₁ P, β ₂ P), private key

5. a kind of signcryption method with equivalence test function based on heterogeneous system according to claim 1, is characterized in that, described step (5) comprises the following steps: (51) Select random numbers x ₁ , x ₂ , and calculate blinded values r ₁ , r ₂ according to the Diffie-Hellman difficulty problem; (52) Use random numbers x ₁ , x ₂ , message M, ID _s of the sender, public key PK _s of the sender, and public keys PK ₁ and PK ₂ of the receiver to obtain the hash value h, thereby obtaining the signature value C ₁ ; (53) Use mixed signcryption to calculate C ₂ , C ₃ , and at the same time obtain C ₄ , C ₅ through XOR operation, so as to obtain signcrypted ciphertext σ=(C ₁ , C ₂ , C ₃ , C ₄ , C ₅ ); (54) Send the signcrypted ciphertext σ=(C ₁ , C ₂ , C ₃ , C ₄ , C ₅ ) and ID _s to the receiving end. 6. a kind of signcryption method with equivalence test function based on heterogeneous system according to claim 1, is characterized in that, described step (6) comprises the following steps: (61) According to system parameters, public key PK _s , signciphered ciphertext σ=(C ₁ , C ₂ , C ₃ , C ₄ , C ₅ ), identity ID _s of the sender and private key of the receiver

Calculate the blinding values r ₁ , r ₂ ; (62) Obtain M||x ₂ through XOR operation, so as to obtain the hash value h; if E(PK _r )=0, check

If yes, output M, otherwise output ⊥; if E(PK _r )=1, check

And only when the blinded value r ₁ =e(C ₁ , PK _s +H ₂ (PK _s )(H ₁ PK _s )P+P _pub )t ^-h , if yes output M; otherwise output "⊥". 7. a kind of signcryption method with equivalence test function based on heterogeneous system according to claim 1, is characterized in that, described step (7) comprises the following steps: According to the sender's ciphertext σ _s = (C _1,s , C _2,s , C _3,s , C _4,s , C _5,s ), the trapdoor td _s , and the receiver's ciphertext σ _r =(C _{1, r} , C _{2, r} , C _{3, r} , C _{4, r} , C _{5, r} ), trapdoor td _r , calculate blinded value r _{2, s} , r _{2, r} ; calculate keywords

Check the equation

Whether they are equal, if yes, the message M _s =M _r ; where,

are the blinded values with keywords at the sender and receiver, respectively. 8. A signcryption system based on a heterogeneous system with an equivalent test function, comprising a memory, a processor and a computer program stored on the memory and operable on the processor, wherein the computer program is loaded When reaching the processor, the signcryption method with equivalence testing function based on the heterogeneous system according to any one of claims 1-7 is realized.

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