TWI859857B - Security credential management system and method based on key expansion - Google Patents

Abstract

A security credential management system and method based on key expansion is provided, the system includes at least one high-efficiency terminal device, a high-efficiency registration center and a high- efficiency authorization credential center. The high-efficiency terminal device includes a RSA key production module for producing RSA caterpillar key pairs. The high-efficiency registration center is communicated connected with the at least one terminal device, the high-efficiency registration center includes the second RSA key expansion module, which is used to receive the RSA caterpillar key pairs and produce a plurality of RSA cocoon public keys. The high- efficiency authorization credential center is communicated connected with the high-efficiency registration center, the high- efficiency authorization credential center includes a first RSA key expansion module, which is used to receive the RSA cocoon public keys and produce a plurality of RSA butterfly public keys.

Description

Security certificate management system and method based on key expansion

The present invention relates to a security certificate management system and method thereof, and in particular to a security certificate management system and method thereof based on key expansion.

Currently, in the vehicle network information security certificate management system, in order to enhance the privacy and confidentiality of vehicle transmission, a pseudonymous certificate mechanism is added to the vehicle network communication standard. In order to establish a pseudonymous certificate mechanism, a gold key expansion method is combined in the vehicle network information security certificate management system, and an expanded public key pair is provided as a pseudonymous certificate based on the existing public key.

The IEEE 1609.2.1 standard proposes a Butterfly Key Expansion (BKE) mechanism in the Security Credential Management System (SCMS) for connected vehicle networks. This mechanism allows vehicles to obtain a large number of required pseudonymous certificates with a single certificate request, and also has the following characteristics: the public key of each certificate is different, and even the Registration Authority (RA) or the Authorization Certificate Authority (ACA) cannot know the true identity of the user through the public information of the certificate. The private key corresponding to each certificate is still owned only by the user.

FIG1 is a system architecture diagram of a security certificate management system of IEEE 1609.2.1. The security certificate management system at least includes an authorization certificate authority 101 (ACA), a registration authority 102 (Registration Authority), and a plurality of end entities 103 (EE).

The authorization certificate center 101 can issue an authorization certificate (AC) to the terminal device 103, and in order to protect the privacy and security of the terminal device 103, the authorization certificate center 101 can issue multiple pseudonym certificates (PC) to the terminal device 103, so that the terminal device 103 can use these pseudonym certificates for communication, avoiding the terminal device 103 from frequently exposing its authorization certificate. The registration center 102 is responsible for the registration review management of the terminal device 103.

FIG2 is a flow chart of the butterfly key extension method of IEEE 1609.2.1. The terminal device 103 can generate a caterpillar key pair, and then the registration center 102 generates a plurality of cocoon public keys, and the authorization certificate center 101 generates a plurality of butterfly public keys, and finally the terminal device 103 generates a plurality of cocoon private keys and a plurality of butterfly private keys.

In step S201 of the butterfly key expansion method, the terminal device 103 generates a plurality of Advanced Encryption Standard (AES) key pairs and Elliptic Curve Cryptography (ECC) key pairs. Step S201 mainly includes steps 1a, 1b, 1c and 1d.

In step 1a, the terminal device 103 generates an AES key ck for use as a signature, and the parameter ck is a symmetric key;

In step 1b, the terminal device 103 generates an AES key ek for encryption, and the parameter ek is a symmetric key;

In step 1c, the terminal device 103 generates an ECC key pair , as the caterpillar key pair, used for signature, parameter a is the private key, parameter A is the public key, parameter G is the reference point of the ellipse curve;

In step 1d, the terminal device 103 generates an ECC key pair , as the caterpillar key pair, used for signature, parameter p is the private key, parameter P is the public key, and parameter G is the reference point of the elliptical curve.

In step S202 of the butterfly key expansion method, the terminal device 103 sends the generated symmetric key and caterpillar public key (ck, ek, A, P) to the registration center 102.

In step S203 of the butterfly key expansion method, the registration center 102 generates a plurality of cocoon public keys according to the caterpillar public key, wherein step S203 mainly includes step 3a and step 3b.

In step 3a, the registration center 102 generates multiple public keys , parameter i is an incremental integer, function f1 is an extended function based on the AES encryption algorithm, and the AES key ck can be used to encrypt the parameter i value to obtain an integer ciphertext;

In step 3b, the registration center 102 generates multiple public keys , parameter i is an incremental integer, function f2 is an extended function based on the AES encryption algorithm, and the AES key ek can be used to encrypt the parameter i value to obtain an integer ciphertext.

In step S204 of the butterfly key expansion method, the registration center 102 sends the generated multiple butterfly public keys (Bi, Qi) to the certification center 101.

In step S205 of the butterfly key expansion method, the certificate authority 101 generates a plurality of butterfly public keys according to the cocoon public keys. The butterfly public keys can be used as public key encryption for pseudonymous certificates. Step S205 mainly includes step 5a, step 5b and step 5c.

In step 5a, the CA 101 generates an ECC key pair , parameter c is the private key, parameter C is the public key, and parameter G is the base point of the ellipse curve;

In step 5b, the certification authority 101 generates a plurality of butterfly public keys (Bi + C);

In step 5c, the CA 101 uses the Qi as public keys to encrypt and sign c using the Elliptic Curve Integrated Encryption Scheme (ECIES) algorithm. The ciphertext of c is c’.

Step S206 of the butterfly key expansion method is that the authorization certificate center 101 sends the ciphertext c’ and the signature to the registration center 102.

Step S207 of the butterfly key expansion method is that the registration center 102 sends a plurality of i values and their corresponding ciphertext c’ and signature to the terminal device 103.

In step S208 of the butterfly key expansion method, the terminal device 103 generates a plurality of private keys according to the i values, wherein step S208 mainly includes step 8a and step 8b.

In step 8a, the terminal device 103 generates a plurality of private keys. , function f1 is an extended function based on the AES encryption algorithm and is the same as the function f1 mentioned in the above paragraph 0014, which can use the AES key ck to encrypt the parameter i value to obtain an integer ciphertext, and the parameter n is the order of the ellipse curve;

In step 8b, the terminal device 103 generates a plurality of private keys. Function f2 is an extended function based on the AES encryption algorithm and is the same as the function f2 mentioned in paragraph 0015. It can use the AES key ek to encrypt the parameter i value to obtain an integer ciphertext. The parameter n is the order of the elliptical curve.

In step S209 of the butterfly key expansion method, the terminal device 103 decrypts the value c according to the coil private key qi, and uses the coil private key bi and the value c to generate a butterfly private key. These butterfly private keys can be used as private key signatures or decryption of pseudonymous certificates. Step S209 mainly includes step 9a and step 9b.

In step 9a, the terminal device 103 uses the private key qi to decrypt the ciphertext c' and obtain the plaintext c;

In step 9b, the terminal device 103 generates a plurality of butterfly private keys , the parameter n is the order of the elliptical curve.

The above-mentioned butterfly key expansion method uses elliptical curve cryptography to provide an expanded public key pair as a pseudonymous certificate based on an existing public key. However, the calculation time for public key expansion in this method is long and the efficiency is low. In addition, the registration center 102 cannot obtain the parameter C, and thus cannot infer the cocoon public key from the butterfly public key. The authorization certificate center 101 cannot obtain the ciphertext c' and cannot infer the caterpillar public key from the cocoon public key.

The present invention provides a security certificate management system and method based on key expansion, which can quickly generate multiple public keys as pseudonymous certificates and has higher key expansion efficiency.

The invention discloses a security certificate management system based on key expansion, comprising at least one high-efficiency terminal device, a high-efficiency registration center and a high-efficiency authorization certificate center. At least one high-efficiency terminal device comprises an RSA key production module for producing RSA caterpillar key pairs. The high-efficiency registration center is connected to the at least one high-efficiency terminal device for communication, and the high-efficiency registration center comprises a second RSA key expansion module for receiving RSA caterpillar key pairs and producing a plurality of RSA cocoon public keys. The high-efficiency authorization certificate center is connected to the high-efficiency registration center. The high-efficiency authorization certificate center includes a first RSA key expansion module. The first RSA key expansion module is used to receive the RSA cocoon public keys and generate a plurality of RSA butterfly public keys.

The present invention discloses a security certificate management method based on key expansion, comprising: generating an RSA caterpillar key pair via at least one high-efficiency terminal device including an RSA key generation module; receiving the RSA caterpillar key pair via a high-efficiency registration center including a second RSA key expansion module to generate a plurality of RSA cocoon public keys; and receiving the RSA cocoon public keys via a high-efficiency authorization certificate center including a first RSA key expansion module to generate a plurality of RSA butterfly public keys.

Based on the above, the present invention provides a security certificate management system and method based on key expansion, adds a pseudonymous certificate mechanism to the vehicle network communication standard, and provides an expanded public key pair as a pseudonymous certificate, which not only improves the privacy and confidentiality of vehicle transmission, but also the calculation time for public key expansion is much lower than the calculation time for generating a new key pair, and can quickly generate multiple public keys as pseudonymous certificates, and the key expansion efficiency is higher.

In order to make the above features and advantages of the present invention more clearly understood, embodiments are specifically cited below and described in detail with reference to the accompanying drawings.

Some embodiments of the present invention will be described in detail below with reference to the accompanying drawings. When the same element symbols appear in different drawings, they will be regarded as the same or similar elements. These embodiments are only part of the present invention and do not disclose all possible implementations of the present invention.

FIG3 is a system architecture diagram of a security certificate management system based on key expansion according to an embodiment of the present invention.

Please refer to FIG3 , the key-based security certificate management system adds a pseudonymous certificate mechanism to the vehicle network communication standard, provides an extended public key pair as a pseudonymous certificate, and includes at least one high-efficiency terminal device 303, a high-efficiency registration center 302, and a high-efficiency authorization certificate center 301. At least one high-efficiency terminal device 303 includes an RSA key generation module 3031 for generating an RSA caterpillar key pair. The high-efficiency registration center 302 is connected to at least one high-efficiency terminal device 303. The high-efficiency registration center 302 includes a second RSA key expansion module 3021. The second RSA key expansion module 3021 is used to receive the RSA caterpillar key pair and generate a plurality of RSA cocoon public keys. The high-efficiency authorization certificate center 301 is connected to the high-efficiency registration center 302. The high-efficiency authorization certificate center 301 includes a first RSA key expansion module 3011. The first RSA key expansion module 3011 is used to receive the RSA cocoon public keys and generate a plurality of RSA butterfly public keys.

The high-efficiency terminal device 303, the high-efficiency registration center 302, and the high-efficiency authorization certificate center 301 can be implemented through software, firmware, hardware circuits, or any combination thereof, and the present disclosure does not limit the implementation method of the high-efficiency terminal device 303, the high-efficiency registration center 302, and the high-efficiency authorization certificate center 301.

Specifically, in order to protect the privacy and security of the high-efficiency terminal device 303, the high-efficiency authorization certificate center 301 can issue multiple pseudonym certificates to at least one high-efficiency terminal device 303, so that the high-efficiency terminal device 303 can use the pseudonym certificate to communicate, avoiding the high-efficiency terminal device 303 from frequently exposing its authorization certificate. The high-efficiency registration center 302 is responsible for the registration review management of the high-efficiency terminal device 303.

The following combines the first to third embodiments to illustrate how the security certificate management system based on key expansion uses an RSA caterpillar key pair, multiple RSA cocoon public keys, and multiple RSA butterfly public keys, so as to use the RSA butterfly public key as the public key encryption of the pseudonymous certificate, and the high-efficiency terminal device 303 uses the RSA caterpillar private key for signing or decryption, and uses the high-efficiency authorization certificate center long-term public key to encrypt the expansion coefficient γ to obtain the ciphertext γ' and use the high-efficiency authorization certificate center long-term private key to decrypt the ciphertext γ'.

FIG4 is a flow chart of a security certificate management method based on key expansion according to a first embodiment of the present invention.

Referring to FIG. 4 , in step S401, the high-efficiency terminal device 303 generates an RSA caterpillar key pair (s, S, φ), and obtains an expansion coefficient λ according to the RSA caterpillar key pair (s, S, φ) and formula 1, where: Formula 1

λ is the expansion coefficient, parameter s is the caterpillar private key, parameter S is the caterpillar public key, parameter φ is the order of the RSA caterpillar key pair, parameter g is a random integer, and parameter h is a random prime number.

In the first embodiment, a 10-bit integer is used as an example for explanation, but the actual online system must be set to an integer larger than 2048 bits.

In step S401, two prime numbers 991 and 827 are randomly selected using the RSA algorithm. The two prime numbers are multiplied to obtain N = 819557. The two prime numbers are subtracted by one and then multiplied to obtain ; Use φ to obtain the caterpillar private key , Caterpillar public key , Caterpillar private key s and Caterpillar public key S meet the conditions , then a positive integer x can be obtained ; Randomly generate integers , , then .

In step S402, the high-efficiency terminal device 303 sends (S, λ) to the high-efficiency registration center 302. The high-efficiency terminal device 303 generates the caterpillar public key and the expansion coefficient. Sent to High Efficiency Registration Center 302.

In step S403, the second RSA key expansion module generates a plurality of RSA cocoon public keys according to the RSA caterpillar key pair (s, S, φ), the expansion coefficient λ and formula 2, wherein, Formula 2

Where λ is the expansion coefficient, parameter S is the caterpillar public key, parameter ri is an integer, and Gi is the RSA cocoon public key.

Take the generation of two RSA public keys as an example: For example, RSA public key ;by For example, RSA public key .

In step S404, the high-efficiency registration center 302 sends a plurality of RSA coil public keys (Gi, λ) to the high-efficiency certification center 301. The high-efficiency registration center 302 generates the RSA coil public keys and the expansion coefficients. Sent to the high-efficiency authorization certificate center 301.

In step S405, the first RSA key expansion module 3011 in the high-efficiency certification center 301 generates a plurality of RSA butterfly public keys according to the RSA butterfly public keys, the expansion coefficient λ and formula 3, wherein: Formula 3

Where λ is the expansion coefficient, parameter oi is an integer, Gi is the RSA cocoon public key, and Hi is the RSA butterfly public key.

Take the generation of two RSA butterfly public keys as an example: For example, RSA butterfly public key ;by For example, RSA butterfly public key .

The parameter ri is a time integer, and the parameter oi is a time integer. The time integer must be the number of seconds from 2004/01/01 00:00:00 to the current time. If the current time is 2022/12/13 15:22:01, the time integer is 598029721, which can be used as the value of ri or oi.

FIG5 is a flow chart of a security certificate management method based on key expansion according to a second embodiment of the present invention.

5, in step S501, the high-efficiency terminal device 303 generates an RSA caterpillar key pair (s, S, φ), and obtains the expansion coefficient λ according to the RSA caterpillar key pair (s, S, φ) and formula 1, where Formula 1

Where λ is the expansion coefficient, parameter s is the caterpillar private key, parameter S is the caterpillar public key, parameter φ is the order of the RSA caterpillar key pair, parameter g is a random integer, and parameter h is a random prime number.

In step S502, the high-efficiency terminal device 303 sends (S, λ) to the high-efficiency registration center 302.

In step S503, the second RSA key expansion module 3021 in the high-efficiency registration center 302 generates an RSA cocoon public key according to the RSA caterpillar key pair (s, S, φ), the expansion coefficient λ and Formula 2, and obtains the expansion coefficient μ according to Formula 4, where Formula 2 Formula 4

Where λ and μ are expansion coefficients, parameter S is the caterpillar public key, parameter ri is an integer, Gi is the RSA cocoon public key, and parameter u is a random integer.

Take the generation of two RSA public keys as an example: For example, RSA public key ;by For example, RSA public key ;by For example, .

In step S504, the high-efficiency registration center 302 sends a plurality of RSA coil public keys (Gi, μ) to the high-efficiency certification center 301. The high-efficiency registration center 302 generates the RSA coil public keys and expansion coefficients. Sent to the high-efficiency authorization certificate center 301.

In step S505, the first RSA key expansion module 3011 generates an RSA butterfly public key according to the RSA butterfly public key, the expansion coefficient μ and formula 5, wherein: Formula 5

Where μ is the expansion coefficient, parameter oi is an integer, Gi is the RSA coil public key, and Hi is the RSA butterfly public key.

Take the generation of two RSA butterfly public keys as an example: For example, RSA butterfly public key ;by For example, RSA butterfly public key .

FIG6 is a flow chart of a security certificate management method based on key expansion according to a third embodiment of the present invention.

Please refer to FIG. 6. In step S601, the high-efficiency terminal device 303 generates an RSA caterpillar key pair (s, S, φ), obtains an expansion coefficient λ according to the RSA caterpillar key pair (s, S, φ) and formula 1, and obtains an expansion coefficient γ according to the RSA caterpillar key pair (s, S, φ) and formula 6, and the high-efficiency terminal device 303 uses the high-efficiency authorization certificate center long-term public key of the high-efficiency authorization certificate center 301 to encrypt γ to obtain a ciphertext γ', wherein, Formula 1 Formula 6

Where λ and γ are expansion coefficients, parameter s is the caterpillar private key, parameter S is the caterpillar public key, parameter φ is the order of the RSA caterpillar key pair, parameter g is a random integer, parameter h is a random prime number, and parameter v is a random integer.

In the third embodiment, two prime numbers 991 and 827 are randomly selected using the RSA algorithm. The two prime numbers are multiplied to obtain N = 819557. The two prime numbers are subtracted by one and then multiplied to obtain ; Use φ to obtain the caterpillar private key , Caterpillar public key , Caterpillar private key s and Caterpillar public key S meet the conditions , then a positive integer x can be obtained ; Randomly generate integers , , , then , ; Use the high-efficiency authorization certificate center long-term public key to encrypt 481499213580 and obtain the ciphertext γ'.

In step S602, the high-efficiency terminal device 303 sends (S, λ, γ') to the high-efficiency registration center 302. The high-efficiency terminal device 303 Sent to High Efficiency Registration Center 302.

In step S603, the second RSA key expansion module 3021 of the high-efficiency registration center 302 generates an RSA public key according to the parameter S, the expansion coefficient λ, the ciphertext γ' and formula 2, and the second RSA key expansion module 3021 obtains the expansion coefficient μ according to the expansion coefficient λ and formula 4, wherein, Formula 2 Formula 4

Where λ and μ are expansion coefficients, parameter S is the caterpillar public key, parameter ri is an integer, Gi is the RSA cocoon public key, and parameter u is a random integer.

In step S604, the high-efficiency registration center 302 sends a plurality of RSA public keys (Gi, μ, γ') to the high-efficiency certification center 301. Sent to the high-efficiency authorization certificate center 301.

In step S605, the high-efficiency certification center 301 uses the caterpillar private key to decrypt the ciphertext γ' to obtain the plaintext γ, and the first RSA key expansion module 3011 generates the RSA butterfly public key according to the RSA cocoon public key, the expansion coefficient μ, the plaintext γ and formula 7, where Formula 7

Where μ is the expansion coefficient, parameter oi is an integer, Gi is the RSA coil public key, and Hi is the RSA butterfly public key.

The steps of generating RSA butterfly public key can be used to decrypt the ciphertext γ' using the long-term private key of the high-efficiency authorization certificate center to obtain the plaintext , and can be calculated Generate multiple RSA butterfly public keys. The parameter oi is an integer.

Take the generation of two RSA butterfly public keys as an example: For example, RSA butterfly public key ;by For example, RSA butterfly public key .

Among them, the information encrypted by the RSA cocoon public key and the RSA butterfly public key produced in the first to third embodiments can be decrypted using the RSA caterpillar private key.

FIG. 7 is a flow chart of a security certificate management method based on key extension according to an embodiment of the present invention.

In step S701, the high-efficiency terminal device 303 generates a RSA caterpillar key pair.

In step S702, the high-efficiency registration center 302 generates a plurality of RSA public keys.

In step S703, the high-efficiency certificate authority 301 generates a plurality of RSA butterfly public keys.

The key-based security certificate management system can use the RSA butterfly public key as the public key of the pseudonymous certificate for encryption, and the terminal device 301 uses the RSA caterpillar private key for signing or decryption.

Based on the above, the present invention provides a security certificate management system and method based on key expansion, adds a pseudonymous certificate mechanism to the vehicle network communication standard, and provides an expanded public key pair as a pseudonymous certificate, which not only improves the privacy and confidentiality of vehicle transmission, but also the calculation time for public key expansion is much lower than the calculation time for generating a new key pair, and reduces the steps in the traditional method of Figure 2, such as generating a butterfly private key, using the butterfly private key to decrypt ciphertext, and generating multiple butterfly private keys. It can quickly generate multiple public keys as pseudonymous certificates, and the key expansion efficiency is higher.

Although the present invention has been disclosed as above by the embodiments, they are not intended to limit the present invention. Any person with ordinary knowledge in the relevant technical field can make some changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be defined by the scope of the attached patent application.

101: Authorization Certificate Center 102: Registration Center 103, 303: Terminal Equipment 301: High-efficiency Authorization Certificate Center 3011: First RSA Key Extension Module 302: High-efficiency Registration Center 3021: Second RSA Key Extension Module 3031: RSA Key Production Module 1a, 1b, 1c, 1d, 3a, 3b, 5a, 5b, 5c, 8a, 8b, 9a, 9b, S201, S202, S203, S204, S205, S206, S207, S208, S209, S401, S402, S403, S404, S405, S501, S502, S5 03. S504, S505, S601, S602, S603, S604, S605: Steps

FIG1 is a system architecture diagram of a known IEEE 1609.2.1 security certificate management system. FIG2 is a flow chart of a known IEEE 1609.2.1 butterfly key expansion method. FIG3 is a system architecture diagram of a key expansion-based security certificate management system according to an embodiment of the present invention. FIG4 is a flow chart of a key expansion-based security certificate management method according to a first embodiment of the present invention. FIG5 is a flow chart of a key expansion-based security certificate management method according to a second embodiment of the present invention. FIG6 is a flow chart of a key expansion-based security certificate management method according to a third embodiment of the present invention. Figure 7 is a flow chart of a security certificate management method based on key expansion according to an embodiment of the present invention.

301: High-efficiency authorization certification center

302: High-efficiency registration center

303: Terminal equipment

3011: The first RSA key extension module

3021: Second RSA key extension module

3031:RSA key production module

Claims (18)

A security certificate management system based on key expansion includes: At least one high-efficiency terminal device, including an RSA key generation module for generating an RSA caterpillar key pair; A high-efficiency registration center, which is connected to the at least one high-efficiency terminal device for communication, and the high-efficiency registration center includes a second RSA key expansion module, and the second RSA key expansion module is used to receive the RSA caterpillar key pair and generate a plurality of RSA cocoon public keys; and The high-efficiency authorization certificate center is connected to the high-efficiency registration center. The high-efficiency authorization certificate center includes a first RSA key expansion module. The first RSA key expansion module is used to receive the RSA cocoon public keys and generate multiple RSA butterfly public keys. The security certificate management system as described in claim 1, wherein the operation of the at least one high-efficiency terminal device for generating the RSA caterpillar key pair further includes: the at least one high-efficiency terminal device for generating the RSA caterpillar key pair (s, S, φ); and the at least one high-efficiency terminal device for obtaining an expansion coefficient λ according to the RSA caterpillar key pair (s, S, φ) and formula 1, wherein, Formula 1 Wherein the λ is the expansion coefficient, the parameter s is the caterpillar private key, the parameter S is the caterpillar public key, the parameter φ is the order of the RSA caterpillar key pair, the parameter g is a random integer, and the parameter h is a random prime number. The security certificate management system as described in claim 2, wherein the second RSA key expansion module is used to receive the RSA caterpillar key pair, and the operation of generating the RSA cocoon public keys further includes: the second RSA key expansion module generates the RSA cocoon public keys according to the RSA caterpillar key pair (s, S, φ), the expansion coefficient λ and formula 2, wherein, Formula 2 Wherein, λ is the expansion coefficient, the parameter S is the caterpillar public key, the parameter ri is an integer, and Gi is the RSA coyote public keys. The security certificate management system as described in claim 3, wherein the first RSA key expansion module is used to receive the RSA cocoon public keys, and the operation of generating the RSA butterfly public keys further includes: the first RSA key expansion module generates the RSA butterfly public keys according to the RSA cocoon public keys, the expansion coefficient λ and formula 3, wherein, Formula 3 Wherein the λ is the expansion coefficient, the parameter oi is an integer, the Gi is the RSA coil public keys, and the Hi is the RSA butterfly public keys. The security certificate management system as described in claim 2, wherein the second RSA key expansion module is used to receive the RSA caterpillar key pair, and the operation of generating the RSA cocoon public keys further includes: the second RSA key expansion module generates the RSA cocoon public keys according to the RSA caterpillar key pair (s, S, φ), the expansion coefficient λ and formula 2, and obtains the expansion coefficient μ according to formula 4, wherein, Formula 2 Formula 4 Wherein, the λ and μ are the expansion coefficients, the parameter S is the caterpillar public key, the parameter ri is an integer, the Gi are the RSA coyote public keys, and the parameter u is a random integer. The security certificate management system as described in claim 5, wherein the first RSA key expansion module is used to receive the RSA cocoon public keys, and the operation of generating the RSA butterfly public keys further includes: the first RSA key expansion module generates the RSA butterfly public keys according to the RSA cocoon public keys, the expansion coefficient μ and formula 5, wherein, Formula 5 Wherein, μ is the expansion coefficient, the parameter oi is an integer, Gi is the RSA coil public keys, and Hi is the RSA butterfly public keys. The security certificate management system as described in claim 1, wherein the operation of the at least one high-efficiency terminal device for generating the RSA caterpillar key pair further includes: the at least one high-efficiency terminal device for generating the RSA caterpillar key pair (s, S, φ); the at least one high-efficiency terminal device for obtaining an expansion coefficient λ based on the RSA caterpillar key pair (s, S, φ) and formula 1; the at least one high-efficiency terminal device for obtaining an expansion coefficient γ based on the RSA caterpillar key pair (s, S, φ) and formula 6, wherein, Formula 1 Formula 6 wherein the λ and the γ are the expansion coefficients, the parameter s is the caterpillar private key, the parameter S is the caterpillar public key, the parameter φ is the order of the RSA caterpillar key pair, the parameter g is a random integer, the parameter h is a random prime number, the parameter v is a random integer, and the at least one high-efficiency terminal device uses the high-efficiency authorization certificate center long-term public key of the high-efficiency authorization certificate center to encrypt γ to obtain a ciphertext γ'. The security certificate management system as described in claim 7, wherein the second RSA key expansion module is used to receive the RSA caterpillar key pair, and the operation of generating the RSA cocoon public keys further includes: the second RSA key expansion module generates the RSA cocoon public keys according to the parameter S, the expansion coefficient λ, the ciphertext γ' and formula 2; and the second RSA key expansion module obtains the expansion coefficient μ according to the expansion coefficient λ and formula 4, wherein, Formula 2 Formula 4 Wherein, the λ and μ are the expansion coefficients, the parameter S is the caterpillar public key, the parameter ri is an integer, the Gi are the RSA coyote public keys, and the parameter u is a random integer. The security certificate management system as described in claim 8, wherein the first RSA key expansion module is used to receive the RSA cocoon public keys, and the operation of generating the RSA butterfly public keys further includes: the high-efficiency authorization certificate center uses the high-efficiency authorization certificate center long-term private key to decrypt the ciphertext γ' to obtain the plaintext γ; and the first RSA key expansion module generates the RSA butterfly public keys according to the RSA cocoon public keys, the expansion coefficient μ, the plaintext γ and formula 7, wherein, Formula 7 Wherein, μ is the expansion coefficient, the parameter oi is an integer, Gi is the RSA coil public keys, and Hi is the RSA butterfly public keys. A method for managing a secure certificate based on key expansion, comprising: Producing an RSA caterpillar key pair via at least one high-efficiency terminal device including an RSA key generation module; Receiving the RSA caterpillar key pair via a high-efficiency registration center including a second RSA key expansion module to generate a plurality of RSA cocoon public keys; and Receiving the RSA cocoon public keys via a high-efficiency authorization certificate center including a first RSA key expansion module to generate a plurality of RSA butterfly public keys. The security certificate management method as described in claim 10, wherein the step of generating the RSA caterpillar key pair through the at least one high-efficiency terminal device further includes: generating the RSA caterpillar key pair (s, S, φ) through the at least one high-efficiency terminal device; obtaining the expansion coefficient λ according to the RSA caterpillar key pair (s, S, φ) and formula 1 through the at least one high-efficiency terminal device, wherein, Formula 1 Wherein the λ is the expansion coefficient, the parameter s is the caterpillar private key, the parameter S is the caterpillar public key, the parameter φ is the order of the RSA caterpillar key pair, the parameter g is a random integer, and the parameter h is a random prime number. The security certificate management method as described in claim 11, wherein the step of receiving the RSA caterpillar key pair via the second RSA key expansion module and generating the RSA cocoon public keys further includes: generating the RSA cocoon public keys via the second RSA key expansion module according to the RSA caterpillar key pair (s, S, φ), the expansion coefficient λ and formula 2, wherein, Formula 2 Wherein, λ is the expansion coefficient, the parameter S is the caterpillar public key, the parameter ri is an integer, and Gi is the RSA coyote public keys. The security certificate management method as described in claim 12, wherein the step of receiving the RSA cocoon public keys through the first RSA key expansion module and generating the RSA butterfly public keys further includes: generating the RSA butterfly public keys through the first RSA key expansion module according to the RSA cocoon public keys, the expansion coefficient λ and formula 3, wherein, Formula 3 Wherein the λ is the expansion coefficient, the parameter oi is an integer, the Gi is the RSA coil public keys, and the Hi is the RSA butterfly public keys. The security certificate management method as described in claim 11, wherein the step of receiving the RSA caterpillar key pair through the second RSA key expansion module and generating the RSA cocoon public keys further includes: generating the RSA cocoon public keys through the second RSA key expansion module according to the RSA caterpillar key pair (s, S, φ), the expansion coefficient λ and formula 2, and obtaining the expansion coefficient μ according to formula 4, wherein, Formula 2 Formula 4 Wherein, the λ and μ are the expansion coefficients, the parameter S is the caterpillar public key, the parameter ri is an integer, the Gi are the RSA coyote public keys, and the parameter u is a random integer. The security certificate management method as described in claim 14, wherein the step of receiving the RSA cocoon public keys through the first RSA key expansion module and generating the RSA butterfly public keys further includes: generating the RSA butterfly public keys through the first RSA key expansion module according to the RSA cocoon public keys, the expansion coefficient μ and formula 5, wherein, Formula 5 Wherein, μ is the expansion coefficient, the parameter oi is an integer, Gi is the RSA coil public keys, and Hi is the RSA butterfly public keys. The security certificate management method as described in claim 10, wherein the step of generating the RSA caterpillar key pair through the at least one high-efficiency terminal device further includes: generating the RSA caterpillar key pair (s, S, φ) through the at least one high-efficiency terminal device; obtaining an expansion coefficient λ based on the RSA caterpillar key pair (s, S, φ) and formula 1 through the at least one high-efficiency terminal device; obtaining an expansion coefficient γ based on the RSA caterpillar key pair (s, S, φ) and formula 6 through the at least one high-efficiency terminal device, wherein, Formula 1 Formula 6 wherein the λ and the γ are the expansion coefficients, the parameter s is the caterpillar private key, the parameter S is the caterpillar public key, the parameter φ is the order of the RSA caterpillar key pair, the parameter g is a random integer, the parameter h is a random prime number, the parameter v is a random integer, and the at least one high-efficiency terminal device uses the high-efficiency authorization certificate center long-term public key of the high-efficiency authorization certificate center to encrypt γ to obtain a ciphertext γ'. The security certificate management method as described in claim 16, wherein the step of receiving the RSA caterpillar key pair through the second RSA key expansion module and generating the RSA cocoon public keys further includes: generating the RSA cocoon public keys through the second RSA key expansion module according to the parameter S, the expansion coefficient λ, the ciphertext γ' and formula 2; and obtaining the expansion coefficient μ through the second RSA key expansion module according to the expansion coefficient λ and formula 4, wherein, Formula 2 Formula 4 Wherein, the λ and μ are the expansion coefficients, the parameter S is the caterpillar public key, the parameter ri is an integer, the Gi are the RSA coyote public keys, and the parameter u is a random integer. The security certificate management method as described in claim 17, wherein the step of receiving the RSA cocoon public keys through the first RSA key expansion module and generating the RSA butterfly public keys further includes: decrypting the ciphertext γ' by the high-efficiency authorization certificate center using the high-efficiency authorization certificate center long-term private key to obtain the plaintext γ; and generating the RSA butterfly public keys through the first RSA key expansion module according to the RSA cocoon public keys, the expansion coefficient μ, the plaintext γ and formula 7, wherein, Formula 7 Wherein, μ is the expansion coefficient, the parameter oi is an integer, Gi is the RSA coil public keys, and Hi is the RSA butterfly public keys.

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