TWI877003B - Anonymous credential method and system based on hash and post-quantum cryptography - Google Patents

Abstract

An anonymous credential method and system based on hash and post-quantum cryptography are provided. The anonymous credential method includes following steps: generating, by a terminal device based on post-quantum cryptography, a random number as a private key corresponding to the post-quantum cryptography, and performing, hash calculation for w times on the private key to obtain a public key corresponding to the post-quantum cryptography; expanding, by an authorization certificate center based on post-quantum cryptography, the public key to obtain an expansion result; and generating, by the authorization certificate center based on post-quantum cryptography, an anonymous certificate of the terminal device based on post-quantum cryptography, wherein the anonymous certificate includes the expansion result.

Description

Anonymous certification method and system based on hashing and post-quantum cryptography

The present invention relates to an anonymous certification method and system based on hashing and post-quantum cryptography.

The current public key encryption method mainly adopts RSA cryptography or Elliptic Curve Cryptography (ECC) method, but it has been proven that it can be cracked. In particular, the prime factorization algorithm can reduce the cracking time of the current mainstream cryptography algorithms (such as RSA and ECC) from exponential time complexity O(2n) to polynomial time complexity O(n).

The anonymous certification method based on hashing and post-quantum cryptography of the present invention comprises the following steps: a terminal device based on post-quantum cryptography generates a random number a as a private key corresponding to post-quantum cryptography, and performs w hashing calculations on the private key to obtain a public key corresponding to post-quantum cryptography; an authorized certification center based on post-quantum cryptography expands the public key to obtain an expanded result; and an authorized certification center based on post-quantum cryptography generates an anonymous certificate _CE of a terminal device based on post-quantum cryptography, wherein the anonymous certificate _CE includes the expanded result.

The anonymous certificate system based on hashing and post-quantum cryptography of the present invention includes an authorized certificate center based on post-quantum cryptography and a terminal device based on post-quantum cryptography, wherein the terminal device based on post-quantum cryptography generates a random number a as a private key corresponding to post-quantum cryptography, and performs w hashing calculations on the private key to obtain a public key corresponding to post-quantum cryptography; the authorized certificate center based on post-quantum cryptography expands the public key to obtain an expanded result; the authorized certificate center based on post-quantum cryptography generates an anonymous certificate _CE based on the terminal device of post-quantum cryptography, wherein the anonymous certificate _CE includes the expanded result.

S10, S30, S50: Steps

S10a-2, S10b-2a, S10b-2b, S30a-2, S30b-2a, S30b-2b, S50-2, S61-2a, S61-2b, S6 2-2, S63-2a, S63-2b, S71-2a, S71-2b, S81-2, S82-2a, S82-2b, S83-2a, S83-2b: Steps

S10a-3, S10b-3, S21-3, S22-3, S23-3, S24-3, S25-3, S30a-3, S30b-3, S30c-3, S50-3, S61-3, S62-3, S63-3, S64-3, S65-3, S66-3, S67-3: Steps

110: Authorization certification center based on post-quantum cryptography

130: Terminal devices based on post-quantum cryptography

130-1: The first terminal device based on post-quantum cryptography

130-2: The second terminal device based on post-quantum cryptography

150: Registration center based on post-quantum cryptography

FIG1 is a flow chart of an anonymous certification method based on hashing and post-quantum cryptography according to an embodiment of the present invention.

FIG2A is an implementation example of the anonymous certification method based on hashing and post-quantum cryptography shown in FIG1.

FIG2B is another implementation example of the anonymous certification method based on hashing and post-quantum cryptography shown in FIG1.

FIG3 is another implementation example of the anonymous certification method based on hashing and post-quantum cryptography shown in FIG1.

FIG1 is a flow chart of an anonymous certification method based on hashing and post-quantum cryptography according to an embodiment of the present invention, wherein the anonymous certification method based on hashing and post-quantum cryptography is suitable for being executed by an anonymous certification system, wherein the anonymous certification system includes an authorized certification center based on post-quantum cryptography and a terminal device based on post-quantum cryptography. Please refer to FIG1.

In step S10, a random number a is generated by a terminal device based on post-quantum cryptography as a private key corresponding to post-quantum cryptography, and w hash calculations are performed on the private key to obtain a public key corresponding to post-quantum cryptography.

In step S30, the public key is expanded by the authorization certificate center based on post-quantum cryptography to obtain an expanded result.

In step S50, an authorized certificate center based on post-quantum cryptography generates an anonymous certificate _CE of a terminal device based on post-quantum cryptography, wherein the anonymous certificate _CE includes an expansion result.

The following will further illustrate the implementation examples of the present invention with examples.

FIG2A is an implementation example of the anonymous certification method based on hashing and post-quantum cryptography shown in FIG1. Please refer to FIG1 and FIG2A at the same time. In this embodiment, the private key includes a post-quantum cryptography private key a, the public key includes a post-quantum cryptography public key A, and the expansion result includes a reconstructed value P. The terminal device 130 based on post-quantum cryptography includes a first terminal device 130-1 based on post-quantum cryptography and a second terminal device 130-2 based on post-quantum cryptography. Further, the terminal device 130 based on post-quantum cryptography includes a post-quantum cryptography key production module. In other words, the first post-quantum cryptography-based terminal device 130-1 and the second post-quantum cryptography-based terminal device 130-2 may both include a post-quantum cryptography key generation module. On the other hand, the post-quantum cryptography-based authorization certificate center 110 includes a first post-quantum cryptography key expansion module.

In step S10a-2, the post-quantum cryptography key generation module of the first post-quantum cryptography-based terminal device 130-1 can generate a random number a as a post-quantum cryptography private key a. The numbers in this embodiment are expressed in hexadecimal. For example, the post-quantum cryptography private key a can be 60B420BB3851D9D47ACB933DBE70399BF6C92DA33AF01D4FB770E98C0325F41D.

In step S10b-2a, the post-quantum cryptography key generation module of the first post-quantum cryptography-based terminal device 130-1 may perform w hashing calculations on the post-quantum cryptography private key a to obtain the post-quantum cryptography public key A. For example, to improve computing efficiency, the first post-quantum cryptography-based terminal device 130-1 may select a w value of 2 bytes, which may be FFFF, but the length may also be increased according to actual application requirements to improve security. The first terminal device 130-1 based on post-quantum cryptography can calculate that the post-quantum cryptography public key A is D98742E324A52127AA02A5DD994D68446EF94E10005B5A1984F5D9F687FAA57D.

After executing step S10a-2 and step S10b-2a (step S10a-2 and step S10b-2a are also referred to as steps of generating a post-quantum cryptography key pair), the first post-quantum cryptography-based terminal device 130-1 can transmit the post-quantum cryptography public key A and the authorization information E of the first post-quantum cryptography-based terminal device 130-1 to the post-quantum cryptography-based authorization certificate center 110.

In step S30a-2, the first post-quantum cryptography key expansion module generates a random number r. For example, to improve computing efficiency, the first post-quantum cryptography key expansion module of the post-quantum cryptography-based authorization certificate center 110 can select a random number r with a length of 2 bytes, which is 30A5. However, the length can also be increased according to the actual application requirements to improve security.

In step S30b-2a, the first post-quantum cryptography key expansion module performs a random number r of hash calculations on the post-quantum cryptography public key A to expand the post-quantum cryptography public key A into a reconstruction value P. In this embodiment, the post-quantum cryptography-based authorization certificate center 110 can use P= H ^r ( A ) to calculate the reconstruction value P. In detail, H ^r ( A ) represents the random number r of hash calculations performed on the post-quantum cryptography public key A. For example, the authentication center 110 based on post-quantum cryptography can calculate the reconstruction value P as A0A7C26314A878A11D5FEE4D65FB5ED78E427733C41A9D42C0F086BE897D9526.

After executing step S30a-2 and step S30b-2a (step S30a-2 and step S30b-2a are also referred to as the step of generating a post-quantum cryptography reconstruction value), in step S50-2, the authorization certificate center 110 based on post-quantum cryptography generates an anonymous certificate _CE of the first terminal device 130-1 based on post-quantum cryptography, wherein the anonymous certificate _CE (at least) includes the reconstruction value P. In detail, the authorization certificate center 110 based on post-quantum cryptography can generate the anonymous certificate _CE of the first terminal device 130-1 based on post-quantum cryptography using an encoding function Encode ( P , E , *). In other words, in this embodiment, the anonymous certificate _CE includes (at least) the reconstructed value P and the authorization information E of the first terminal device 130-1 based on post-quantum cryptography. In this embodiment, the encoding function Encode ( P , E , *) can be in the Octet Encoding Rules (OER) format.

After executing step S50-2 (also referred to as the step of generating a post-quantum cryptography anonymous certificate), in step S61-2a, the first post-quantum cryptography key expansion module generates a hash value h _of ^the anonymous certificate CE . For example, the hash value h of _the anonymous certificate CE (i.e., H1 ( CE ₎ ) can be 2A93A8A442E305E84DA02D6620F77F97EC9EBBCA18ABEF6F64DAF110C3992937. To improve computing efficiency, the post -quantum cryptography-based authentication center 110 may select the last 2 bytes of the hash value as the hash value h , which is 2937. However, the length may be increased to improve security according to actual application requirements.

In step S62-2, the first post-quantum cryptography key expansion module obtains the reconstructed private key b according to the hash value h (of the anonymous certificate _CE ) and the random number r. In detail, the reconstructed private key b can be obtained by the following calculation formula, and the reconstructed private key b is 59DC; b = h + r

Then, the post-quantum cryptography-based authorization certificate center 110 may transmit the reconstructed value private key b and the anonymous certificate _CE to the first post-quantum cryptography-based terminal device 130-1.

In step S63-2a, the post-quantum cryptography key generation module (of the first post-quantum cryptography-based terminal device 130-1) generates an extended post-quantum cryptography private key q according to the reconstructed value private key b. Specifically, the post-quantum cryptography key generation module of the first post-quantum cryptography-based terminal device 130-1 can use the following calculation formula to obtain the extended post-quantum cryptography private key q: q = H ^b ( a ) (i.e., performing b hash calculations on the post-quantum cryptography private key a)

For example, the post-quantum cryptography key production module of the first post-quantum cryptography-based terminal device 130-1 can calculate the expanded post-quantum cryptography private key q as 44A8598BB7D14F4C50183BDF70AF631029F5EA622C54D4C791A847393F967287.

After executing step S61-2a, step S62-2, and step S63-2a (step S61-2a, step S62-2, and step S63-2a are also referred to as steps for generating an extended post-quantum cryptography private key), in step S71-2a, the first post-quantum cryptography-based terminal device 130-1 can generate an extended post-quantum cryptography public key Q according to the following calculation formula: Q = H ^b (A) = H ^h ( P ) = H ^w ( q )

In step S81-2, the second terminal device 130-2 based on post-quantum cryptography obtains the anonymous certificate _CE of the first terminal device 130-1 based on post-quantum cryptography from the authorization certificate center 110 based on post-quantum cryptography.

In step S82-2a, the hash value h of the anonymous certificate _CE is calculated by the second post-quantum cryptography-based terminal device 130-2.

In step S83-2a, the second post-quantum cryptography-based terminal device 130-2 generates an extended post-quantum cryptography public key Q according to the hash value h and the reconstructed value P in _the anonymous certificate CE of the first post-quantum cryptography-based terminal device 130-1. Based on the above example, the hash value h of _the anonymous certificate CE is 2937, and the reconstructed value P is A0A7C26314A878A11D5FEE4D65FB5ED78E427733C41A9D42C0F086BE897D9526. The second terminal device 130-2 based on post-quantum cryptography can generate an extended post-quantum cryptography public key Q according to the following calculation formula: Q=H ^h (P) (H ^h (P) represents h times of hashing calculation on P)

For example, the second post-quantum cryptography-based terminal device 130-2 can generate an extended post-quantum cryptography public key Q of 93AA6322F2A17FC3C41C03E928ECECF858173F57E0E33C4B4BA0915CE44EB1E7.

It is worth noting that step S81-2, step S82-2a, and step S83-2a are also referred to as steps for generating an extended post-quantum cryptography public key.

In one embodiment, the terminal device 130 based on post-quantum cryptography corresponds to a vehicle network terminal device. The anonymous certificate method of this embodiment further includes the following steps: the terminal device 130 based on post-quantum cryptography sends a vehicle network packet. Furthermore, the vehicle network packet may include an anonymous certificate CE . The vehicle network packet may also include the terminal device 130 based on post-quantum cryptography using an extended post-quantum cryptography private key _q to sign the content of the vehicle network packet, or the vehicle network packet may also include the terminal device 130 based on post-quantum cryptography using an extended post-quantum cryptography private key q to sign the hash value h' of the vehicle network packet.

In one embodiment, the terminal device 130 based on post-quantum cryptography corresponds to a personal terminal device. The anonymous certification method of this embodiment further includes the following steps: anonymous voting is performed by the terminal device 130 based on post-quantum cryptography. Further, the anonymous voting may include an anonymous certificate _CE . The anonymous voting may further include the terminal device 130 based on post-quantum cryptography using an extended post-quantum cryptography private key q to sign the content of the anonymous vote, or the anonymous voting may further include the terminal device 130 based on post-quantum cryptography using an extended post-quantum cryptography private key q to sign the hash value h' of the anonymous vote.

FIG2B is an implementation example of the anonymous certification method based on hashing and post-quantum cryptography shown in FIG1 . Please refer to FIG1 , FIG2A and FIG2B at the same time. Similar to the implementation example of FIG2A , in the implementation example of FIG2B , the private key includes a post-quantum cryptography private key a, the public key includes a post-quantum cryptography public key A, and the expansion result includes a reconstructed value P. The terminal device 130 based on post-quantum cryptography includes a first terminal device 130-1 based on post-quantum cryptography and a second terminal device 130-2 based on post-quantum cryptography. Furthermore, the terminal device 130 based on post-quantum cryptography includes a post-quantum cryptography key production module. In other words, the first post-quantum cryptography-based terminal device 130-1 and the second post-quantum cryptography-based terminal device 130-2 may both include a post-quantum cryptography key generation module. On the other hand, the post-quantum cryptography-based authorization certificate center 110 includes a first post-quantum cryptography key expansion module.

It should be noted here that one of the differences between FIG. 2B and FIG. 2A is that in the implementation example of FIG. 2B , the hash calculation includes pseudo-random number generator calculation. In addition, in FIG. 2B , the first post-quantum cryptography key expansion module of the post-quantum cryptography-based authorization certificate center 110, the first post-quantum cryptography-based terminal device 130-1 post-quantum cryptography key production module, and the second post-quantum cryptography-based terminal device 130-2 post-quantum cryptography key production module can all include pseudo-random number generators. The detailed steps of FIG. 2B will be further described below.

In step S10a-2, the post-quantum cryptography key generation module of the first post-quantum cryptography-based terminal device 130-1 can generate a random number a as a post-quantum cryptography private key a. The numbers in this embodiment are expressed in hexadecimal. For example, the post-quantum cryptography private key a can be 806B32813B08F97.

In step S10b-2b, the pseudo-random number generator of the post-quantum cryptography key production module of the first post-quantum cryptography-based terminal device 130-1 can perform w pseudo-random number generator calculations on the post-quantum cryptography private key a to obtain the post-quantum cryptography public key A. For example, the pseudo-random number generator used in this embodiment can be a pseudo-random number generator of the Java built-in Random class. The post-quantum cryptography public key A is obtained using the following calculation formula, where the G function is represented by the pseudo-random number generator function, and Gw (a ⁾ is represented by setting a as the initial random number seed, executing w pseudo-random number generator calculations, and taking the tth random number each time. In this embodiment, t is set to 1, then G1 ( a ) is expressed as setting a ^as a random number seed and obtaining the first random number as the value of G1 (a ⁾ . G2 ( a ) is expressed as setting G1 ( a ) as ^a random number ^seed and obtaining the first random number as the value of G2 ( a ), that is, G2 ⁽ a ⁾ = G1 ( ^G1 ( ^a ) ) .

The post-quantum cryptography public key of this embodiment is A = Gw ( a ⁾

To improve computational efficiency, the first terminal device 130-1 based on post-quantum cryptography can select a w value of 2 bytes, which can be FFFF, but the length can also be increased according to actual application requirements to improve security. The first terminal device 130-1 based on post-quantum cryptography can calculate that the post-quantum cryptography public key A is 720405EEF70B774E.

After executing step S10a-2 and step S10b-2b (step S10a-2 and step S10b-2b are also referred to as steps of generating a post-quantum cryptography key pair), the first post-quantum cryptography-based terminal device 130-1 can transmit the post-quantum cryptography public key A and the authorization information E of the first post-quantum cryptography-based terminal device 130-1 to the post-quantum cryptography-based authorization certificate center 110.

In step S30a-2, the first post-quantum cryptography key expansion module generates a random number r. For example, to improve computing efficiency, the first post-quantum cryptography key expansion module of the post-quantum cryptography-based authorization certificate center 110 can select a random number r with a length of 2 bytes, which is 4729. However, the length can also be increased according to the actual application requirements to improve security.

In step S30b-2b, the pseudo-random number generator of the first post-quantum cryptography key expansion module performs pseudo-random number generator calculations on the post-quantum cryptography public key A for a random number of r times to expand the post-quantum cryptography public key A into a reconstruction value P. In this embodiment, the authorization certificate center 110 based on post-quantum cryptography can use P= G ^r ( A ) to calculate the reconstruction value P. In detail, G ^r ( A ) is represented by performing pseudo-random number generator calculations on A r times. For example, the authorization certificate center 110 based on post-quantum cryptography can calculate the reconstruction value P as EC3085D9A2DFF8B6.

After executing step S30a-2 and step S30b-2b (step S30a-2 and step S30b-2b are also referred to as the step of generating a post-quantum cryptography reconstruction value), in step S50-2, the authorization certificate center 110 based on post-quantum cryptography generates an anonymous certificate _CE of the first terminal device 130-1 based on post-quantum cryptography, wherein the anonymous certificate _CE (at least) includes the reconstruction value P. In detail, the authorization certificate center 110 based on post-quantum cryptography can generate the anonymous certificate _CE of the first terminal device 130-1 based on post-quantum cryptography using an encoding function Encode ( P , E , *). In other words, in this embodiment, the anonymous certificate _CE includes (at least) the reconstructed value P and the authorization information E of the first terminal device 130-1 based on post-quantum cryptography. In this embodiment, the encoding function Encode ( P , E , *) can be in the Octet Encoding Rules (OER) format.

After executing step S50-2 (also referred to as the step of generating a post-quantum cryptography anonymous certificate), in step S61-2b, the pseudo-random number generator of the first post-quantum cryptography key expansion module generates a pseudo-random value _h of the anonymous certificate CE . For example, the pseudo _- random value h of _the anonymous certificate CE (i.e., ^G1 ( CE )) can be B18D9F7BA00A68CC. To improve computing efficiency, the authorization certificate center 110 based on post-quantum cryptography can select the last 2 bytes of the pseudo-random value as the pseudo-random value h, and the pseudo-random value h is 68CC. However, the length can also be increased according to the requirements of the actual application scenario to improve security.

In step S62-2, the pseudo-random number generator of the first post-quantum cryptography key expansion module obtains the reconstructed private key b according to the pseudo-random number h (of the anonymous certificate _CE ) and the random number r. In detail, the reconstructed private key b can be obtained by the following calculation formula, and the reconstructed private key b is obtained by calculation as AFF5; b = h + r

Then, the post-quantum cryptography-based authorization certificate center 110 may transmit the reconstructed value private key b and the anonymous certificate _CE to the first post-quantum cryptography-based terminal device 130-1.

In step S63-2b, the pseudo random number generator of the post-quantum cryptography key generation module (of the first post-quantum cryptography-based terminal device 130-1) generates an extended post-quantum cryptography private key q according to the reconstructed value private key b. In detail, the pseudo random number generator of the post-quantum cryptography key generation module of the first post-quantum cryptography-based terminal device 130-1 can use the following calculation formula to obtain the extended post-quantum cryptography private key q: q = G ^b ( a ) (i.e., perform b pseudo random number generator calculations on the post-quantum cryptography private key a)

For example, the post-quantum cryptography key production module of the first post-quantum cryptography-based terminal device 130-1 can calculate the expanded post-quantum cryptography private key q as FCCD109657606A0E.

After executing step S61-2b, step S62-2, and step S63-2b (step S61-2b, step S62-2, and step S63-2b are also referred to as steps for generating an extended post-quantum cryptography private key), in step S71-2b, the first post-quantum cryptography-based terminal device 130-1 may generate an extended post-quantum cryptography public key Q according to the following calculation formula: Q = G ^b (A) = G ^h ( P ) = G ^w ( q )

In step S81-2, the second terminal device 130-2 based on post-quantum cryptography obtains the anonymous certificate _CE of the first terminal device 130-1 based on post-quantum cryptography from the authorization certificate center 110 based on post-quantum cryptography.

In step S82-2b, the pseudo random number generator of the post-quantum cryptography key generation module of the second post-quantum cryptography-based terminal device 130-2 calculates the pseudo random number h of the anonymous certificate _CE .

In step S83-2b, the pseudo random number generator of the post-quantum cryptography key generation module of the second post-quantum cryptography-based terminal device 130-2 generates an extended post-quantum cryptography public key Q according to the pseudo random number h and the reconstructed value P _in the anonymous certificate CE of the first post-quantum cryptography-based terminal device 130-1. Based on the above example, the pseudo random number h of the anonymous _certificate CE is 68CC, and the reconstructed value P is EC3085D9A2DFF8B6. The second terminal device 130-2 based on post-quantum cryptography can generate an extended post-quantum cryptography public key Q according to the following calculation formula: Q= ^Gh (P) ( ^Gh (P) represents h pseudo-random number generator calculations performed on P)

For example, the second post-quantum cryptography-based terminal device 130-2 can generate an extended post-quantum cryptography public key Q of 9CE63D981FF19202.

It is worth noting that step S81-2, step S82-2b and step S83-2b are also called steps for generating the extended post-quantum cryptography public key.

FIG3 is another implementation example of the anonymous certification method based on hashing and post-quantum cryptography shown in FIG1. Please refer to FIG1 and FIG3 at the same time. In this embodiment, the private key includes a post-quantum cryptography caterpillar private key a for signature, the public key includes a post-quantum cryptography caterpillar public key A for signature, and the expansion result includes a post-quantum cryptography butterfly public key Qι for signature. Further, the anonymous certification system further includes a registration center 150 based on post-quantum cryptography. Further, the authorization certificate center 110 based on post-quantum cryptography includes a first post-quantum cryptography key expansion module. The terminal device 130 based on post-quantum cryptography includes a post-quantum cryptography key production module. The post-quantum cryptography-based registration center 150 includes a second post-quantum cryptography key expansion module.

In step S10a-3, the terminal device 130 based on post-quantum cryptography generates a random number a as a post-quantum cryptography caterpillar private key a for signature. The numbers in this embodiment are expressed in hexadecimal, and the value of the post-quantum cryptography caterpillar private key a for signature is 60B420BB3851D9D47ACB933DBE70399BF6C92DA33AF01D4FB770E98C0325F41D.

In step S10b-3, the terminal device 130 based on post-quantum cryptography performs w hash calculations on the post-quantum cryptography caterpillar private key a for signature to obtain the post-quantum cryptography caterpillar public key A for signature. In this embodiment, a w value of 2 bytes is selected to improve the calculation efficiency. The w value is FFFF, but the length can be increased according to the actual application field requirements to improve security. The post-quantum cryptography caterpillar public key A for signature obtained by calculation is D98742E324A52127AA02A5DD994D68446EF94E10005B5A1984F5D9F687FAA57D.

After executing step S10a-3 and step S10b-3 (step S10a-3 and step S10b-3 are also called the step of generating a post-quantum cryptography caterpillar key pair), the post-quantum cryptography registration center 150 can execute the step of generating a post-quantum cryptography cocoon public key (i.e., steps S21-3, S22-3, S23-3, S24-3, and S25-3). It is worth mentioning here that the step of generating a post-quantum cryptography cocoon public key is that the post-quantum cryptography registration center 150 based on the post-quantum cryptography caterpillar public key A for signature is expanded to the post-quantum cryptography cocoon public key Bι for signature. The following will continue to explain.

In step S21-3, the terminal device 130 based on post-quantum cryptography generates an AES key ck. Specifically, the terminal device 130 based on post-quantum cryptography can use the AES-128 algorithm to generate the AES key ck, and the AES key ck is 23C29B624DE9EF9C2F931EFC580F9AFB, and the AES key ck can be used to execute the AES encryption algorithm.

In step S22-3, the post-quantum cryptography key production module produces a post-quantum cryptography key pair (p, P) for encryption, including a post-quantum cryptography private key p for encryption and a post-quantum cryptography public key P for encryption. In detail, the post-quantum cryptography key pair (p, P) for encryption is a Kyber cryptography algorithm key pair, the post-quantum cryptography private key p for encryption is a Kyber cryptography private key, and the post-quantum cryptography public key P for encryption is a Kyber cryptography public key. However, the present invention is not limited to this.

In step S23-3, the terminal device 130 based on post-quantum cryptography sends (ck, A, P) to the registration center 150 based on post-quantum cryptography.

In step S24-3, a plurality of ι values are generated by the post-quantum cryptography-based registration center 150, and an extended value rι is calculated using the AES key ck and the expansion function F(ck,ι). In this embodiment, the ι value is 01. The value of the expansion function F(ck,ι) is the ciphertext obtained by using the AES key ck to execute the AES encryption algorithm on the plaintext ι value. For example, the value of the expansion function F(ck,ι) can be 83DE7844AFE1C80645B4F20BAC594B5C. In this embodiment, in order to improve the computing efficiency, the registration center 150 based on post-quantum cryptography can select the last 2 bytes of the ciphertext as the extension value rι, and the extension value rι is 4B5C, but the length can be increased according to the actual application field requirements to improve security.

In step S25-3, the second post-quantum cryptography key expansion module (of the post-quantum cryptography registration center 150) performs a hashing calculation based on the expansion value rι and the post-quantum cryptography caterpillar public key A for signature to generate the post-quantum cryptography cocoon public key Bι for signature. In detail, the signature post-quantum cryptography cocoon public key Bι can be obtained by the following calculation formula, where H ^rι ( A ) represents the execution of the extended value rι hash calculation on the signature post-quantum cryptography caterpillar public key A, and the signature post-quantum cryptography cocoon public key Bι is obtained by calculation as 1804C0EEFF11F3262DF7B957EFF9F0487DD19E3DD4CCDDDA9EE59B058BCCEB76; B _ι = H ^rι ( A )

After executing step S21-3, step S22-3, step S23-3, step S24-3 and step S25-3 (i.e., the step of generating the post-quantum cryptography cocoon public key), the authorization certificate center 110 based on post-quantum cryptography can execute the step of generating the post-quantum cryptography butterfly public key (i.e., step S30a-3, step S30b-3, and step S30c-3). It is worth mentioning here that the step of generating the post-quantum cryptography butterfly public key is that the authorization certificate center 110 based on post-quantum cryptography expands the post-quantum cryptography cocoon public key Bι for signature into the post-quantum cryptography butterfly public key Qι for signature. The following will continue to explain.

In step S30a-3, the registration center 150 based on post-quantum cryptography sends the post-quantum cryptography public key Bι for signing and the post-quantum cryptography public key P for encryption to the authorization certification center 110 based on post-quantum cryptography.

In step S30b-3, the first post-quantum cryptography key expansion module (of the post-quantum cryptography-based authorization certificate center 110) generates a random number c. In this embodiment, a random number c of 2 bytes is selected to improve computing efficiency. The random number c is EB76, but the length can be increased according to the actual application requirements to improve security.

In step S30c-3, the first post-quantum cryptography key expansion module (of the post-quantum cryptography-based certification center 110) performs a hashing calculation on the post-quantum cryptography butterfly public key Bι for signature according to a random number c to generate the post-quantum cryptography butterfly public key Qι for signature. In detail, the post-quantum cryptography butterfly public key Qι for signature can be obtained by the following calculation formula, where H ^c ( B ι ) represents the execution of c hash calculations on the post-quantum cryptography butterfly public key B ι for signature. The post-quantum cryptography butterfly public key Q ι for signature obtained by calculation is 6ACBBFBDD7E69C26C37619B3D30627D12F376935C9652ACA514E7445C08EDBB5; Q _ι = H ^c ( B _ι )

After executing step S30a-3, step S30b-3, and step S30c-3 (i.e., the step of generating a post-quantum cryptography butterfly public key), in step S50-3, the authorization certificate center 110 based on post-quantum cryptography can generate an anonymous certificate _CE for the terminal device 130 based on post-quantum cryptography, wherein the anonymous certificate _CE may include a post-quantum cryptography butterfly public key Qι for signature.

After executing step S50-3 (step S50-3 is also called the step of generating a post-quantum cryptography anonymous certificate), the terminal device 130 based on post-quantum cryptography can execute the step of generating a post-quantum cryptography butterfly private key (i.e., step S61-3, step S62-3, step S63-3, step S64-3, step S65-3, step S66-3, and step S67- 3). The following will continue to explain.

In step S61-3, the authorization certificate center 110 based on post-quantum cryptography uses the encryption post-quantum cryptography public key P to encrypt the random number c.

Next, the authorization certificate center 110 based on post-quantum cryptography transmits the ciphertext of the random number c to the terminal device 130 based on post-quantum cryptography. In detail, in step S62-3, the authorization certificate center 110 based on post-quantum cryptography can transmit the ciphertext of the random number c and the signature of the random number c to the registration center 150 based on post-quantum cryptography. Then, in step S63-3, the registration center 150 based on post-quantum cryptography can transmit multiple ι values, the ciphertext of the random number c and the signature of the random number c to the terminal device 130 based on post-quantum cryptography.

Next, in step S64-3, the terminal device 130 based on post-quantum cryptography uses the AES key ck, ι value and expansion function F(ck, ι) to calculate the expansion value rι.

In step S65-3, the post-quantum cryptography key generation module (of the terminal device 130 based on post-quantum cryptography) performs hashing calculation based on the extended value rι and the post-quantum cryptography caterpillar private key a for signature to generate the post-quantum cryptography caterpillar private key bι for signature. For example, the post-quantum cryptography caterpillar private key bι for signature can be 0E233E7F441C76998990C7D697E4362C67EA9F1A621767E6E9A555EF67A727CA.

In step S66-3, the post-quantum cryptography key generation module (of the terminal device 130 based on post-quantum cryptography) uses the encryption post-quantum cryptography private key p to decrypt the ciphertext of the random number c to obtain the plaintext of the random number c.

In step S67-3, the post-quantum cryptography key generation module performs hashing calculation on the post-quantum cryptography butterfly private key bι for signature according to the random number c to generate the post-quantum cryptography butterfly private key qι for signature. In detail, the post-quantum cryptography butterfly private key qι for signature can be 9C85CAD311430F4DE81DC07182489C95942FC728FBF99F8A28029249E8D34116.

In one embodiment, the terminal device 130 based on post-quantum cryptography corresponds to a vehicle network terminal device. The anonymous certificate method of this embodiment further includes the following steps: the terminal device 130 based on post-quantum cryptography sends a vehicle network packet. Furthermore, the vehicle network packet may include an anonymous certificate _CE . The vehicle network packet may also include the terminal device 130 based on post-quantum cryptography using a signature using a post-quantum cryptography butterfly private key qι to sign the content of the vehicle network packet, or the vehicle network packet may also include the terminal device 130 based on post-quantum cryptography using a signature using a post-quantum cryptography butterfly private key qι to sign the hash value h' of the vehicle network packet.

It should be noted here that the anonymous certification method of the present embodiment further includes the following steps: obtaining the signature post-quantum cryptography butterfly public key Qι in the anonymous certificate _CE by the terminal device 130 based on post-quantum cryptography, and using the signature post-quantum cryptography butterfly public key Qι to verify the signature of the content of the vehicle network packet, or verify the signature of the hash value h' of the vehicle network packet.

In one embodiment, the terminal device 130 based on post-quantum cryptography corresponds to a personal terminal device. The anonymous certification method of this embodiment further includes the following steps: anonymous voting is performed by the terminal device 130 based on post-quantum cryptography. Further, the anonymous voting includes an anonymous certificate _CE . Anonymous voting may further include the terminal device 130 based on post-quantum cryptography using a signature using a post-quantum cryptography butterfly private key qι to sign the content of the anonymous vote, or anonymous voting may further include the terminal device 130 based on post-quantum cryptography using a signature using a post-quantum cryptography butterfly private key qι to sign the hash value h' of the anonymous vote.

It should be noted here that the anonymous certification method of this embodiment further includes the following steps: the terminal device 130 based on post-quantum cryptography obtains the signature post-quantum cryptography butterfly public key Qι in the anonymous certificate _CE , and uses the signature post-quantum cryptography butterfly public key Qι to verify the signature of the content of the anonymous vote, or to verify the signature of the hash value h' of the anonymous vote.

The present invention further provides an anonymous certificate system based on hashing and post-quantum cryptography. The anonymous certificate system includes an authorized certificate center based on post-quantum cryptography and a terminal device based on post-quantum cryptography, wherein the terminal device based on post-quantum cryptography generates a random number a as a private key corresponding to post-quantum cryptography, and performs w hashing calculations on the private key to obtain a public key corresponding to post-quantum cryptography; the authorized certificate center based on post-quantum cryptography expands the public key to obtain an expanded result; the authorized certificate center based on post-quantum cryptography generates an anonymous _certificate CE based on the terminal device of post-quantum cryptography, wherein the anonymous _certificate CE includes the expanded result. The anonymous certification system has been described in the above embodiments. In one embodiment, the anonymous certification system further includes a registration center based on post-quantum cryptography to execute the implementation example of the anonymous certification method based on hashing and post-quantum cryptography described in FIG. 3 above.

In summary, the anonymous certificate method and system based on hashing and post-quantum cryptography of the present invention can be expanded by an authorized certificate center based on post-quantum cryptography (corresponding to post-quantum cryptography) to obtain an expanded result. Then, the authorized certificate center based on post-quantum cryptography can generate an anonymous certificate _CE of a terminal device based on post-quantum cryptography, and the anonymous certificate _CE can include the expanded result. In this way, it is possible to prevent the public key from being easily cracked by a prime factor decomposition algorithm.

S10, S30, S50: Steps

Claims (23)

An anonymous certification method based on hashing and post-quantum cryptography is suitable for being executed by an anonymous certification system, wherein the anonymous certification system includes an authorized certification center based on post-quantum cryptography and a terminal device based on post-quantum cryptography, wherein the anonymous certification method includes the following steps: the terminal device based on post-quantum cryptography generates a random number a as a random number corresponding to the post-quantum cryptography. A private key is obtained, and w hash calculations are performed on the private key to obtain a public key corresponding to the post-quantum cryptography; the authorized certificate center based on post-quantum cryptography expands the public key to obtain an expanded result; and the authorized certificate center based on post-quantum cryptography generates an anonymous certificate of the terminal device based on post-quantum cryptography, wherein the anonymous certificate includes the expanded result. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 1, wherein the private key includes a post-quantum cryptography private key a, wherein the public key includes a post-quantum cryptography public key A, and wherein the expansion result includes a reconstructed value P. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 2, wherein the authorization certification center based on post-quantum cryptography includes a first post-quantum cryptography key expansion module, wherein the step of the authorization certification center based on post-quantum cryptography expanding the public key to obtain the expansion result includes: generating a random number r by the first post-quantum cryptography key expansion module, and performing the hashing calculation r times on the post-quantum cryptography public key A to expand the post-quantum cryptography public key A to the reconstructed value P. The anonymous certificate method based on hashing and post-quantum cryptography as described in claim 3 further includes the following steps: the first post-quantum cryptography key expansion module generates a hash value h of the anonymous certificate, and obtains a reconstructed value private key b based on the hash value h and the random number r. As described in claim 4, the anonymous certification method based on hashing and post-quantum cryptography, wherein the terminal device based on post-quantum cryptography includes a post-quantum cryptography key generation module, wherein the anonymous certification method further includes the following steps: the post-quantum cryptography key generation module generates an extended post-quantum cryptography private key q according to the reconstructed value private key b. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 5, wherein the terminal device based on post-quantum cryptography includes a first terminal device based on post-quantum cryptography and a second terminal device based on post-quantum cryptography, and wherein the anonymous certification method further includes the following steps: the second terminal device based on post-quantum cryptography obtains the anonymous certificate of the first terminal device based on post-quantum cryptography from the authorized certification center based on post-quantum cryptography; and the second terminal device based on post-quantum cryptography calculates the hash value h of the anonymous certificate, and generates an extended post-quantum cryptography public key Q based on the hash value h and the reconstructed value P in the anonymous certificate of the first terminal device based on post-quantum cryptography. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 5, wherein the terminal device based on post-quantum cryptography corresponds to a vehicle network terminal device, wherein the anonymous certification method further comprises the following steps: the terminal device based on post-quantum cryptography sends a vehicle network packet, wherein the vehicle network packet includes the anonymous certificate; the vehicle network packet further includes the terminal device based on post-quantum cryptography using the extended post-quantum cryptography private key q to sign the content of the vehicle network packet, or includes the vehicle network packet further including the terminal device based on post-quantum cryptography using the extended post-quantum cryptography private key q to sign the hash value h' of the vehicle network packet. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 5, wherein the terminal device based on post-quantum cryptography corresponds to a personal terminal device, wherein the anonymous certification method further comprises the following steps: anonymous voting is performed by the terminal device based on post-quantum cryptography, wherein the anonymous voting includes the anonymous certificate; the anonymous voting further includes the terminal device based on post-quantum cryptography using the extended post-quantum cryptography private key q to sign the content of the anonymous vote, or the anonymous voting further includes the terminal device based on post-quantum cryptography using the extended post-quantum cryptography private key q to sign the hash value h' of the anonymous vote. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 2, wherein the hashing calculation includes a pseudo-random number generator calculation. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 9, wherein the authorization certificate center based on post-quantum cryptography includes a first post-quantum cryptography key expansion module, and the first post-quantum cryptography key expansion module includes a pseudo-random number generator, wherein the authorization certificate center based on post-quantum cryptography expands the public key to obtain the The step of obtaining the expansion result includes: generating a random number r by the first post-quantum cryptography key expansion module, and executing the pseudo-random number generator calculation r times on the post-quantum cryptography public key A by the pseudo-random number generator of the first post-quantum cryptography key expansion module to expand the post-quantum cryptography public key A to the reconstructed value P. The anonymous certificate method based on hashing and post-quantum cryptography as described in claim 10 further includes the following steps: the pseudo-random number generator of the first post-quantum cryptography key expansion module generates the pseudo-random value h of the anonymous certificate, and obtains the reconstructed value private key b according to the pseudo-random value h and the random number r. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 11, wherein the terminal device based on post-quantum cryptography includes a post-quantum cryptography key generation module, and the post-quantum cryptography key generation module includes the pseudo-random number generator, wherein the anonymous certification method further includes the following steps: the pseudo-random number generator of the post-quantum cryptography key generation module generates an extended post-quantum cryptography private key q according to the reconstructed value private key b. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 12, wherein the terminal device based on post-quantum cryptography includes a first terminal device based on post-quantum cryptography and a second terminal device based on post-quantum cryptography, wherein the post-quantum cryptography key generation module of the second terminal device based on post-quantum cryptography includes the pseudo-random number generator, and wherein the anonymous certification method further includes the following steps: the second terminal device based on post-quantum cryptography generates a pseudo-random number from the pseudo-random number generator; The post-quantum cryptography-based authorization certificate center obtains the anonymous certificate of the first post-quantum cryptography-based terminal device; and the pseudo-random number generator of the post-quantum cryptography key production module of the second post-quantum cryptography-based terminal device calculates the pseudo-random value h of the anonymous certificate, and generates an extended post-quantum cryptography public key Q based on the pseudo-random value h and the reconstructed value P in the anonymous certificate of the first post-quantum cryptography-based terminal device. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 1, wherein the private key includes a post-quantum cryptography caterpillar private key a for signature, wherein the public key includes a post-quantum cryptography caterpillar public key A for signature, wherein the extended result includes a post-quantum cryptography butterfly public key Qι for signature, wherein the anonymous certification system further includes a registration center based on post-quantum cryptography, wherein the anonymous certification method further includes the following steps: The registration center based on post-quantum cryptography expands the post-quantum cryptography caterpillar public key A for signature into the post-quantum cryptography cocoon public key Bι for signature; wherein the step of the authorization certificate center based on post-quantum cryptography expanding the public key to obtain the expansion result includes: The authorization certificate center based on post-quantum cryptography expands the post-quantum cryptography cocoon public key Bι for signature into the post-quantum cryptography butterfly public key Qι for signature. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 14, wherein the terminal device based on post-quantum cryptography includes a post-quantum cryptography key generation module, wherein the registration center based on post-quantum cryptography includes a second post-quantum cryptography key expansion module, wherein the step of the registration center based on post-quantum cryptography expanding the post-quantum cryptography caterpillar public key A for signature into the post-quantum cryptography cocoon public key Bι for signature includes: the post-quantum cryptography key generation module generates a post-quantum cryptography private key p for encryption and a post-quantum cryptography public key P for encryption key pair (p, P); the terminal device based on post-quantum cryptography generates an AES key ck; the terminal device based on post-quantum cryptography sends (ck, A, P) to the registration center based on post-quantum cryptography; the registration center based on post-quantum cryptography generates a plurality of ι values, and uses the AES key ck and the expansion function F(ck, ι) to calculate the expansion value rι; and the second post-quantum cryptography key expansion module performs the hashing calculation based on the expansion value rι and the post-quantum cryptography caterpillar public key A for signature to generate the post-quantum cryptography cobweb public key Bι for signature. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 15, wherein the authorization certificate center based on post-quantum cryptography includes a first post-quantum cryptography key expansion module, wherein the step of the authorization certificate center based on post-quantum cryptography expanding the signature post-quantum cryptography butterfly public key Bι to the signature post-quantum cryptography butterfly public key Qι includes: The registration center sends the post-quantum cryptography butterfly public key Bι for signature and the post-quantum cryptography butterfly public key P for encryption to the authorization certificate center based on post-quantum cryptography; and the first post-quantum cryptography key expansion module generates a random number c, and performs the hash calculation on the post-quantum cryptography butterfly public key Bι for signature according to the random number c to generate the post-quantum cryptography butterfly public key Qι for signature. The anonymous certification method based on hashing and post-quantum cryptography as described in claim 16 further includes the following steps: the authorization certification center based on post-quantum cryptography uses the encryption post-quantum cryptography public key P to encrypt the random number c, and transmits the ciphertext of the random number c to the terminal device based on post-quantum cryptography; the terminal device based on post-quantum cryptography uses the AES key ck, the ι value and the expansion function F(ck,ι) to calculate the expansion value rι; the post-quantum cryptography uses the AES key ck, the ι value and the expansion function F(ck,ι) to calculate the expansion value rι; The cryptographic key generation module performs the hashing calculation based on the extended value rι and the post-quantum cryptographic caterpillar private key a for signature to generate the post-quantum cryptographic cocoon private key bι for signature; and the post-quantum cryptographic key generation module uses the post-quantum cryptographic private key p for encryption to decrypt the ciphertext of the random number c to obtain the plaintext of the random number c, and performs the hashing calculation on the post-quantum cryptographic cocoon private key bι for signature based on the random number c to generate the post-quantum cryptographic butterfly private key qι for signature. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 17, wherein the terminal device based on post-quantum cryptography corresponds to a vehicle network terminal device, wherein the anonymous certification method further comprises the following steps: the terminal device based on post-quantum cryptography sends a vehicle network packet, wherein the vehicle network packet includes the anonymous certificate; the vehicle network packet further includes the terminal device based on post-quantum cryptography using the signature post-quantum cryptography butterfly private key qι to sign the content of the vehicle network packet, or the vehicle network packet further includes the terminal device based on post-quantum cryptography using the signature post-quantum cryptography butterfly private key qι to sign the hash value h' of the vehicle network packet. The anonymous certification method based on hashing and post-quantum cryptography as described in claim 18 further includes the following steps: the terminal device based on post-quantum cryptography obtains the signature post-quantum cryptography butterfly public key Qι in the anonymous certificate, and uses the signature post-quantum cryptography butterfly public key Qι to verify the signature of the content of the vehicle network packet, or verify the signature of the hash value h' of the vehicle network packet. An anonymous certification method based on hashing and post-quantum cryptography as described in claim 17, wherein the terminal device based on post-quantum cryptography corresponds to a personal terminal device, wherein the anonymous certification method further comprises the following steps: The terminal device based on post-quantum cryptography performs anonymous voting, wherein the anonymous voting includes the anonymous certificate; the anonymous voting further comprises the terminal device based on post-quantum cryptography using the signature post-quantum cryptography butterfly private key qι to sign the content of the anonymous vote, or the anonymous voting further comprises the terminal device based on post-quantum cryptography using the signature post-quantum cryptography butterfly private key qι to sign the hash value h' of the anonymous vote. The anonymous certification method based on hashing and post-quantum cryptography as described in claim 20 further includes the following steps: the terminal device based on post-quantum cryptography obtains the signature post-quantum cryptography butterfly public key Qι in the anonymous certificate, and uses the signature post-quantum cryptography butterfly public key Qι to verify the signature of the content of the anonymous vote, or verify the signature of the hash value h' of the anonymous vote. An anonymous certificate system based on hashing and post-quantum cryptography includes an authorized certificate center based on post-quantum cryptography and a terminal device based on post-quantum cryptography, wherein the terminal device based on post-quantum cryptography generates a random number a as a private key corresponding to the post-quantum cryptography, and performs w hashing calculations on the private key to obtain a public key corresponding to the post-quantum cryptography; the authorized certificate center based on post-quantum cryptography expands the public key to obtain an expansion result; the authorized certificate center based on post-quantum cryptography generates an anonymous certificate for the terminal device based on post-quantum cryptography, wherein the anonymous certificate includes the expansion result. An anonymous certificate system based on hashing and post-quantum cryptography as described in claim 22, wherein the private key includes a post-quantum cryptography caterpillar private key a for signature, wherein the public key includes a post-quantum cryptography caterpillar public key A for signature, wherein the expansion result includes a post-quantum cryptography butterfly public key Qι for signature, wherein the anonymous certificate system further includes a registration center based on post-quantum cryptography, wherein the registration center based on post-quantum cryptography expands the post-quantum cryptography caterpillar public key A for signature into a post-quantum cryptography cocoon public key Bι for signature; and the authorized certificate center based on post-quantum cryptography expands the post-quantum cryptography cocoon public key Bι for signature into the post-quantum cryptography butterfly public key Qι for signature.

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