Multivariable public key encryption method

Abstract

The invention discloses a multivariable public key encryption method. According to the multivariable public key encryption method, when a key is generated, a matrix is constructed according to an iterative method, the length of the key is greatly reduced, and the key can be managed conveniently; a probability encryption method is adopted, random parameters are introduced into encryption, the random parameters must be solved by a deciphering party through a deciphering process, the random parameters take part in decryption of a plaintext, the plaintext can be deciphered only under the condition that the random parameters are known, the difficulty of ciphertext decryption by an attacker is increased, ciphertexts are different even if public keys are the same, the public keys can be released in the forms such as telephone numbers, and encryption security is improved; based on the combinatorial optimization difficulty and multivariable quadratic polynomial, attack of a quantum computer can be resisted, both the encryption speed and the decryption speed are high, and the method can be applied to mobile terminals such as mobile phones; based on calculation on a finite field, the calculation process is simplified; the addition homomorphism and the subtraction homomorphism are achieved, the multiplication homomorphism can be achieved under special conditions, and the method can be applied to the newly-developed fields such as cloud computing.

Description

technical field

[0001] The invention belongs to the technical field of information security, and more specifically relates to a multivariate public key encryption method. Background technique

[0002] With the continuous development of computers and networks, people have higher and higher requirements for information integrity and security. Therefore, cryptography came into being. Due to its different encryption key and decryption key, public key cryptography has become a key means to solve some security problems of network security and information security. However, with the continuous development of information technology, people have higher and higher requirements for the performance of the system, not only the integrity and security of information, but also the simplicity and speed of the process of transmitting information.

[0003] At present, the key management and transmission process of mainstream symmetric cryptography is relatively complicated, and the calculatio...

Examples

Embodiment 1

[0067] The random parameter ε is obtained through the decryption method, and the method includes the following steps:

[0068] (1) Generate a key. Further include the following steps:

[0069] (1-1) Construct a k×n-dimensional full-rank matrix A in an iterative manner. Further include the following steps:

[0070] (1-1-1) Determine k=2.

[0071] (1-1-2) Select finite field Z, and 2 integers p in finite field Z 1 ,p 2 .

[0072] (1-1-3) Select the following integers on the finite field Z: (β 11 ,β 12 ), (β 21 ,β 22 ) and (x 1 ,x 2 ). Order a 11 = β 11 p 1 , a 12 = β 12 p 1 2 , a 21 = β 21 p 2 , a 22 = β 22 p 2 2 .

[0073] (1-1-4) Construction matrix A=(a ij ), wherein,...

Embodiment 2

[0102] The random parameter ε is obtained through a synchronous method. This method includes the following steps:

[0103] (1) Generate a key. Further include the following steps:

[0104] (1-1) Construct a k×n-dimensional full-rank matrix A in an iterative manner. Further include the following steps:

[0105] (1-1-1) Determine k=2.

[0106] (1-1-2) Select finite field Z, and 2 integers p in finite field Z 1 ,p 2 .

[0107] (1-1-3) Select the following integers on the finite field Z: (β 11 ,β 12 ), (β 21 ,β 22 ) and (x 1 ,x 2 ). Order a 11 = β 11 ,a 12 = β 12 p 1 ,a 21 = β 21 ,a 22 = β 22 p 2 .

[0108] (1-1-4) Construction matrix A=(a ij ), wherein, when i=1,2, j=1,...,n, j>2, a ij = x i p i 2 a i ( j - 2 ...

Embodiment 3

[0136] This method comprises the steps:

[0137] (1) Generate a key. Further include the following steps:

[0138] (1-1) Construct a k×n-dimensional full-rank matrix A in an iterative manner. Further include the following steps:

[0139] (1-1-1) Determine k=2, n=4.

[0140] (1-1-2) Select the finite field Z, and 2 integer numbers p in the finite field Z 1 = 3,p 2 =7.

[0141] (1-1-3) Select the following integers on the finite field Z: β 11 =28,β 12 =10,β 21 =345,β 22 =52,x 1 =5,x 2 =9. Order a 11 = β 11 p 1 =84, a 21 = β 21 p 2 =2415, a 22 = β 22 p 2 2 = 2548 .

[0142] (1-1-4) Construction matrix A=(a ij ), wherein, i=1,2, j=1,...,4, when j>2, a ij = x i p i 2 ...

technical field

[0001] The invention belongs to the technical field of information security, and more specifically relates to a multivariate public key encryption method. Background technique

[0002] With the continuous development of computers and networks, people have higher and higher requirements for information integrity and security. Therefore, cryptography came into being. Due to its different encryption key and decryption key, public key cryptography has become a key means to solve some security problems of network security and information security. However, with the continuous development of information technology, people have higher and higher requirements for the performance of the system, not only the integrity and security of information, but also the simplicity and speed of the process of transmitting information.

[0003] At present, the key management and transmission process of mainstream symmetric cryptography is relatively complicated, and the calculatio...

Examples

Embodiment 1

[0067] The random parameter ε is obtained through the decryption method, and the method includes the following steps:

[0068] (1) Generate a key. Further include the following steps:

[0069] (1-1) Construct a k×n-dimensional full-rank matrix A in an iterative manner. Further include the following steps:

[0070] (1-1-1) Determine k=2.

[0071] (1-1-2) Select finite field Z, and 2 integers p in finite field Z 1 ,p 2 .

[0072] (1-1-3) Select the following integers on the finite field Z: (β 11 ,β 12 ), (β 21 ,β 22 ) and (x 1 ,x 2 ). Order a 11 = β 11 p 1 , a 12 = β 12 p 1 2 , a 21 = β 21 p 2 , a 22 = β 22 p 2 2 .

[0073] (1-1-4) Construction matrix A=(a ij ), wherein,...

Embodiment 2

[0102] The random parameter ε is obtained through a synchronous method. This method includes the following steps:

[0103] (1) Generate a key. Further include the following steps:

[0104] (1-1) Construct a k×n-dimensional full-rank matrix A in an iterative manner. Further include the following steps:

[0105] (1-1-1) Determine k=2.

[0106] (1-1-2) Select finite field Z, and 2 integers p in finite field Z 1 ,p 2 .

[0107] (1-1-3) Select the following integers on the finite field Z: (β 11 ,β 12 ), (β 21 ,β 22 ) and (x 1 ,x 2 ). Order a 11 = β 11 ,a 12 = β 12 p 1 ,a 21 = β 21 ,a 22 = β 22 p 2 .

[0108] (1-1-4) Construction matrix A=(a ij ), wherein, when i=1,2, j=1,...,n, j>2, a ij = x i p i 2 a i ( j - 2 ...

Embodiment 3

[0136] This method comprises the steps:

[0137] (1) Generate a key. Further include the following steps:

[0138] (1-1) Construct a k×n-dimensional full-rank matrix A in an iterative manner. Further include the following steps:

[0139] (1-1-1) Determine k=2, n=4.

[0140] (1-1-2) Select the finite field Z, and 2 integer numbers p in the finite field Z 1 = 3,p 2 =7.

[0141] (1-1-3) Select the following integers on the finite field Z: β 11 =28,β 12 =10,β 21 =345,β 22 =52,x 1 =5,x 2 =9. Order a 11 = β 11 p 1 =84, a 21 = β 21 p 2 =2415, a 22 = β 22 p 2 2 = 2548 .

[0142] (1-1-4) Construction matrix A=(a ij ), wherein, i=1,2, j=1,...,4, when j>2, a ij = x i p i 2 ...

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