Symmetric quantum-resistant encryption method based on key encapsulation technology

Abstract

The present invention relates to a symmetric quantum-resistant encryption method based on key encapsulation technology, which is used for transmitting data between a sending client terminal and a receiving client terminal, and includes the following steps: step S1, a public parameter generation step; step S2, an encryption step; step S3, a sending step; step S4, a receiving step; and step S5, a decryption step. The present invention can be combined with quantum key distribution or a public key encryption algorithm with quantum resistance to form a quantum-resistant encryption system, which can efficiently encrypt data, and the generated ciphertext is much shorter than the key generated by the common quantum-resistant encryption algorithm, and has great advantages in speed and storage efficiency; at the same time, it can be combined with the existing encryption system, with high encryption efficiency and less ciphertext expansion, and has good application prospects.

Description

Technical Field

[0001] The present invention belongs to the technical field of data security, and in particular relates to a symmetric quantum-resistant encryption method based on key encapsulation technology. Background Art

[0002] The field of quantum-resistant encryption algorithms is a new field in cryptography. Unlike quantum cryptography, post-quantum cryptography uses existing electronic computers and does not rely on quantum mechanics. It relies on computational problems that cryptographers believe cannot be effectively solved by quantum computers.

[0003] The current mainstream construction method is to use lattice cryptography to construct quantum-resistant cryptography. However, quantum-resistant encryption based on lattice cryptography has the following disadvantages:

[0004] (1) Low efficiency: Traditional quantum-resistant encryption is based on lattice cryptography, which involves a large number of matrix operations and is encrypted bit by bit. This results in high algorithm execution time complexity, making it difficult to use in actual engineering. In addition, it violates the requirements of the hybrid encryption system and uses a public key encryption algorithm to act directly on data.

[0005] (2) Ciphertext expansion: The ciphertext produced by quantum-resistant encryption algorithms on lattices is multiple large matrices, while the input plaintext is bits. This will increase the storage space occupied by the data by thousands of times, seriously reducing storage efficiency. Summary of the invention

[0006] The present invention is made to solve the above-mentioned problem, and its purpose is to provide a symmetric quantum-resistant encryption method based on key encapsulation technology.

[0007] In order to achieve the above object, the present invention adopts the following scheme:

[0008] The present invention provides a symmetric quantum-resistant encryption method based on key encapsulation technology, which is used to transmit data between a sending client terminal and a receiving client terminal, and has the following characteristics, including the following steps:

[0009] Step S1, public parameter generation step, input security parameter λ, and generate public-private key pair pk according to the security parameter λ f ,sk f ;

[0010] Step S2, encryption step, encrypts a data m to be encrypted to obtain a ciphertext (c1, c2, c 3,1 ,c 3,2 ), is implemented according to the following process:

[0011] First, randomly select two large prime numbers p and q, with |p|=|q|=λ; let N=pq, generate random numbers r1 and r2, is a simplified remainder class modulo N; select hash function H0:{0,1} * →{0,1} 2λ ;

[0012] Secondly, calculate d1 and d2 according to the following formula:

[0013] d1p≡1 modφ(N)

[0014] d2q≡1 modφ(N)

[0015] Where φ(N) is the Euler function of N;

[0016] Then, calculate the inverse of r1 and r2,

[0017] r1 -1 r1≡1 mod p

[0018] r2 -1 r2≡1 mod q

[0019] Finally, the data m is encrypted according to the following formula to obtain the ciphertext (c1, c2, c 3,1 ,c 3,2 ),

[0020]

[0021]

[0022]

[0023]

[0024] Where, d = p||q;

[0025] Step S3, sending step, the ciphertext (c1, c2, c 3,1 ,c 3,2 ) is sent to the receiving client terminal;

[0026] Step S4, receiving step, receiving the ciphertext (c1, c2, c 3,1 ,c 3,2 );

[0027] Step S5, decryption step, decrypt the ciphertext (c1, c2, c 3,1 ,c 3,2 ) is decrypted to obtain the plaintext m, which is achieved according to the following process:

[0028] First, we need to get p and q:

[0029]

[0030]

[0031] By performing bit splitting on d, we can obtain p and q;

[0032] Secondly, we can invert p and q respectively to get:

[0033] q -1 q≡1 mod p

[0034] p -1 p≡1 mod q

[0035] Then, calculate M according to the following formula: p 、M q ,

[0036] M p =c1 mod p

[0037] M q =c2 mod q

[0038] Finally, the Chinese remainder theorem gives:

[0039]

[0040] In the symmetric quantum-resistant encryption method based on the key encapsulation technology of the present invention, it can also have the following characteristics: wherein the public-private key pair is a public-private key pair based on a one-way trapdoor function.

[0041] In the symmetric quantum-resistant encryption method based on the key encapsulation technology of the present invention, it can also have the following characteristics: wherein, φ(N)=(p-1)(q-1).

[0042] Compared with the prior art, the advantages of the present invention are: the present invention can be combined with quantum key distribution or a public key encryption algorithm with quantum resistance to form a quantum-resistant encryption system, which can efficiently encrypt data, and the generated ciphertext is much shorter than the key generated by the common quantum-resistant encryption algorithm, and has great advantages in speed and storage efficiency; at the same time, it can be combined with the existing encryption system, with high encryption efficiency and less ciphertext expansion, and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of a symmetric quantum-resistant encryption method based on key encapsulation technology in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the symmetric anti-quantum encryption method based on key encapsulation technology of the present invention is specifically described below in combination with embodiments and drawings.

[0045] <Example>

[0046] Figure 1 It is a flow chart of a symmetric quantum-resistant encryption method based on key encapsulation technology in an embodiment of the present invention.

[0047] like Figure 1 As shown, in this embodiment, a symmetric quantum-resistant encryption method based on key encapsulation technology is used to transmit data between a sending client terminal and a receiving client terminal, including the following steps:

[0048] Step S1, public parameter generation step, input security parameter λ, and generate public-private key pair pk according to the security parameter λ f ,sk f .

[0049] In this embodiment, the public-private key pair pk f ,sk f It is a public-private key pair based on a one-way trapdoor function.

[0050] Step S2, encryption step, encrypts a data m to be encrypted to obtain a ciphertext (c1, c2, c 3,1 ,c 3,2 ).

[0051] In this embodiment, the encryption step is implemented according to the following process:

[0052] First, randomly select two large prime numbers p and q, with |p|=|q|=λ; let N=pq, generate random numbers r1 and r2, is a simplified remainder class modulo N; select hash function H0:{0,1} * →{0,1} 2λ ;

[0053] Secondly, calculate d1 and d2 according to the following formula:

[0054] d1p≡1 modφ(N)

[0055] d2q≡1 modφ(N)

[0056] Wherein, φ(N) is the Euler function of N. In this embodiment, φ(N)=(p-1)(q-1);

[0057] Then, calculate the inverse of r1 and r2,

[0058] r1 -1 r1≡1 mod p

[0059] r2 -1 r2≡1 mod q

[0060] Finally, the data m is encrypted according to the following formula to obtain the ciphertext (c1, c2, c 3,1 ,c 3,2 ),

[0061]

[0062]

[0063]

[0064]

[0065] Where, d = p||q;

[0066] Step S3, sending step, the ciphertext (c1, c2, c 3,1 ,c 3,2 ) is sent to the receiving client terminal.

[0067] Step S4, receiving step, receiving the ciphertext (c1, c2, c 3,1 ,c 3,2 ).

[0068] Step S5, decryption step, decrypt the ciphertext (c1, c2, c 3,1 ,c 3,2 ) is decrypted to obtain the plaintext m.

[0069] In this embodiment, the decryption step is implemented according to the following process:

[0070] First, we need to get p and q:

[0071]

[0072]

[0073] By performing bit splitting on d, we can obtain p and q;

[0074] Secondly, we can invert p and q respectively to get:

[0075] q -1 q≡1 mod p

[0076] p -1 p≡1 mod q

[0077] Then, calculate M according to the following formula: p 、M q ,

[0078] M p =c1 mod p

[0079] M q =c2 mod q

[0080] Finally, the Chinese remainder theorem gives:

[0081]

[0082] The above-mentioned embodiments are preferred examples of the present invention and are not intended to limit the protection scope of the present invention.

Claims

1. A symmetric quantum-resistant encryption method based on key encapsulation technology for transmitting data between a sending client terminal and a receiving client terminal, characterized in that: The following steps are involved: Step S1, public parameter generation step, input security parameter λ, and generate public-private key pair pk according to the security parameter λ f ,sk f ; Step S2, encryption step, encrypts a data m to be encrypted to obtain a ciphertext (c1, c2, c 3,1 ,c 3,2 ), is implemented according to the following process: First, randomly select two large prime numbers p and q, with |p|=|q|=λ; let N=pq, generate random numbers r1 and r2, is a simplified remainder class modulo N; select hash function H0:{0,1} * →{0,1} 2λ ; Secondly, calculate d1 and d2 according to the following formula: d1p≡1 mod φ(N) d2q≡1 mod φ(N) Where φ(N) is the Euler function of N; Then, calculate the inverse of r1 and r2, r1 -1 r1≡1 vs p r2 -1 r2≡1 mod q Finally, the data m is encrypted according to the following formula to obtain the ciphertext (c1, c2, c 3,1 ,c 3,2 ), Where, d = p||q; Step S3, sending step, the ciphertext (c1, c2, c 3,1 ,c 3,2 ) is sent to the receiving client terminal; Step S4, receiving step, receiving the ciphertext (c1, c2, c 3,1 ,c 3,2 ); Step S5, decryption step, decrypting the ciphertext (c1, c2, c 3,1 ,c 3,2 ) is decrypted to obtain the plaintext m, which is achieved according to the following process: First, we need to get p and q: By performing bit splitting on d, we can obtain p and q; Secondly, we can invert p and q respectively to get: q -1 q≡1 mod p p -1 p≡1 mod q Then, calculate M according to the following formula: p 、M q , M p =c1 mod p M q =c2 mod q Finally, the Chinese remainder theorem gives:

2. The symmetric quantum-resistant encryption method based on key encapsulation technology according to claim 1, characterized in that: in, The public-private key pair is a public-private key pair based on a one-way trapdoor function.

3. The symmetric quantum-resistant encryption method based on key encapsulation technology according to claim 1, characterized in that: in, The φ(N)=(p-1)(q-1).

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