Symmetric Encryption and Decryption Method Based on Exponential Complexity

Abstract

The present invention discloses a symmetric encryption and decryption method based on exponential complexity, belonging to the field of information technology, and comprising the following steps: Step 1, determining a basic code table and making it public; Step 2, performing digital encoding on the information plaintext to obtain a digital plaintext; Step 3, encrypting the digital plaintext by using a symmetric encryption method based on exponential complexity to obtain an information ciphertext; Step 4, information transmission; Step 5, decrypting the information ciphertext by using a symmetric decryption method based on exponential complexity to generate a random hidden text; Step 6, decrypting the random hidden text according to the corresponding relationship to obtain a digital plaintext; Step 7, decoding the digital plaintext to obtain the information plaintext. The present invention satisfies exponential-level security while having a low ciphertext expansion rate, and can achieve efficient encryption and decryption.

Description

Technical Field

[0001] The present invention is a symmetric encryption and decryption method based on exponential complexity, belonging to the field of information security technology, and relates to the improvement of symmetric encryption and decryption methods. Background Art

[0002] With the development of Internet technology, information security is involved in all aspects of people's lives. More and more fields such as mobile payment, social software, and personal information query have higher and higher requirements for information security.

[0003] In the field of information security technology, information encryption is a core of information security. The cryptographic schemes in modern cryptography are all based on computational complexity assumptions of various degrees, generally assumed to be NP-hard. Many commercial schemes, such as DES, RSA, ECC, Elgamal, etc., assume that the corresponding cryptographic attacks are complex problems. However, these assumptions do not have a strict proof. Worse still, quantum algorithms have now been found that can factorize any integer in polynomial time. Therefore, designing encryption schemes based on problems with definite exponential complexity has important theoretical and practical application values.

[0004] The symmetric cryptoscheme based on exponential complexity proposed in the present invention application is based on a strict exponential complexity problem, and both the encryption and decryption processes are very efficient. Therefore, it can be widely applied to many technical fields such as information communication security and computer network security. Summary of the Invention

[0005] The purpose of the present invention is to provide a symmetric cryptography method with high efficiency and strict theoretical guarantee to provide technical support for ensuring the security of information communication. This technology fully develops a set of efficient key generation technologies to ensure that cryptographic attacks are an exponential problem.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A symmetric encryption and decryption method based on exponential complexity, characterized in that it comprises the following steps:

[0008] Step 1: Determine the basic code table according to the information content to be transmitted and make it public;

[0009] Step 2: The sender inputs the information plaintext on the encoding device, and the encoding device encodes the information plaintext corresponding to the basic code table into a digital plaintext;

[0010] Step 3: The encryption device uses a symmetric encryption method based on exponential complexity to generate a random key, a seed key, a random recursive function, and its corresponding starting key, and then encrypts the digital plaintext to obtain an information ciphertext;

[0011] Step 4: The information network device makes the encrypted information public through a public channel, and transmits the random key, the seed key, the random recursive function, and its corresponding starting key to the decryption device through a secure channel;

[0012] Step 5: The decryption device decrypts the encrypted information using a symmetric decryption method based on exponential complexity to generate random hidden text;

[0013] Step 6: The decryption device decrypts the digital plaintext corresponding to the random hidden text using the random key according to the correspondence between the random hidden text and the digital plaintext;

[0014] Step 7: The decoding device decodes the digital plaintext into information plaintext and displays the information plaintext content to the recipient through the output end.

[0015] Furthermore, the basic code table described in Step 1 is determined by any one or both of the recipient or the sender, or a third party as needed, and is a one-to-one correspondence between the set of basic elements of the information content and the integer interval. Once determined, it is fixed; among them, the number of basic elements of the information content is K, and the integer interval is [0, K - 1].

[0016] Furthermore, the symmetric encryption method based on exponential complexity described in Step 3 is specifically as follows: (1) Group the digital plaintext; (2) Randomly select a finite field, and on this finite field, select a random key to randomly encrypt each group of the digital plaintext to obtain the random hidden text of the new group; (3) Randomly select a polynomial matrix as the seed key M(x) on the said finite field, and randomly select a recursive function σ and its corresponding starting key Uσ based on the number of groups t (t) , and encrypt the random hidden text using the seed key and the starting key to obtain the encrypted information.

[0017] Even further, the specific operation of grouping the digital plaintext described in step (1) is as follows: For the digital plaintext V, in sequence, randomly take a fixed length L and divide it into t groups, where the grouping result is V = {V j |j = 1, 2, …, t}, where V j =(v j,1 , v j,2 , …, v j,L ), v j,i is the i-th corresponding single digital plaintext element in the j-th group; if the length of the last group is insufficient, fix a method to add redundancy to make its length L.

[0018] Even further, the number of elements q of the said finite field F q = p k , where p is a randomly selected prime number, integer k ≥ λ, and λ is based on the artificially set number of adversary attacks 2 λTo be determined.

[0019] Furthermore, step (2) is specifically as follows: Select a random key s=(s1,…,s L ,θ,c) on a finite field. For each plaintext block V j , randomly generate a block random key u j =(u j,1 ,u j,2 ,…,u j,c ) with a length of c, satisfying 0≤u j,i ≤q, 0≤i≤c. Use the hash function H θ with θ as the key to act on the vector (s,u j ) to obtain the block random encryption key H j (s,u θ ). Encrypt V j with H θ (s,u j ) to obtain the random ciphertext U j =(V j +H j (s,u θ ),u j ), where the elements of (s1,…,s j ) are respectively an element on the finite field, θ is the key value of a hash function H L that maps from an L + c - dimensional finite field to an L - dimensional finite field (i.e., F q L+c →F q L ), and c is an integer greater than or equal to 1.

[0020] Furthermore, the seed key M(x) is the product of 2(L + c) random triangular polynomial matrices, where there are L + c upper triangular polynomial matrices and L + c lower triangular polynomial matrices respectively; the diagonals of the upper triangular polynomial matrix and the lower triangular polynomial matrix are non - zero elements on the algebraic field F θ q , and the non - diagonal elements of the non - zero elements are sparse polynomials; the sparse polynomials are obtained by sampling without replacement from a sparse polynomial set; the sparse polynomial set is recursively constructed according to the following steps: (a) Randomly select K elements from the set {1,2,…,q} to form a new set m={m k |k = 1,2,…,N}, where N is the ceiling of q / 2; (b) Randomly select a corresponding m q for each element m k of the set m on the finite field F k ​The monomials of degree are summed up to construct a polynomial; (c) If the polynomial generated in step (b) is not in the sparse polynomial set, put this polynomial into the sparse polynomial set, otherwise return to step (b); (d) Repeat steps (a) - (c) until the number of elements in the sparse polynomial set is (L + c) 3 until it reaches

[0021] Furthermore, the recursive function σ is a one-to-one mapping function randomly selected from the set {1, 2,..., t} to itself; the initial key Uσ (t) is the random ciphertext corresponding to the σ(t)-th group.

[0022] Furthermore, the encrypted random ciphertext is specifically: First, starting from the first new group, use the seed key M(x) and the initial key Uσ (t) to calculate the information key Xσ (1) = M(Uσ (t) ), and the information ciphertext corresponding to the first new group is Cσ (1) = Xσ (1) ·Uσ (1) ; Then, for the other new groups where 1 < n ≤ t in turn, their corresponding information keys Xσ (n) = M(Uσ (n-1) ) and their corresponding information ciphertexts Cσ (n) = Xσ (n) ·Uσ (n) .

[0023] Further, the symmetric decryption method based on exponential complexity in step five is specifically: (1) Use the seed key M(x) and the initial key Uσ (t) to calculate the random ciphertext Uσ (1) corresponding to the information ciphertext Cσ (1) = M -1 (Uσ (t) )·Cσ (1) ; (2) For the other new groups where 1 < n ≤ t in turn, decrypt the random ciphertext Uσ (n) corresponding to the information ciphertext Cσ (n) = M -1 (Uσ (n-1) )·Cσ (n) in a recursive manner.

[0024] Further, the correspondence between the random ciphertext and the digital plaintext in step six is V j = U j [1:L] - H θ (s, U j[L+1:L+c]), where 1:L represents the elements in the vector in sequence from 1 to L.

[0025] Furthermore, the encoding device is a computer device integrating a data information collector and a processor loaded with a basic code table; the encryption device is a computer device connected to the encoding device and the information network device, integrating an output port and a processor, and loaded with a symmetric encryption method based on exponential complexity; the information network device is a computer device integrating an output port and a processor for converting the information ciphertext into a standard encrypted signal; the decryption device is a computer device connected to the decoding device and the information network device, integrating an output port and a processor, and loaded with a symmetric encryption method based on exponential complexity; the decoding device is a computer device integrating an output port and a processor loaded with a basic code table; the public channel is an open network channel; the secure channel is a secure and private network channel set by the dominant party or both parties among the recipient or the sender.

[0026] Furthermore, the data information collector is usually a camera, various keyboards (including smartphone screen input keyboards, ATM buttons, etc.), microphones, etc.; the information content to be transmitted is usually data such as user passwords and chat records.

[0027] The beneficial effects of the present invention: By using the technology of using a random polynomial matrix as a seed key and random hidden text to generate a random key for encrypting plaintext, the seed key attack problem is converted into a problem of solving polynomial reduction, and the password security is established on an exponentially difficult problem. While meeting the security requirements, the ciphertext expansion rate is also relatively low, and efficient encryption and decryption can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to make the objectives, technical solutions, and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0029] Figure 1 It is a flowchart of the symmetric encryption and decryption method based on exponential complexity in an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0030] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0031] It should be noted that the illustrations provided in the following embodiments only schematically illustrate the basic concept of the present invention. Therefore, only the components related to the present invention are shown in the drawings, rather than being drawn according to the number, shape, and size of the components in actual implementation. The types, quantities, and proportions of the components in actual implementation can be arbitrarily changed, and the component layout type may also be more complex.

[0032] In the process of information transmission, for the sake of confidentiality, we need to encrypt the information to be transmitted; then, the ciphertext is transmitted to the target recipient through an economical and fast channel. At the same time, the password corresponding to the ciphertext needs to be transmitted to the information recipient in a certain confidential manner; the information recipient uses the password to decrypt the ciphertext to obtain the information.

[0033] Embodiment 1: In this embodiment, assume that a user (sender) of a certain chat software sends a message to a friend (recipient) through a smartphone loaded with the software. For the convenience of demonstrating the method of the present invention, assume that the content of the sent message is "Hello".

[0034] As Figure 1 shown, the symmetric encryption and decryption method based on exponential complexity in this embodiment includes:

[0035] S1: Determine the basic code table according to the information content to be transmitted and make it public;

[0036] S2: The sender inputs the plaintext of the information on the input keyboard of the smartphone, and the encoding device encodes the plaintext of the information into digital plaintext corresponding to the basic code table;

[0037] S3: The smartphone of the sender uses the symmetric encryption method based on exponential complexity to generate a random key, a seed key, a random recursive function, and its corresponding starting key, and then encrypts the digital plaintext to obtain the information ciphertext;

[0038] S4: The communication module of the sender's smartphone publicly transmits the information ciphertext through a public channel via a wireless network / mobile network, and transmits the random key, the seed key, the random recursive function, and its corresponding starting key to the smartphone of the recipient through a secure channel;

[0039] S5: The smartphone of the recipient uses the symmetric decryption method based on exponential complexity to decrypt the information ciphertext and generate a random hidden text;

[0040] S6: The smartphone of the recipient decrypts the digital plaintext corresponding to the random hidden text using the random key according to the correspondence between the random hidden text and the digital plaintext;

[0041] S7: The smartphone of the recipient decodes the digital plaintext into the plaintext of the information using a decoding algorithm and displays the content of the plaintext of the information to the recipient through the display screen.

[0042] In step S1:

[0043] The official of the chat software uses the English letter numbers corresponding to the pinyin letters as the information to be transmitted. It can be determined that the basic alphabet is the 27-letter alphabet of ∑ = a, b, c, …, z, *, and the elements of this alphabet are used to form the information plaintext through permutation and combination, where * is the grouping redundancy supplement character. According to the number of elements 27 in the basic alphabet, the integer interval is determined as [0, 26], and each letter in Σ is mapped to this integer interval one by one for alphabet digital encoding: "a → 0, b → 1, …, z → 25, * → 26".

[0044] In step S2:

[0045] The sender inputs the information plaintext "Hello" into the chat software on the smartphone input keyboard and clicks send. The encoding program of the chat software running on the smartphone encodes the information plaintext to obtain the digital plaintext V = "13 8 7 014".

[0046] In step S3:

[0047] The symmetric encryption method based on exponential complexity is specifically as follows: S301 groups the digital plaintext; S302 randomly selects a finite field, and on this finite field, a random key is selected to randomly encrypt each group of the digital plaintext to obtain the random hidden text of the new group; S303 randomly selects a polynomial matrix as the seed key M(x) on the said finite field, and randomly selects a recursive function σ and its corresponding starting key Uσ (t) , and uses the seed key and the starting key to encrypt the random hidden text to obtain the information ciphertext.

[0048] Assumed number of adversary attacks 2 100 , randomly select a finite field F q , the number of its elements q = 3 100 .

[0049] The seed key M(x) is the product of 2(L + c) random triangular polynomial matrices, where there are L + c upper triangular polynomial matrices and L + c lower triangular polynomial matrices respectively; the diagonals of the said upper triangular polynomial matrix and lower triangular polynomial matrix are non-zero elements in the algebraic field F q The non-diagonal elements of the non-zero elements are sparse polynomials; the sparse polynomials are obtained by drawing without replacement from the sparse polynomial set; the sparse polynomial set is recursively constructed according to the following steps: (a) randomly select K elements in the set {1, 2, …, q} to form a new set m = {m k |k = 1, 2, …, N}, where N is the ceiling of q / 2; (b) in the finite field F qRandomly for each element \(m\) of the set \(m\) k Select a corresponding \(m\) k Degree monomials for \(N\) times, and sum these \(N\) monomials to construct a polynomial; (c) If the polynomial generated in step (b) is not in the sparse polynomial set, put this polynomial into the sparse polynomial set, otherwise return to step (b); (d) Repeat steps (a) - (c) until the number of elements in the sparse polynomial set is \((L + c)\) 3 Until it reaches this number.

[0050] The recursive function \(\sigma\) is a one - to - one mapping function randomly selected from the set \(\{1,2,\cdots,t\}\) to itself; the starting key \(U_{\sigma}\) (t) Is the random ciphertext corresponding to the \(\sigma(t)\) - th group.

[0051] S301: For the digital plaintext \(V\) in sequence, considering the computational complexity and readability of the embodiment, in this embodiment, a fixed length \(L = 3\) is selected and divided into \(t = 2\) groups, \(V=\{V\) j |j = 1,2\}=\{(13\ 8\ 7),(0\ 14\ 26)\}. If the number of digits in the last block is different from the previous ones, the grouping redundancy supplementary character '*' must be added, that is, the last block becomes \((0\ 14\ 26)\).

[0052] S302: Select a random key \(s=(1,2,3,\theta,c)\) in the finite field. For each plaintext group \(V\) j Randomly generate a group random key \(u\) with a length \(c = 2\) j =(1,2), satisfying \(0\leq u\) j,i \leq q\), \(0\leq i\leq c\). Use the hash function \(H\) with \(\theta = 2\) as the key θ Act on the vector \((s,u\) j ) to obtain the group \(V\) j Random encryption key \(H\) θ (s,u\) j ). Encrypt \(V\) θ (s,u\) j ) to obtain the random ciphertext \(U\) of this group j =(V\) j +H\) j (s,u\) θ ),u\) j ), where the elements of \((s_1,\cdots,s\) j ) are respectively an element in the finite field, \(\theta\) is a mapping from the \((L + c)\) - dimensional finite field to the \(L\) - dimensional finite field (i.e., \(F\) L \to F\) q L+c \to F\) q L ) and the hash function \(H\) θThe key value, where c is an integer greater than or equal to 1.

[0053] S303: The encrypted random hidden text is specifically as follows: First, at the start of the first new group, use the seed key M(x) and the starting key Uσ (t) Calculate the information key Xσ corresponding to the first new group (1) = M(Uσ (t) ), and the information ciphertext corresponding to the first new group is Cσ (1) = Xσ (1) ·Uσ (1) ; Then, for the other new groups where 1 < n ≤ t, calculate their corresponding information keys Xσ (n) = M(Uσ (n-1) ) and their corresponding information ciphertexts Cσ (n) = Xσ (n) ·Uσ (n) .

[0054] In step S5:

[0055] The symmetric decryption method based on exponential complexity is specifically as follows: (1) Use the seed key M(x) and the starting key Uσ (t) Calculate the random hidden text Uσ corresponding to the information ciphertext Cσ of the first new group (1) = M (1) (Uσ -1 )·Cσ (t) ; (2) For the other new groups where 1 < n ≤ t, decrypt the random hidden text Uσ corresponding to the information ciphertext Cσ of the nth new group in a recursive manner (1) = M (n) (Uσ (n) )·Cσ -1 (Uσ (n-1) )·Cσ (n) .

[0056] In step S6:

[0057] The corresponding relationship between the random hidden text and the digital plaintext is V j = U j [1:L] - H θ (s, U j [L + 1:L + c]), where 1:L represents the elements in the vector from 1 to L in sequence.

[0058] The above embodiments are only illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Any person familiar with this technology can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes made by those with ordinary knowledge in the technical field without departing from the spirit and technical idea disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. A symmetric encryption and decryption method based on exponential complexity, characterized in that It includes the following steps: Step 1: Determine and disclose the basic code table according to the information content to be transmitted; Step 2: The sender inputs the plaintext information on the encoding device, and the encoding device encodes the plaintext information corresponding to the basic code table into digital plaintext; Step 3: The encryption device uses a symmetric encryption method based on exponential complexity to generate a random key, a seed key, a random recursive function, and its corresponding starting key, and then encrypts the digital plaintext to obtain the encrypted information; The symmetric encryption method based on exponential complexity described in Step 3 is specifically as follows: (1) Group the digital plaintext; (2) Randomly select a finite field, and on this finite field, select a random key to perform randomized encryption on each group of the digital plaintext to obtain the random hidden text of the new group; (3) Randomly select a polynomial matrix as the seed key M(x) on the said finite field, and randomly select a recursive function σ and its corresponding starting key Uσ based on the number of groups t (t) , and use the seed key and the starting key to encrypt the random hidden text to obtain the information ciphertext; The recursive function σ is a one-to-one mapping function randomly selected from the set {1, 2, ..., t} to itself; the starting key Uσ (t) is the random hidden text corresponding to the σ(t)-th block; The encrypted random hidden text is specifically as follows: First, when the first new group starts, the information key Xσ corresponding to the first new group is calculated using the seed key M(x) and the starting key Uσ (t) = M(Uσ (1) ), and the information ciphertext Cσ corresponding to the first new group is (t) = Xσ (1) · Uσ (1) ; Then, for the other new groups where 1 < n ≤ t, the information keys Xσ (1) corresponding to them are calculated respectively as (n) = M(Uσ (n-1) ), and their corresponding information ciphertexts Cσ (n) = Xσ (n) · Uσ (n) ; Step 4: The information network device makes the encrypted information public through a public channel, and transmits the random key, the seed key, the random recursive function, and its corresponding starting key to the decryption device through a secure channel; Step 5: The decryption device decrypts the encrypted information using a symmetric decryption method based on exponential complexity to generate random hidden text; Step 6: The decryption device decrypts the digital plaintext corresponding to the random hidden text using the random key according to the correspondence between the random hidden text and the digital plaintext; Step 7: The decoding device decodes the digital plaintext into plaintext information and displays the plaintext information content to the receiver through the output end.

2. The symmetric encryption and decryption method based on exponential complexity according to claim 1, wherein The basic code table described in Step 1 is determined by any one or both of the receiver and the sender, or a third party according to needs, and is a one-to-one correspondence between the set of basic elements of the information content and the integer interval. Once determined, it is fixed. Among them, the number of basic elements of the information content is K, and the integer interval is [0, K-1].

3. According to step (1) described in claim 1, it is characterized in that The specific grouping of the digital plaintext in step (1) is as follows: The digital plaintext V is taken in a random order with a fixed length L in sequence and divided into t groups, where the grouping result is V = {V j | j = 1, 2, …, t}, where V j = (v j,1 , v j,2 , …, v j,L ), and v j,i is the i-th corresponding single digital plaintext element in the j-th group; if the length of the last group is insufficient, a redundant part is added in a fixed way to make its length L.

4. A randomly selected finite field according to claim 1, wherein The finite field F q has an element number q = p k , where p is a random prime number, integer k ≥ λ, and λ is determined according to the number of adversary attacks 2 λ set by humans.

5. According to step (2) as claimed in claim 4, wherein Step (2) is as follows: select a random key s=(s1, …, s L , θ, c), for each plaintext group V j A random group key u of length c is randomly generated j =(u j,1 , u j,2 , …, u j,c ), satisfying 0≤u j,i ≤q, 0≤i≤c, using the hash function H with θ as the key θ Acting on the vector (s, u j ) on the scoring group V j Random encryption key H θ (s, u j ), use H θ (s, u j ) Encryption V j Get the random hidden text U of the group j =(V j +H θ (s, u j ), u j ), where (s1, …, s L ) is an element on the finite field, and θ is a mapping from the L+c-dimensional finite field to the L-dimensional finite field. The hash function H θ The key value of c is an integer greater than or equal to 1.

6. According to step (3) described in claim 5, it is characterized in that The seed key M(x) is the product of 2(L + c) random triangular polynomial matrices, including L + c upper triangular polynomial matrices and L + c lower triangular polynomial matrices respectively; the diagonals of the upper triangular polynomial matrices and the lower triangular polynomial matrices are non-zero elements in the algebraic field F q . The non-diagonal elements of the non-zero elements are sparse polynomials; the sparse polynomials are obtained by drawing without replacement from a set of sparse polynomials. The set of sparse polynomials is recursively constructed according to the following steps: (a) Randomly select K elements from the set {1, 2, …, q} to form a new set m = {m k |k = 1, 2, …, N}, where N is the ceiling of q / 2; (b) Randomly select a monomial of degree m q corresponding to each element m k of the set m in the finite field F k , and sum these N monomials to construct a polynomial; (c) If the polynomial generated in step (b) is not in the set of sparse polynomials, put this polynomial into the set of sparse polynomials, otherwise return to step (b); (d) Repeat steps (a) - (c) until the number of elements in the set of sparse polynomials is (L + c) 3 .

7. The symmetric encryption and decryption method based on exponential complexity according to claim 1, wherein The symmetric decryption method based on exponential complexity described in Step Five is specifically as follows: (1) Use the seed key M(x) and the starting key Uσ (t) to calculate the ciphertext Cσ of the first new packet information (1) and the corresponding random hidden text Uσ (1) = M -1 (Uσ (t) ) · Cσ (1) ; (2) For the other new packets where 1 < n ≤ t, decrypt the ciphertext Cσ of the nth new packet information in a recursive manner (n) and the corresponding random hidden text Uσ (n) = M -1 (Uσ (n-1) ) · Cσ (n) .

8. The symmetric encryption and decryption method based on exponential complexity according to claim 1, characterized in that, The encoding device is a computer device integrating a data information collector and a processor loaded with the basic code table; the encryption device is a computer device connected to the encoding device and the information network device, integrating an output port and a processor, and loaded with a symmetric encryption method based on exponential complexity; the information network device is a computer device integrating an output port and a processor, which converts the encrypted information into a standard encrypted signal; the decryption device is a computer device connected to the decoding device and the information network device, integrating an output port and a processor, and loaded with a symmetric decryption method based on exponential complexity; the decoding device is a computer device integrating an output port and a processor loaded with the basic code table; the public channel is an open network channel; the secure channel is a secure and private network channel set by the dominant party or both of the receiver and the sender.

Images