Method for constructing first-order elastic five-spectrum value function based on disjoint linear codes
By constructing a first-order elastic five-spectral value function based on the direct construction method of disjoint linear codes, the problems of high construction complexity and insufficient elasticity in the existing technology are solved, and an efficient and secure plaintext encryption method is realized.
Patent Information
- Application Number
- CN202511764916.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-27
- Publication Date
- 2026-02-27
AI Technical Summary
Most existing methods for constructing five-spectral-valued functions are indirect methods, which are computationally expensive and complex to implement. They cannot effectively achieve a good trade-off between nonlinearity and elasticity, and the constructed functions can only achieve equilibrium but cannot satisfy elasticity.
A direct construction method based on disjoint linear codes is adopted. By setting parameters and generating disjoint linear codes, the space is divided, the support set is defined, and a first-order elastic quinary value function is constructed. This function is then used to generate a key sequence for plaintext encryption.
It reduces construction complexity and computational cost, improves construction efficiency, and the constructed function has near-optimal nonlinearity and a certain degree of elasticity, which can effectively resist various attacks and improve the security and computational efficiency of the cryptographic system.
Smart Images
Figure CN121585368A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of cryptography technology, specifically relating to a method for constructing a first-order elastic pentspectral value function based on disjoint linear codes. Background Technology
[0002] Symmetric cryptosystems are divided into stream ciphers and block ciphers. The Boolean function is the core component of a stream cipher system, and its properties directly determine the security of the system. A well-designed Boolean function needs to possess certain essential properties, primarily including high nonlinearity and elasticity. High nonlinearity ensures the cryptosystem's resistance to optimal affine approximation attacks and linear attacks, while elasticity reflects its ability to resist fast correlation attacks. The first-order elastic pentspectral value function possesses almost optimal nonlinearity and first-order elasticity, making it directly applicable to stream cipher systems and thus enhancing their security. Therefore, theoretical research on constructing the first-order elastic pentspectral value Boolean function is of great significance.
[0003] Most existing methods for constructing pentaspectral value functions indirectly utilize a special class of Boolean functions, such as the bent function and the semi-bent function, and can only construct balanced pentaspectral value functions.
[0004] In their paper "CAO X, HU L. Two Boolean Functions with Five-Valued Walsh Spectra and High Nonlinearity[J]. International Journal of Foundations of Computer Science, 2014, 26(5): 537-556," Cao and Hu proposed a method for constructing balanced five-valued Walsh spectral functions with low Walsh spectra and high nonlinearity using trace functions over finite fields. In the reference "XU G, CAO X, XU S. Several classes of Boolean functions with few Walsh transform values[J]. Applicable Algebra in Engineering, Communication and Computing, 2017, 28(2):155-176," Xu and Cao proposed a method that adds the product of two or three linear functions to some existing bent or semi-bent functions, which can also effectively construct balanced five-valued Walsh spectral functions. People such as "Hodži" S, PASALIC E, ZHANG W G. Generic constructions of five-valued spectra Boolean functions[J]. IEEE Transactions on Information Theory, 2019, 65(11): 7554–7565.” This paper first utilized the concept of plateaued functions to provide a concise description of five-valued Walsh spectra functions in the spectral domain, and constructed balanced five-valued spectra functions using completely disjoint spectra. Zhang et al., in their paper “ZHANG Y, DU X, JIN W, et al. Constructions of Boolean functions with five-valued Walsh spectra and their applications[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2024, 107(7): 997-1002.”, used a quadratic construction method to generate Boolean functions with at most five-valued Walsh spectra. Song et al., based on Hodži… The construction method of completely disjoint spectral functions proposed by SONG CF, JI YH, SUN Y J. Construction of Even-Variable 2-Output Almost Optimal Five-Valued Spectra Boolean Functions[J]. Journal of Cryptologic Research, 2025, 12(03): 714-728. proposes a method for constructing even-variable two-output balanced five-valued spectral functions and provides another special class of single-output balanced five-valued spectral functions.
[0005] As mentioned above, most existing methods for constructing pentaspectral value functions are indirect construction methods. Indirect construction methods typically require additional transformation steps, resulting in high computational costs and implementation complexity. Furthermore, indirect construction methods cannot effectively achieve a good trade-off between nonlinearity and elasticity. Currently constructed pentaspectral value functions can only achieve equilibrium but cannot satisfy elasticity requirements. Summary of the Invention
[0006] To address the aforementioned problems in the prior art, this invention provides a method for constructing a first-order elastic pentspectral value function based on disjoint linear codes and a plaintext encryption method based on the first-order elastic pentspectral value function. The technical problem to be solved by this invention is achieved through the following technical solutions: In a first aspect, embodiments of the present invention provide a method for constructing a first-order elastic pentspectral value function based on disjoint linear codes, the method comprising: S1, Based on the relevant knowledge of finite fields, set the parameters. , , The relationship is used to obtain a set of disjoint linear codes to divide the entire... Space; in which, It is a binary finite field of 3D vector space; S2, based on the aforementioned set of disjoint linear codes, reset the parameters. The range of values is generated based on the generation principle of disjoint linear codes. indivual Linear code and 1 Linear code; S3, define two sets and To define the support set of the function; S4, based on the generated linear code and the defined support set, constructs a first-order elastic five-spectral value function by giving two methods of defining the function and using the one-choice method; S5. Based on the defined first-order elastic five-spectral value function, a truth table and Walsh spectrum are given for characterization and verification, thereby constructing a Boolean function; wherein, the Boolean function is used to generate a key sequence to encrypt the plaintext to be processed.
[0007] Secondly, embodiments of the present invention provide a plaintext encryption method based on a first-order elastic pentspectral value function, the plaintext encryption method based on a first-order elastic pentspectral value function comprising: Obtain the plaintext to be processed and the constructed Boolean function; wherein the Boolean function is obtained according to the construction method of the first-order elastic five-spectrum value function based on the disjoint linear code described in the first aspect; Generate a cryptographic function based on the Boolean function; The key sequence generator consists of the cryptographic function and the linear feedback shift register; The key sequence generator is used to generate a key sequence; The plaintext to be processed is encrypted using the key sequence.
[0008] The beneficial effects of this invention are: The method for constructing first-order elastic pentspectral value functions based on disjoint linear codes provided in this invention is a direct construction method for first-order elastic pentspectral value functions based on disjoint linear codes. This type of construction method does not need to start from existing Boolean functions, greatly reducing the application conditions and construction complexity. Furthermore, based on this construction theory, a series of first-order elastic pentspectral value functions can be directly constructed, significantly improving construction efficiency and reducing computational costs. Moreover, the functions constructed by this method can directly achieve near-optimal nonlinearity and a certain degree of elasticity by transforming the support set.
[0009] Based on this, the plaintext encryption method constructed using the first-order elastic pentagonal value function provides the cryptographic function obtained using the first-order elastic pentagonal value function provided by this invention. This enables the cryptographic system to effectively resist various attack methods, improve computational efficiency, and reduce complexity. Attached Figure Description
[0010] Figure 1 A flowchart illustrating a method for constructing a first-order elastic pentspectral value function based on disjoint linear codes, provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the core process of a method for constructing a first-order elastic five-spectral value function based on disjoint linear codes, provided in an embodiment of the present invention. Figure 3 This is a flowchart illustrating a plaintext encryption method based on a first-order elastic pentspectral value function provided in an embodiment of the present invention. Detailed Implementation
[0011] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.
[0012] To facilitate understanding of the present invention, the relevant concepts will be briefly explained first.
[0013] Definition of Boolean function: Let It is a binary finite field (composed of 0s and 1s) In a 3D vector space, a Boolean function can be represented as a... arrive The mapping, i.e. Among them, vectors .vector elements in Equal to, are vectors The value at the corresponding position belongs to a binary finite field and can be either 0 or 1.
[0014] Support set: satisfies of The set of functions is called a function. The support set.
[0015] Hamming weight: vector The number of 1s in a vector is called the Hamming weight of the vector, denoted as . .
[0016] Walsh Spectrum: The Walsh spectrum of a Boolean function is an important tool for studying its cryptographic properties. (The last sentence appears to be incomplete and possibly refers to plotting the Boolean function at a point.) The Walsh spectral transform at point is denoted as Specifically defined as: ; in, , , . Nonlinearity: Based on the Walsh spectral transform, the nonlinearity is denoted as... Specifically defined as: ; Xiao-Massey Theorem: Let... yes Meta-Boolean function and .like For any If all of them are true, then it is called a function. for The elastic function of order 1.
[0017] For the specific meaning of each parameter above, please refer to the relevant existing technology for an understanding.
[0018] This invention specifically provides a construction scheme for Boolean functions based on disjoint linear codes, thereby constructing a series of first-order elastic pentspectral valued Boolean functions. The main purpose of this invention is to study the support set distribution of Boolean functions using the structure of disjoint linear codes, and to construct a series of first-order elastic pentspectral valued functions using a direct construction method of elastic functions. The details are described below.
[0019] In a first aspect, embodiments of the present invention provide a method for constructing a first-order elastic five-spectral value function based on disjoint linear codes. Please refer to [link to relevant documentation]. Figure 1 and Figure 2 Understood, this method may include the following steps S1~S5: S1, Based on the relevant knowledge of finite fields, set the parameters. , , The relationship is used to obtain a set of disjoint linear codes to divide the entire... space; S1 of this invention studies a disjoint linear code structure based on the relevant knowledge of finite fields. This set of disjoint linear codes can precisely divide the entire... Space. Among them, It is a binary finite field of 3D vector space; To facilitate understanding of this step and subsequent solutions, some relevant concepts in the prior art will be explained here.
[0020] Definition of a linear code: Linear codes are One Dimensional subspace.
[0021] Definition of disjoint linear codes: If a set of linear codes satisfies: , It is then called a set of disjoint linear codes.
[0022] Definition of dual key: If It is A linear code, then its dual code is defined as .
[0023] Go to 0 space: If It is A linear code must have a vector of all zeros. Remove The next step is to go to the 0 space, specifically defined as follows: .
[0024] Regarding S1, those skilled in the art will understand that, during the construction of the linear code, the parameters... , , These are necessary parameters, and their specific meanings will not be detailed here.
[0025] Specifically, S1 may include the following steps: S11, order , , , yes Elements in; let For a finite field One of the fundamental elements, then In a finite field A set of bases; Among them, the set parameters , , The relationship is , And set ,but Elements in can be written as .
[0026] S12, define a bijection for The specific mapping relationship is as follows: ; S13, Order linear code The generating matrix, where ;according to Different ranges of values are used to obtain the generator matrix. This generates a set of partitions of the entire Disjoint linear codes in space. There are multiple generator matrices. Subscript This indicates the corresponding number.
[0027] Specifically, S13 includes: S131, for ,make ,in yes an identity matrix of order 1, and if ,but yes The zero matrix, otherwise: ; The specific form of the generated matrix is as follows: ; ; The generator matrix obtained by S131 for The generator matrix of a linear code; S132, for ,make , express The generator matrix of the dual code; at this time for The generator matrix of a linear code has the following specific form: ; S133, obtain the linear code ,in It is by A set of disjoint linear codes was generated and the entire space was filled. Classified as Disjoint linear codes: Among them, if let For the dual code of the above disjoint linear codes, then for any... Will A different dual key Each appears once in the middle, and Covering the entire space ,in .
[0028] Please understand the relevant concepts and processing procedures in S1 in conjunction with the relevant technologies.
[0029] S2, based on the aforementioned set of disjoint linear codes, reset the parameters. The range of values is generated based on the generation principle of disjoint linear codes. indivual Linear code and 1 Linear code; Specifically, S2 is based on a set of disjoint linear codes obtained in S1, and the parameters are reset according to the required number of spectral values. and Based on the generation principle of disjoint linear codes, the following is generated: indivual Linear code and 1 Linear code.
[0030] S3, define two sets and To define the support set of the function; Specifically, S3 defines two sets. and As a support set for functions, and Used to store The basic condition that the subscript of a linear code must satisfy is: .
[0031] S4, based on the generated linear code and the defined support set, constructs a first-order elastic five-spectral value function by giving two methods of defining the function and using the one-choice method; It is understandable that once the support set is determined, the function to be constructed can also be determined (please refer to the definition of the support set for details). In S4 of this invention, conditions are given to select a suitable function. and This allows us to determine the support set of the function.
[0032] This invention utilizes the structure of disjoint linear codes to study the support set distribution of Boolean functions, and constructs a series of first-order elastic pentspectral valued functions using a direct construction method of elastic functions, without starting from existing Boolean functions. Furthermore, it provides two methods for defining the functions, allowing users to choose either one to construct first-order elastic pentspectral valued functions. Specifically: (a) The first definition method: The first method of defining the function described in S4 is as follows: To one The total space is divided into an even number of... Linear code and 1 Linear codes; based on appropriate selection criteria, from an even number of... Select half of the linear code, determining that the corresponding output of a vector used as input to a function is 1; determine the other half... When a vector in a linear code is used as input to a function, the corresponding output is 0; finally, the remaining one is determined. When a vector in a linear code is used as input to a function, the corresponding output is a linear function.
[0033] Specifically, the process of constructing the first-order elastic five-spectral value function using the first definition method includes: Step a1, set parameters And its Hamming weight meets the requirements. ; Step a2: Design the code space subscript partitioning conditions to find sets that meet the conditions. and ,include: Partition condition 1, let ; It will appear in 4 different dual code spaces ; Command code space subscript Any two elements in the set belong to the set. And let the other two elements belong to the set. ; Partition condition 2, let ,and ; It will appear in 4 different dual code spaces One of the code space indices is determined as ; Command code space subscript Any two elements in the set belong to the set. And let the other two elements belong to the set. ; Partition condition 3, for all and Both must satisfy partitioning condition 1 and partitioning condition 2; Step a3: If a set satisfying partitioning conditions 1 to 3 is successfully found and Then the function is defined as: ; in, , ; , ;function This is the first-order elastic five-spectral value function constructed using the first definition method.
[0034] The proof is given below: 1) Walsh spectral value distribution: .
[0035] ; Scenario 1: When At that time, due to It is balanced and Therefore, we have: ; therefore, .
[0036] Obviously, when , , ,so The balance is clearly established.
[0037] Scenario 2: When hour, (1) If ,have , , ,so .
[0038] (2) If ,have , ,so .
[0039] Based on scenarios 1 and 2, we can obtain , and .
[0040] 2) The following is a detailed analysis and proof. hour, .
[0041] when , hour, The situation falls under situation 1, and has .
[0042] when , hour, The situation belongs to case 2(2) and according to the code space subscript partitioning condition 2, we have .
[0043] In summary, And for any , .
[0044] Therefore, the function It is a first-order elastic five-spectral value function.
[0045] (ii) The second definition method: The second method of defining the function described in S4 is as follows: To one The total space is divided into an even number of... Linear code and 1 Linear codes, starting with an even number of... Choose any half of the linear code; if one half is used as the input to a function, the corresponding output will be 1; if the other half is used... Linear code and 1 When a vector in a linear code is used as input to a function, the corresponding output is 0; then the function is transformed to obtain a new function that meets the requirements.
[0046] Specifically, the process of constructing the first-order elastic five-spectral value function using the second definition method includes: Step b1, based on the set and Basic conditions to be met, settings and and initially define the function for: ; in, , ; ; Step b2: Find parameters that meet the conditions. and ,include: Condition 1, and ; Condition 2: Assume there exists a set of linearly independent vectors. And satisfy , ;make ;in, Representation function Walsh's spectrum.
[0047] Step b3, if parameters that meet conditions 1 and 2 are successfully found and Then for Performing function transformations to define new functions includes: ; ; Among them, the function It is a first-order elastic five-spectral value function constructed using the second definition method.
[0048] The proof is given below: 1) Walsh spectral value distribution: .
[0049] ; Scenario 1: When At that time, due to It is balanced, therefore: ; Obviously, when , , .
[0050] so .
[0051] Scenario 2: When hour, It will appear in 4 different dual code spaces: (1) If only the following conditions are met ,have , ,so .
[0052] (2) If only the following conditions are met ,have , ,so .
[0053] (3) If both conditions are met and ,have , ,so .
[0054] Based on scenarios 1 and 2, we can obtain , .
[0055] according to The Walsh spectral distribution can be used to obtain the existence of Make Therefore, a function transformation is performed. and prove exist Walsh spectrum at that time: .
[0056] Suppose there exists a set of linearly independent vectors. And satisfy , .make And perform function transformation: .
[0057] 2) The following is a detailed analysis and proof. hour, , for identity matrix of order The OK.
[0058] ; In summary, And for any , .
[0059] Therefore, the function It is a first-order elastic five-spectral value function.
[0060] S5. Based on the defined first-order elastic five-spectral value function, the truth table and Walsh spectrum are given for characterization and verification, thereby constructing a Boolean function; The process of constructing the Boolean function by giving the truth table and Walsh spectrum based on the first-order elastic five-spectral value function defined by S4 can be understood in conjunction with relevant technologies.
[0061] Here is an example.
[0062] make ,and , By using primitive polynomials on , It can be divided into The generator matrices of the disjoint linear codes are shown below: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; Its dual code generator matrix is as follows: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; make The code space generated by the above generator matrix.
[0063] Set collection and The basic conditions to be met are: .
[0064] First definition method: 1. Set parameters And its Hamming weight meets the requirements. .
[0065] 2. Select appropriate indexes based on the code space subscript partitioning conditions. and : (1) For all : when , ,make , when , ,make , when , ,make , when , ,make .
[0066] (2) For all : when , ,make , when , ,make , when , ,make , when , ,make .
[0067] The above set partitioning is merely an example and does not represent the correct set. and .
[0068] 3. After searching, a suitable set was found. and The above division conditions must be met: .
[0069] The function is defined as:
[0070] Based on the above construction, the function can be obtained. The truth table and Walsh spectrum are as follows. Where Var represents the input variables of the function. middle It is the output of the function. This is the output of the Walsh spectrum.
[0071] Table 1 Truth table and Walsh spectrum
[0072] According to Table 1, it is easy to verify: ; And there are: For any .
[0073] Therefore, the function It is a first-order elastic pentathlon value function.
[0074] The second definition method: 1. Set up a collection: The function is defined based on the initial definition of the set. : ; function The truth table is as follows: ; 2. According to The truth table can be used to find values that meet the criteria. and order .
[0075] function The truth table is as follows: ; according to The truth table can be used to find values that meet the criteria. : ; 3. Finally, perform the function transformation and define the new function: .
[0076] Based on the above construction, the function can be obtained. The truth table and Walsh spectrum are as follows.
[0077] Table 2 Truth table and Walsh spectrum
[0078] According to Table 2, it is easy to verify. ; And there are For any .
[0079] Therefore, the function It is a first-order elastic pentathlon value function.
[0080] The core of this invention lies in directly constructing a first-order elastic quintic value function, thereby obtaining a Boolean function. This Boolean function is used to generate a key sequence for encrypting the plaintext to be processed.
[0081] Specifically, in a stream cipher system, the Boolean function can utilize relevant techniques to generate a key sequence, which is then used to encrypt the plaintext to be processed. The Boolean function obtained in this embodiment of the invention can be used in specific data encryption scenarios to address problems such as low encryption efficiency, high computational cost, and weak resistance to attacks during data encryption.
[0082] The process of generating a key sequence from a Boolean function and encrypting the plaintext to be processed using the key sequence can be found in the relevant technical explanations and will not be explained here.
[0083] The method for constructing first-order elastic pentspectral value functions based on disjoint linear codes provided in this invention is a direct construction method for first-order elastic pentspectral value functions based on disjoint linear codes. This type of construction method does not need to start from existing Boolean functions, greatly reducing the application conditions and construction complexity. Furthermore, based on this construction theory, a series of first-order elastic pentspectral value functions can be directly constructed, significantly improving construction efficiency and reducing computational costs. Moreover, the functions constructed by this method can directly achieve near-optimal nonlinearity and a certain degree of elasticity by transforming the support set.
[0084] Secondly, based on the above embodiments of the construction method of the first-order elastic pentspectral value function based on disjoint linear codes, this invention also provides a plaintext encryption method based on the construction of the first-order elastic pentspectral value function, such as... Figure 3 As shown, this plaintext encryption method based on the construction of a first-order elastic five-spectral value function includes: S100, obtain the plaintext to be processed and the constructed Boolean function; Depending on the application scenario, various types of raw data can be used as plaintext to be processed, such as: text-based data, including text documents, emails, chat logs, source code, JSON / XML data, financial transaction instructions, and personal identification information; numerical data, such as sensor readings, scientific computing data, stock prices, and account balances; multimedia data, such as images, audio, and video files; and program-based data, such as executable files and software update packages. As long as the data can be converted into a binary bit stream (i.e., a sequence of 0s and 1s), it can be encrypted using a key sequence.
[0085] The Boolean function is obtained according to the construction method of the first-order elastic five-spectrum value function based on disjoint linear codes described in the first aspect; for details, please refer to the relevant content in the first aspect, which will not be repeated here.
[0086] S200, Generate a cryptographic function based on the Boolean function; S200 integrates the single Boolean function constructed in the embodiments of the present invention into a fully functional cryptographic component suitable for key stream generation. Specifically, this typically employs a nonlinear combination model. That is, multiple linear feedback shift registers (LFSRs) are used in parallel, and their outputs are fed into the Boolean function of the embodiments of the present invention as input. Due to the first-order elasticity and other properties of the Boolean function constructed in the embodiments of the present invention, this step enables the entire key sequence generator to resist cryptanalysis such as correlation attacks.
[0087] S300, a key sequence generator composed of the cryptographic function and a linear feedback shift register; S300 is a modular assembly of the cryptographic functions and linear feedback shift registers described in S200. The hardware circuitry is designed and connected, or the software module is written.
[0088] This process may include: Initialize multiple LFSRs: Set an initial state (called a "seed") for each LFSR, which is part of the key.
[0089] Connect the cryptographic function: correctly connect the outputs of each LFSR to the cryptographic function. The input terminal.
[0090] The purpose of S300 is to construct a complete logical structure for a key sequence generator. The LFSR provides a source of long-period, pseudo-random linear sequences, while the cryptographic function acts as a non-linear combiner, merging multiple linear sequences into a secure, non-linear key sequence.
[0091] S400, a key sequence is generated using the key sequence generator; The general processing steps of the S400 may include: starting the assembled key sequence generator.
[0092] Execute on each clock pulse: All LFSRs are shifted once to generate new output bits.
[0093] cryptographic functions Immediately read these new output bits and calculate a result bit.
[0094] The calculated result bits are the key sequence bits generated at the current moment.
[0095] This process is repeated continuously to generate a pseudo-random key sequence of the same length as the plaintext to be processed.
[0096] Understandably, the generated key sequence should have good randomness (unpredictable and unbiased) to ensure security.
[0097] S500, the plaintext to be processed is encrypted using the key sequence.
[0098] This is the final step in stream cipher encryption, typically using the simplest bit-by-bit XOR operation.
[0099] Specifically, this may involve converting the plaintext to be processed into a raw binary bitstream. Then, the plaintext bitstream is XORed with the key sequence bitstream generated in S400. This converts readable plaintext into unreadable ciphertext.
[0100] The processing procedures for S200-S500 can be understood by referring to the standard implementation framework of stream ciphers.
[0101] In stream cipher systems, the randomness of the key sequence determines the security of the stream cipher. The key sequence generator consists of a linear feedback shift register and a cryptographic function. The cryptographic function is obtained using the first-order elastic pentspectral value function described in the embodiments of this invention, which enables the cryptographic system to effectively resist various attack methods.
[0102] To facilitate understanding of the specific application scenarios of the embodiments of the present invention, two scenario examples are given below.
[0103] (I) Scenario Example 1 - Encrypted Transmission of High-Definition Remote Sensing Images in the Military / Intelligence Field In this scenario, a reconnaissance satellite needs to transmit high-resolution remote sensing images it captures back to a ground command center (ground station) in real time and securely. Due to the massive amount of image data and its highly classified content, the reconnaissance satellite and the ground command center constitute an encrypted system. A key sequence generator needs to be designed, whose generated keystream must be highly random and unpredictable, resistant to strong cryptanalysis by adversaries (such as correlation attacks), ensuring that even if the signal is intercepted, the content cannot be deciphered. Corresponding plaintext encryption methods based on the construction of a first-order elastic five-spectral value function include: S100, obtain the plaintext to be processed and the constructed Boolean function; The plaintext to be processed in this step is a binary data stream of a high-resolution remote sensing image file (such as GeoTIFF format).
[0104] Then, a Boolean function is constructed using the construction method of the first-order elastic five-spectral value function based on disjoint linear codes provided in the first aspect of the present invention. It possesses the "first-order elasticity" property. This property means that the output of the function has extremely low correlation with any one of the input bits (or any linear combination thereof), thereby cutting off the shortcut for attackers to reverse-engineer the initial state of the LFSR from the keystream.
[0105] S200, Generate a cryptographic function based on the Boolean function; In the satellite's encryption chip, the system will use multiple LFSRs (e.g., 5) running in parallel. The Boolean function pre-loaded in the previous step will be used as a non-linear combination function. That is, the cryptographic function is... (LFSR1_out, LFSR2_out, ..., LFSR5_out).
[0106] This step instantiates the theoretical Boolean function into a runnable component. Its purpose is to leverage the function's first-order resilience to ensure that even if an adversary intercepts a portion of the keystream, they cannot crack the state of a single LFSR by analyzing its statistical properties, thus directly solving the core technical problem of resisting correlation attacks.
[0107] S300, a key sequence generator composed of the cryptographic function and a linear feedback shift register; When the encryption command is issued, the system uses the session key for this communication (generated by the higher-level key protocol) to initialize the initial state of each LFSR. Then, the outputs of these LFSRs are connected to Boolean functions. The input terminal completes the assembly of the generator in hardware logic.
[0108] Since different session keys will generate different LFSR initial states, it means that even if images from the same location are transmitted, the generated key streams will be completely different each time, thus realizing the "one-time pad" security concept.
[0109] S400, a key sequence is generated using the key sequence generator; The reconnaissance satellite begins reading remote sensing image data into its buffer and simultaneously activates a key sequence generator. The key sequence generator outputs one key bit each clock cycle, forming a key sequence of the same length as the image data stream. The generated key sequence exhibits extremely high randomness, meeting the stringent strength requirements of military encryption.
[0110] S500, the plaintext to be processed is encrypted using the key sequence. This step involves performing a bit-by-bit XOR operation between the binary stream of image data and the generated key sequence to produce a ciphertext data stream. The ciphertext is then transmitted to the ground station via the downlink.
[0111] This encryption process is highly efficient and fast, suitable for the limited computing resources and real-time transmission needs of satellites. The ground station can decrypt and reconstruct the image by XORing the same keystream again. The core security of the entire scheme is rooted in a carefully designed Boolean function within the S100 that can resist specific attacks.
[0112] (II) Scenario Example 2 - Encryption of Real-Time Payment Instructions in Financial Transactions In this scenario, Bank A's server needs to send a high-value cross-border payment instruction to Bank B's server. The instruction data is small in size but high in value, making it a primary target for hackers. The two banks jointly form an encrypted system. It is necessary to ensure that the payment instruction (e.g., "transfer Z yuan from account X to account Y") is absolutely confidential and tamper-proof during transmission, and that the encryption system can resist known attacks against stream ciphers to prevent the theft of large sums of money. The corresponding plaintext encryption methods based on the first-order elastic five-spectral value function include: S100, obtain the plaintext to be processed and the constructed Boolean function; The plaintext to be processed in this step is structured payment instruction data (such as in ISO 8583 or JSON format), for example, {"from": "A123", "to": "B456", "amount": "1000000", "currency": "USD"}, which is then converted into a binary stream.
[0113] During the development phase of a bank's core encryption system (such as the HSM - Hardware Security Module), cryptographic engineers obtain a first-order elastic Boolean function based on the construction method of a first-order elastic five-spectrum value function based on disjoint linear codes provided in this invention. This ensures that the generated keystream has no statistical weaknesses, preventing attackers from discovering patterns by analyzing large amounts of transaction data, thereby protecting the financial security of each transaction.
[0114] S200, Generate a cryptographic function based on the Boolean function; Internally, the payment gateway invokes an encryption library when encryption is required. This encryption library has pre-designed Boolean functions integrated into it. Similarly, a nonlinear combination model is used, taking the outputs of multiple LFSRs as... The input. The cryptographic function at this point is... itself.
[0115] This step transforms the static security components (Boolean functions) into dynamic encryption logic. Its first-order resilience directly serves the need to "protect short data packets," as attackers find it difficult to extract useful information from a single or small amount of encrypted data to break the system.
[0116] S300, a key sequence generator composed of the cryptographic function and a linear feedback shift register; S400, a key sequence is generated using the key sequence generator; When a payment instruction arrives, the system uses a temporary key generated from the transaction serial number, timestamp, etc., to initialize the LFSR and immediately runs the key sequence generator to produce a sufficiently long key sequence.
[0117] By generating a unique key for each specific transaction, forward security is achieved. Even if a hacker cracks the key for one transaction, they cannot use it to decrypt the next transaction.
[0118] S500, the plaintext to be processed is encrypted using the key sequence. The binary data of the payment instruction is XORed with the newly generated key sequence to generate ciphertext. This ciphertext is then sent to the receiving bank via a private financial network (such as SWIFT). This ensures the confidential transmission of the payment instruction. The receiving bank generates a key using the same method, decrypts the instruction, verifies it, and executes the transfer. The security foundation of this entire process lies in the Boolean function design, determined at the S100 stage, which fundamentally guarantees the quality of the key stream.
[0119] Of course, the application of the method for constructing a first-order elastic pentagonal value function based on disjoint linear codes provided in the embodiments of the present invention in the encryption system is not limited to the specific description of S100-S500 in the plaintext encryption method based on the first-order elastic pentagonal value function in the second aspect. Moreover, the application scenarios of the plaintext encryption method based on the first-order elastic pentagonal value function provided in the second aspect of the embodiments of the present invention are not limited to the above two scenario examples.
[0120] The plaintext encryption method based on a first-order elastic pentspectral value function provided by this invention has the core value of fundamentally constructing a secure, universal, and efficient stream cipher system by introducing a first-order elastic Boolean function. This method closely integrates theoretical innovation with engineering practice, and has the following outstanding effects: 1. Root Cause Defense: The core first-order resilience property enables the system to effectively resist cryptographic analysis such as fast correlation attacks, providing a provable and stronger security foundation for the key sequence.
[0121] 2. Widely applicable and highly efficient: It adopts a mature stream cipher framework, which is suitable for various environments from IoT terminals to cloud servers. It can efficiently encrypt massive data streams and high-value short instructions, achieving a balance between high performance and high security.
[0122] 3. Solving specific technical problems: This solution systematically solves the technical challenge of "how to improve the actual anti-attack capability of stream ciphers while ensuring efficiency", transforming profound mathematical properties into deployable engineering security advantages.
[0123] In summary, this invention provides an end-to-end data encryption solution with significantly enhanced security and ease of implementation for a wide range of scenarios, including military, finance, and healthcare.
[0124] It should be noted that, in the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.
[0125] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.
Claims
1. A method for constructing a first-order elastic pentspectral value function based on disjoint linear codes, characterized in that, include: S1, Based on the relevant knowledge of finite fields, set the parameters. , , The relationship is used to obtain a set of disjoint linear codes to divide the entire... Space; in which, It is a binary finite field of 3D vector space; S2, based on the aforementioned set of disjoint linear codes, reset the parameters. The range of values is generated based on the generation principle of disjoint linear codes. indivual Linear code and 1 Linear code; S3, define two sets and To define the support set of the function; S4, based on the generated linear code and the defined support set, constructs a first-order elastic five-spectral value function by giving two methods of defining the function and using the one-choice method; S5. Based on the defined first-order elastic five-spectral value function, a truth table and Walsh spectrum are given for characterization and verification, thereby constructing a Boolean function; wherein, the Boolean function is used to generate a key sequence to encrypt the plaintext to be processed.
2. The method for constructing the first-order elastic five-spectral value function based on disjoint linear codes according to claim 1, characterized in that, S1 includes: S11, order , , , yes Elements in; let For a finite field One of the fundamental elements, then In a finite field A set of bases; S12, define a bijection for The specific mapping relationship is as follows: ; S13, Order linear code The generating matrix, where ;according to Different ranges of values are used to obtain the generator matrix. This generates a set of partitions of the entire Disjoint linear codes in space.
3. The method for constructing the first-order elastic five-spectral value function based on disjoint linear codes according to claim 2, characterized in that, S13 includes: S131, for ,make ,in yes an identity matrix of order 1, and if ,but yes The zero matrix, otherwise: ； The specific form of the generated matrix is as follows: ； ； The generator matrix obtained by S131 for The generator matrix of a linear code; S132, for ,make , express The generator matrix of the dual code; at this time for The generator matrix of a linear code has the following specific form: ； S133, obtain the linear code ,in It is by A set of disjoint linear codes was generated and the entire space was filled. Classified as Disjoint linear codes: Among them, if let For the dual code of the above disjoint linear codes, then for any... Will A different dual key Each appears once in the middle, and Covering the entire space ,in .
4. The method for constructing the first-order elastic five-spectral value function based on disjoint linear codes according to claim 3, characterized in that, S2 includes: Based on the set of disjoint linear codes obtained in S1, the parameters are reset. and Based on the generation principle of disjoint linear codes, the following is generated: indivual Linear code and 1 Linear code.
5. The method for constructing the first-order elastic five-spectral value function based on disjoint linear codes according to claim 4, characterized in that, S3 includes: Define two sets and As a support set for functions, and Used to store The basic condition that the subscript of a linear code must satisfy is: 。 6. The method for constructing the first-order elastic five-spectral value function based on disjoint linear codes according to claim 5, characterized in that, The first method of defining the function described in S4 is as follows: To one The total space is divided into an even number of... Linear code and 1 Linear codes; based on appropriate selection criteria, from an even number of... Select half of the linear code, determining that the corresponding output of a vector used as input to a function is 1; determine the other half... When a vector in a linear code is used as input to a function, the corresponding output is 0; finally, the remaining one is determined. When a vector in a linear code is used as input to a function, the corresponding output is a linear function.
7. The method for constructing the first-order elastic five-spectral value function based on disjoint linear codes according to claim 6, characterized in that, The process of constructing the first-order elastic pentspectral value function using the first definition method includes: Step a1, set parameters And its Hamming weight meets the requirements. ; Step a2: Design the code space subscript partitioning conditions to find sets that meet the conditions. and ,include: Partition condition 1, let ; It will appear in 4 different dual code spaces ; Command code space subscript Any two elements in the set belong to the set. And let the other two elements belong to the set. ; Partition condition 2, let ,and ; It will appear in 4 different dual code spaces One of the code space indices is determined as ; Command code space subscript Any two elements in the set belong to the set. And let the other two elements belong to the set. ; Partition condition 3, for all and Both must satisfy partitioning condition 1 and partitioning condition 2; Step a3: If a set satisfying partitioning conditions 1 to 3 is successfully found and Then the function is defined as: ； in, , ; , ;function This is the first-order elastic five-spectral value function constructed using the first definition method.
8. The method for constructing the first-order elastic five-spectral value function based on disjoint linear codes according to claim 5, characterized in that, The second method of defining the function described in S4 is as follows: To one The total space is divided into an even number of... Linear code and 1 Linear codes, starting with an even number of... Choose any half of the linear code; if one half is used as the input to a function, the corresponding output will be 1; if the other half is used... Linear code and 1 When a vector in a linear code is used as input to a function, the corresponding output is 0; then the function is transformed to obtain a new function that meets the requirements.
9. The method for constructing the first-order elastic five-spectral value function based on disjoint linear codes according to claim 8, characterized in that, The process of constructing the first-order elastic pentspectral value function using the second definition method includes: Step b1, based on the set and Basic conditions to be met, settings and and initially define the function for: ； in, , ; ; Step b2: Find parameters that meet the conditions. and ,include: Condition 1, and ; Condition 2: Assume there exists a set of linearly independent vectors. And satisfy , ;make ; Step b3, if parameters that meet conditions 1 and 2 are successfully found and Then for Performing function transformations to define new functions includes: ； ； Among them, the function It is a first-order elastic five-spectral value function constructed using the second definition method.
10. A plaintext encryption method based on a first-order elastic five-spectral value function, characterized in that, include: Obtain the plaintext to be processed and the constructed Boolean function; wherein the Boolean function is obtained by the construction method of the first-order elastic five-spectrum value function based on disjoint linear codes according to any one of claims 1-9; Generate a cryptographic function based on the Boolean function; The key sequence generator consists of the cryptographic function and the linear feedback shift register; The key sequence generator is used to generate a key sequence; The plaintext to be processed is encrypted using the key sequence.