NFC encryption authentication system based on algebraic number theory

Abstract

The invention discloses an NFC encryption authentication system based on an algebraic number theory, and belongs to the technical field of information security. The system comprises an NFC encryption authentication module, a data transmission optimization module and an intelligent interaction expansion module: generating public and private keys based on ideal operation by constructing an algebraic number field and an algebraic integer ring, and mapping NFC data into a ring element sequence to complete encryption and decryption; the transmission efficiency is optimized through number theory channel coding and data grouping, and the stability of big data transmission is improved; intelligent interaction and security enhancement are realized through user behavior modeling and a dynamic one-time key. Based on mathematical problem characteristics of algebraic number theory, attack means such as man-in-the-middle attack and cryptographic analysis are effectively resisted, NFC transmission efficiency and application expansibility are improved, and the method is suitable for scenes such as mobile payment, digital car keys and intelligent access control.

Description

Technical Field

[0001] This invention relates to the field of near field communication (NFC) technology, specifically to an NFC system that enables encrypted authentication, data transmission optimization, and intelligent interaction extension. Background Technology

[0002] Near Field Communication (NFC), a short-range, high-frequency wireless communication technology, has been widely used in various public and industrial applications, including mobile payments, smart access control, electronic ticketing, and digital car keys. However, with the continuous expansion of these applications, traditional NFC systems exhibit significant shortcomings in security, transmission efficiency, and functional scalability.

[0003] 1. Insufficient security protection: Traditional NFC encryption solutions are mostly based on conventional symmetric / asymmetric encryption algorithms, which are vulnerable to man-in-the-middle attacks, data sniffing, replay attacks and cryptanalysis attacks, posing security risks such as user privacy leakage, theft of funds and unauthorized access to devices;

[0004] 2. Limited data transmission efficiency: The existing NFC transmission encoding and channel mechanism is not optimized for large data volume scenarios. The data transmission rate of large-capacity data such as high-definition images and video streams is low and the anti-interference ability is poor, which cannot meet the high-speed transmission requirements.

[0005] 3. Limited application functionality: Traditional NFC only realizes basic identity authentication and data transmission, without combining user behavior to realize intelligent interaction, thus limiting the application boundaries.

[0006] Algebraic number theory, as a core branch of modern mathematics, encompasses mature theories such as number fields, algebraic integer rings, ideal theory, lattice theory, and class field theory. Its operational characteristics, based on mathematical problems such as large integer factorization, ideal operations, and discrete logarithms, can provide a high-security underlying mathematical support for cryptographic systems. Currently, algebraic number theory has not yet achieved systematic and engineering applications in the field of NFC technology, and its mathematical characteristics cannot be used to solve the existing security, efficiency, and functional bottlenecks of NFC. Summary of the Invention

[0007] Purpose of the invention: To address the aforementioned existing technologies, this invention proposes an NFC encryption authentication system based on algebraic number theory, thereby improving the security, transmission efficiency, and application value of the NFC system.

[0008] Technical solution: An NFC encryption authentication system based on algebraic number theory, the system including an NFC encryption authentication module;

[0009] The NFC encryption authentication module includes:

[0010] Algebraic number field construction unit: used to construct a quadratic field or a cycloid field as an algebraic number field K, define an algebraic integer ring on the number field K, and determine the rules for addition, multiplication, and ideal operations within the ring;

[0011] Key generation unit: Select coprime nonzero ideals I and J from the algebraic integer ring, and generate the public key PK = I·J and the private key SK = I through ideal operations. -1 Public and private keys are stored in a secure area of ​​the device;

[0012] Data encryption unit: Converts the NFC data to be transmitted into a byte stream, groups it into fixed byte lengths and maps it to a sequence of elements in an algebraic integer ring, encrypts the element sequence using a public key PK through ideal multiplication, and obtains the encrypted ring element sequence, which is then transmitted through the NFC antenna.

[0013] Data decryption unit: The receiver performs an ideal multiplication inverse operation using the private key SK to restore the original ring element sequence, and decodes it in reverse according to the preset mapping rules to obtain the original NFC data and complete the identity authentication.

[0014] Furthermore, the algebraic number field K is specifically a quadratic number field. , where D is a positive integer without square factors.

[0015] Furthermore, in the data encryption unit, the data mapping rule is that every 4 bytes corresponds to an algebraic integer ring element, and if there are less than 4 bytes, 0x00 is used for padding.

[0016] Furthermore, the system also includes an NFC data transmission optimization module;

[0017] The NFC data transmission optimization module includes:

[0018] Data grouping unit: The large-capacity NFC data is grouped into fixed-length 32-byte groups. If the last byte is less than 32 bytes, it is padded with 0x00. The grouping order and total number are recorded.

[0019] Element mapping unit: Converts each set of data into algebraic integer elements in the quadratic algebraic field K through a polynomial mapping function, thus completing compact encoding;

[0020] Channel coding unit: A 4×4 channel coding matrix is ​​constructed based on an ideal lattice, and the element sequence is redundantly encoded;

[0021] Decoding and reconstruction unit: The receiver uses congruence operations and ideal inversion operations to remove channel noise and coding redundancy, and restores the original data in the order of grouping.

[0022] Furthermore, the 4×4 channel coding matrix is ​​as follows:

[0023] The matrix elements are taken from algebraic integers in the algebraic number field K.

[0024] Furthermore, the large-capacity NFC data includes high-resolution images, device configuration files, and firmware packages.

[0025] Furthermore, the system also includes an NFC smart interaction extension module;

[0026] The NFC smart interaction extension module includes:

[0027] User Behavior Modeling Unit: Collects user NFC interaction behavior data, and uses algebraic number theory vector space theory to abstract the data into a 5-dimensional behavior vector on the quadratic algebraic number field K, and constructs an algebraic model of user behavior.

[0028] Personalized service push unit: When a user enters the NFC sensing range, the usage scenario is matched through the ideal matching algorithm on the number field K, and corresponding service instructions are generated and pushed.

[0029] Interactive security enhancement unit: Using timestamps, behavior vectors, and number field congruence relations as seeds, a one-time key is generated through ideal multiplication and congruence operations to encrypt interactive data once.

[0030] Furthermore, the 5-dimensional behavior vector is V=(t,id,f,s,m), where t is the timestamp parameter, id is the device identifier, f is the usage frequency, s is the scene code, and m is the transaction amount parameter.

[0031] Furthermore, the one-time key generation formula is as follows: The key is valid for the current interaction period and expires immediately after the interaction is completed.

[0032] Furthermore, the user NFC interaction behavior data includes card swipe time, device ID, usage frequency, scenario type, and transaction amount, with a collection period of 7 days.

[0033] Beneficial effects: 1. Significantly improved security: Based on complex mathematical structures such as algebraic number fields and ideals, encryption is achieved by solving the problems of large integer factorization and discrete logarithms, which effectively resists man-in-the-middle attacks, cryptanalysis, and replay attacks. The security strength is higher than that of traditional encryption algorithms.

[0034] 2. Significantly improved transmission efficiency: Through data compact coding and number-theoretic channel coding optimization, it supports high-speed transmission of large data volumes such as high-definition images and video streams without increasing hardware bandwidth, and enhances anti-interference capabilities;

[0035] 3. Deep expansion of application scenarios: Combining user behavior modeling to achieve personalized intelligent interaction, taking into account both service accuracy and communication security, and expanding the application boundaries of NFC in the fields of Internet of Things, smart living, and intelligent transportation;

[0036] 4. High adaptability: Lightweight and low power consumption, it fits the technical characteristics of NFC, which is close-range, small data, and fast interaction. It is compatible with existing NFC hardware devices and does not require large-scale hardware modification.

[0037] Application scenarios of the method of this invention:

[0038] 1. Mobile payment

[0039] Ensuring transaction security: In various mobile payment services, NFC card emulation enables contactless payments. Algebraic number theory-based encryption authentication systems can encrypt critical information during the payment process, such as transaction amounts and user accounts, preventing information leakage and tampering, thus ensuring payment security.

[0040] Preventing fraudulent transactions: By using algorithms based on algebraic number theory, a unique digital signature or dynamic key is generated for each transaction, ensuring that only authorized devices and users can complete the payment, thus reducing the risk of fraudulent transactions.

[0041] 2. Digital car key

[0042] Vehicle unlocking and starting: By connecting the mobile phone and vehicle via NFC, the car key function is integrated into the mobile terminal; this invention ensures that only authorized devices can communicate securely to perform operations such as unlocking and starting the vehicle, preventing unauthorized opening. Access control: For shared vehicles or vehicles used by multiple family members, different permissions can be set for different users through this system, such as only being able to unlock or start the vehicle, ensuring vehicle safety and convenient management.

[0043] 3. Smart access control

[0044] Authentication: Users use NFC-enabled devices, such as smartphones, to simulate access cards and unlock doors by communicating with the card reader in the access control system via NFC. An encryption authentication system based on algebraic number theory rigorously verifies user identity; only authorized user devices can open the access control system, thus enhancing its security.

[0045] Recording and Traceability: The system can record the time of each access control opening, user information, and other data, and uses encryption technology to ensure the integrity and authenticity of the data, facilitating subsequent query and management, and enabling traceability in the event of security issues. Attached Figure Description

[0046] Figure 1 This is a diagram of the encryption authentication system architecture of the present invention;

[0047] Figure 2 Flowchart of an NFC data transmission scheme optimized for algebraic number theory;

[0048] Figure 3 This is a schematic diagram illustrating the extended applications of NFC smart interaction based on algebraic number theory. Detailed Implementation

[0049] The invention will now be further explained with reference to the accompanying drawings.

[0050] An NFC encryption authentication system based on algebraic number theory includes an NFC encryption authentication module, an NFC data transmission optimization module, and an NFC smart interaction extension module.

[0051] 1. System Initialization:

[0052] Before the NFC reader / writer and the NFC tag device establish communication for the first time, the following initialization steps should be performed:

[0053] 1) Initialization of algebraic number field building units: Selecting a quadratic number field As the working algebraic field, to ensure the security and operability of the encryption system, a quadratic field is defined. algebraic integer ring on The rules for addition, multiplication, ideal multiplication, and ideal inversion within a ring are pre-defined, satisfying the basic axioms of algebraic number theory, and providing a unified mathematical foundation for subsequent encryption operations.

[0054] 2) Key generation unit initialization: in the algebraic integer ring Internally, coprime nonzero ideals I and J are selected using number theory algorithms, and public key PK = I· J and private key SK = I are generated through ideal operations. -1 The public key PK is stored in the public area of ​​the sending end, while the private key SK is stored only in the secure area of ​​the device and is not involved in plaintext transmission.

[0055] 3) General parameter configuration: Set the data mapping rule to one algebraic integer ring element for every 4 bytes, configure the data check polynomial to CRC-16, and determine the communication handshake timeout to 100ms.

[0056] 2. For example Figure 1 As shown, the specific encryption and authentication process of the NFC encryption and authentication module is as follows:

[0057] 1) Data encryption unit (sender):

[0058] 1.1) Construction of number fields and algebraic integer rings in algebraic numbers:

[0059] The sending and receiving ends synchronously load the initialized binary field. and the ring of algebraic integers Unified operation rules.

[0060] 1.2) Loading public and private keys:

[0061] The sending end calls the public key PK=I·J, and the receiving end calls the locally stored private key SK=I. -1 Complete key preparation.

[0062] 1.3) Data Mapping and Encrypted Transmission:

[0063] NFC data to be transmitted (such as ID, account, and commands) is converted into a byte stream using ASCII / UTF-8 encoding.

[0064] Map the byte stream to an algebraic integer ring in groups of 4 bytes. One of the elements M;

[0065] Encryption is performed using ideal multiplication: C = M · PK, where M is the plaintext ring element, PK is the public key, and C is the encrypted ring element;

[0066] The encrypted ring element sequence is converted into a communication byte stream and sent to the receiving end via the NFC antenna.

[0067] 2) Data decryption process (receiving end):

[0068] 2.1) The receiving end receives the NFC signal and demodulates it to obtain the encrypted ring element sequence C;

[0069] 2.2) Call the local private key SK = I⁻¹ and perform the ideal inverse operation to decrypt: M = C · SK, to restore the original plaintext ring element M;

[0070] 2.3) The decrypted ring element M is reverse-transformed according to the preset mapping rules to obtain the original plaintext byte stream;

[0071] 2.4) The receiving end verifies the data integrity using CRC-16. After successful verification, it outputs the original authentication data, thus completing NFC device identity authentication and data transmission.

[0072] In this embodiment, the data to be transmitted is 16 bytes of user identity information. After being mapped by 4 sets of ring elements, encrypted by ideal multiplication, and decrypted by ideal inverse operation, the data restoration accuracy is 100%, which can effectively resist man-in-the-middle attacks and data tampering, and meet the requirements of NFC near-field encryption authentication.

[0073] 3. NFC data transmission optimization module:

[0074] This module is suitable for scenarios involving large-capacity data transmission such as NFC high-definition images, device configuration files, and firmware packages, using quadratic algebraic data fields. As the basis for operation, combined with Figure 2 The process shown is implemented in the following steps:

[0075] 1) Data Packetization: Large amounts of data to be transmitted are grouped into fixed-length 32-byte blocks. If a block is less than 32 bytes at the end, it is padded with 0x00 to make it 32 bytes. Each data block is treated as an independent processing unit, corresponding to an algebraic field. An algebraic integer element in the array records the total number of groups and the group sequence number.

[0076] 2) Element mapping: Convert each group of 32 bytes of data into a hexadecimal byte stream, and then convert it into an algebraic field using a polynomial mapping function f(x). The algebraic integer elements in the dataset complete the compact encoding from data to number-theoretic elements, and the mapping formula is:

[0077] ;

[0078] Where a and b are the integer coefficients obtained from the byte stream conversion; ensure that all grouped data are converted into an element sequence that conforms to the K operation rules of the number field.

[0079] 3) Number-theoretic channel coding: A 4×4 channel coding matrix G is constructed based on an ideal lattice, with matrix elements taken from the algebraic number field. Algebraic integers, matrix construction formula:

[0080] ;

[0081] Matrix multiplication is used to perform redundant encoding on the element sequence, increasing the data's anti-interference redundancy and optimizing the NFC transmission code rate.

[0082] 4) Data reception: The receiving NFC device receives the encoded number theory element sequence through the antenna, completes signal demodulation and data buffering, and temporarily stores the encoded data according to the group order.

[0083] 5) Decoding and reconstruction: The receiving end uses a modulus... Congruence operations and ideal inversion operations remove channel noise and coding redundancy. The rules for congruence operations are as follows:

[0084] ;

[0085] Where C is the encoded element, G -1 It is the inverse of the encoding matrix; after removing the padding data, all elements are reorganized according to the grouping order, and the reverse mapping is performed to obtain the original byte stream, thus restoring the complete large-capacity original data.

[0086] This embodiment performs the entire process of grouping, mapping, encoding, transmission, and decoding on 128KB high-definition image data, achieving 100% data restoration accuracy. It can effectively resist NFC channel noise interference and meet the needs of high-speed transmission of large-capacity data.

[0087] 4. NFC Smart Interaction Extension Module:

[0088] This module focuses on quadratic algebraic number fields. Based on computational foundations, and relying on algebraic number theory, vector space theory, and ideal operations, this system enables user behavior modeling and dynamic secure interaction. It is suitable for intelligent interaction scenarios such as NFC access control, mobile payment, and digital car keys. Figure 3The process shown is implemented in the following steps:

[0089] 1) User behavior data collection: Real-time collection of user interaction data via NFC terminal. Collection dimensions include: card swipe timestamp, device ID, usage frequency, scenario type, and transaction amount. The sampling frequency is 1 time per interaction. The data is encrypted with AES-128 and stored in the secure area of ​​the NFC device. The collection period is 7 days, and expired data is automatically overwritten.

[0090] 2) User behavior model construction and updating: The collected five types of behavioral data are abstracted into a number field using algebraic number theory and vector space theory. A 5-dimensional behavioral vector V is defined by the vector quantization rule: V = (t, id, f, s, m); where: t = timestamp parameter, id = device identifier, f = usage frequency, s = scene code, and m = amount parameter; all vector elements are mapped to an algebraic number field. Using algebraic integers, we construct an algebraic model of user behavior, and automatically update the model parameters at 0:00 every day.

[0091] 3) Personalized service matching generation: When a user enters the NFC sensing range (≤5cm), the device reads the behavior vector V and generates a personalized service through the data domain. The ideal matching algorithm calculates the similarity between the vector and the scene. When the matching threshold is ≥0.85, the corresponding service instructions (access control unlocking, quick payment access, car key control) are generated to complete the intelligent service generation.

[0092] 4) Service command push: The NFC terminal will push the generated service command to the user's NFC device through the NFC lightweight communication channel. The command data is transmitted in the data field element format to ensure push efficiency and security.

[0093] 5) Dynamic one-time key encryption interaction: based on timestamps (accurate to the second), 5-dimensional behavioral vector V, and algebraic number fields. Congruence relations are used as seeds, and ideal multiplication and modular arithmetic are applied. Congruence operations generate a one-time key K otp :

[0094] ;

[0095] PK is the system public key, and its validity period is the current interaction cycle; it expires immediately upon completion of the interaction. A one-time key K is used. otp Encrypt interactive data to achieve one-time encryption, resist replay attacks and man-in-the-middle attacks, and complete secure intelligent interaction.

[0096] In this embodiment, the user's NFC device collects a total of 120 interaction data, constructs a 5-dimensional algebraic behavior vector, and the dynamic one-time key generation takes ≤10ms, which can realize secure and efficient NFC smart interaction and meet the needs of smart scenario applications.

[0097] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An NFC encryption authentication system based on algebraic number theory, characterized in that, The system includes an NFC encryption authentication module; The NFC encryption authentication module includes: Algebraic number field construction unit: used to construct a quadratic field or a cycloid field as an algebraic number field K, define an algebraic integer ring on the number field K, and determine the rules for addition, multiplication, and ideal operations within the ring; Key generation unit: Select coprime nonzero ideals I and J from the algebraic integer ring, and generate the public key PK = I·J and the private key SK = I through ideal operations. -1 Public and private keys are stored in a secure area of ​​the device; Data encryption unit: Converts the NFC data to be transmitted into a byte stream, groups it into fixed byte lengths and maps it to a sequence of elements in an algebraic integer ring, encrypts the element sequence using a public key PK through ideal multiplication, and obtains the encrypted ring element sequence, which is then transmitted through the NFC antenna. Data decryption unit: The receiver performs an ideal multiplication inverse operation using the private key SK to restore the original ring element sequence, and decodes it in reverse according to the preset mapping rules to obtain the original NFC data and complete the identity authentication.

2. The NFC encryption authentication system based on algebraic number theory according to claim 1, characterized in that, The algebraic number field K is specifically a quadratic number field. , where D is a positive integer without square factors.

3. The NFC encryption authentication system based on algebraic number theory according to claim 1, characterized in that, In the data encryption unit, the data mapping rule is that every 4 bytes corresponds to an algebraic integer ring element, and if there are less than 4 bytes, 0x00 is used to pad the bits.

4. The NFC encryption authentication system based on algebraic number theory according to any one of claims 1-3, characterized in that, The system also includes an NFC data transmission optimization module; The NFC data transmission optimization module includes: Data grouping unit: The large-capacity NFC data is grouped into fixed-length 32-byte groups. If the last byte is less than 32 bytes, it is padded with 0x00. The grouping order and total number are recorded. Element mapping unit: Converts each set of data into algebraic integer elements in the quadratic algebraic field K through a polynomial mapping function, thus completing compact encoding; Channel coding unit: A 4×4 channel coding matrix is ​​constructed based on an ideal lattice, and the element sequence is redundantly encoded; Decoding and reconstruction unit: The receiver uses congruence operations and ideal inversion operations to remove channel noise and coding redundancy, and restores the original data in the order of grouping.

5. The NFC encryption authentication system based on algebraic number theory according to claim 4, characterized in that, The 4×4 channel coding matrix is: The matrix elements are taken from algebraic integers in the algebraic number field K.

6. The NFC encryption authentication system based on algebraic number theory according to claim 4, characterized in that, The large-capacity NFC data includes high-resolution images, device configuration files, and firmware packages.

7. The NFC encryption authentication system based on algebraic number theory according to any one of claims 1-3, characterized in that, The system also includes an NFC smart interaction extension module; The NFC smart interaction extension module includes: User Behavior Modeling Unit: Collects user NFC interaction behavior data, and uses algebraic number theory vector space theory to abstract the data into a 5-dimensional behavior vector on the quadratic algebraic number field K, and constructs an algebraic model of user behavior. Personalized service push unit: When a user enters the NFC sensing range, the usage scenario is matched through the ideal matching algorithm on the number field K, and corresponding service instructions are generated and pushed. Interactive security enhancement unit: Using timestamps, behavior vectors, and number field congruence relations as seeds, a one-time key is generated through ideal multiplication and congruence operations to encrypt interactive data once.

8. The NFC encryption authentication system based on algebraic number theory according to claim 6, characterized in that, The 5-dimensional behavior vector is V=(t,id,f,s,m), where t is the timestamp parameter, id is the device identifier, f is the usage frequency, s is the scene code, and m is the transaction amount parameter.

9. The NFC encryption authentication system based on algebraic number theory according to claim 6, characterized in that, The formula for generating the one-time key is: The key is valid for the current interaction period and expires immediately after the interaction is completed.

10. The NFC encryption authentication system based on algebraic number theory according to claim 6, characterized in that, The user's NFC interaction behavior data includes card swipe time, device ID, usage frequency, scenario type, and transaction amount, and the collection period is 7 days.

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