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CN-122028052-A - NFC encryption authentication system based on algebraic number theory

CN122028052ACN 122028052 ACN122028052 ACN 122028052ACN-122028052-A

Abstract

The invention discloses an NFC encryption authentication system based on algebraic numerology, 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, wherein a public and private key is generated based on ideal operation by constructing algebraic digit fields and algebraic integer rings, NFC data are mapped into a ring element sequence to finish encryption and decryption, transmission efficiency is optimized through number theory channel coding and data grouping, large data transmission stability is improved, and intelligent interaction and safety enhancement are realized through user behavior modeling and dynamic one-time keys. The invention relies on the mathematical difficult characteristics of algebraic numerology, effectively resists attack means such as man-in-the-middle attack and password analysis, improves NFC transmission efficiency and application expansibility, and is suitable for scenes such as mobile payment, digital car keys, intelligent access control and the like.

Inventors

  • Ju Tengxia
  • YU YUE
  • WU TONG

Assignees

  • 南通大学

Dates

Publication Date
20260512
Application Date
20260324

Claims (10)

  1. 1. An NFC encryption authentication system based on algebraic numerology is characterized by comprising an NFC encryption authentication module; The NFC encryption authentication module comprises: The algebraic number domain construction unit is used for constructing a secondary domain or a semicircle domain as an algebraic number domain K, defining algebraic integer rings on the number domain K, and determining in-ring addition, multiplication and ideal operation rules; The key generation unit selects a mutual element non-zero true ideal I, J from the algebraic integer ring, generates a public key PK=I.J and a private key SK=I -1 through ideal operation, and stores the public key and the private key in a device safety area; The data encryption unit is used for converting NFC data to be transmitted into byte streams, grouping and mapping the byte streams into element sequences in algebraic integer rings according to fixed byte lengths, encrypting the element sequences by adopting a public key PK through ideal multiplication to obtain encrypted ring element sequences and transmitting the encrypted ring element sequences through NFC antennas; And the data decryption unit is used for enabling the receiver to execute ideal multiplication inverse operation through the private key SK, restore the original ring element sequence, reversely decode according to a preset mapping rule to obtain the original NFC data, and complete identity authentication.
  2. 2. The NFC encryption authentication system based on algebraic numerology of claim 1 wherein the algebraic number field K is specifically a quadratic number field Wherein D is a positive integer without a square factor.
  3. 3. The NFC encryption and authentication system based on algebraic theory of claim 1, wherein the data encryption unit has a data mapping rule corresponding to an algebraic integer ring element every 4 bytes, and less than 4 bytes uses 0x00 bits.
  4. 4. An NFC encryption authentication system based on algebraic numerology according to any of claims 1-3, wherein the system further comprises an NFC data transfer optimization module; the NFC data transmission optimization module comprises: A data grouping unit for grouping the high-capacity NFC data according to a fixed length of 32 bytes, adopting 0x00 complementary bit for less than 32 bytes at the tail, and recording grouping sequence and total number; the element mapping unit converts each group of data into algebraic integer elements in a quadratic algebraic digital domain K through a polynomial mapping function to finish compact coding; The channel coding unit constructs a4 multiplied by 4 channel coding matrix based on the ideal lattice and performs redundancy coding on the element sequence; And the decoding reconstruction unit is used for removing channel noise and coding redundancy by adopting congruence operation and ideal inversion operation at the receiving end and restoring the original data according to the grouping sequence.
  5. 5. The algebraic digital theory-based NFC encryption authentication system of claim 4, wherein the 4 x 4 channel coding matrix is: The matrix elements are taken from algebraic integers of algebraic number field K.
  6. 6. The algebraic digital theory-based NFC encryption authentication system of claim 4, wherein the high-capacity NFC data comprises a high-definition picture, a device profile, a firmware package.
  7. 7. An NFC encryption authentication system based on algebraic numerology according to any of claims 1-3, wherein the system further comprises an NFC intelligent interaction expansion module; the NFC intelligent interaction expansion module comprises: The user behavior modeling unit is used for collecting user NFC interaction behavior data, abstracting the data into a 5-dimensional behavior vector on a secondary algebraic numerical domain K through algebraic numerical theory vector space theory, and constructing a user behavior algebraic model; When a user enters the NFC induction range, matching the use scene through an ideal matching algorithm on the number domain K to generate and push a corresponding service instruction; and the interaction security enhancement unit takes the timestamp, the action vector and the congruence relation of the number domain as seeds, generates a disposable key through ideal multiplication and congruence operation, and performs one-time encryption on interaction data.
  8. 8. The algebraic numerology based NFC encryption authentication system of claim 6 wherein the 5-dimensional behavior vector is v= (t, id, f, s, m), where t is a timestamp parameter, id is a device identification, f is a frequency of use, s is a scene code, and m is a transaction amount parameter.
  9. 9. The algebraic number theory-based NFC encryption authentication system of claim 6, wherein the one-time key generation formula is: the key validity period is the current interaction period, and the key is immediately invalid after the interaction is completed.
  10. 10. The NFC encryption and authentication system based on algebraic theory of claim 6, wherein the user NFC interaction data comprises a card swiping time, a device ID, a frequency of use, a scene type, a transaction amount, and a collection period of 7 days.

Description

NFC encryption authentication system based on algebraic number theory Technical Field The invention relates to the technical field of Near Field Communication (NFC), in particular to an NFC system for realizing encryption authentication, data transmission optimization and intelligent interaction expansion. Background Near Field Communication (NFC) is widely applied to civilian and industrial scenes such as mobile payment, intelligent access control, electronic ticketing, digital car keys and the like as a short-distance high-frequency wireless communication technology. Along with the continuous expansion of application scenes, the traditional NFC system has obvious defects in the aspects of safety, transmission efficiency and function expansibility: 1. The traditional NFC encryption scheme is based on a conventional symmetric/asymmetric encryption algorithm, is easy to suffer man-in-the-middle attack, data sniffing, replay attack and cryptanalysis attack, and has security risks of user privacy disclosure, funds theft, illegal equipment access and the like; 2. The data transmission efficiency is limited in that the existing NFC transmission coding and channel mechanism is not optimized for large data volume scenes, the high-capacity data transmission rate of high-definition pictures, video streams and the like is low, the anti-interference capability is poor, and the high-rate transmission requirement cannot be met; 3. the application function is single, the traditional NFC only realizes basic identity authentication and data transmission, intelligent interaction is realized without combining with user behaviors, and the application boundary is limited. Algebraic number theory is used as modern mathematical core branch, and comprises mature theory such as number domain, algebraic integer ring, ideal theory, lattice theory, domain-like theory and the like, and can provide high-security bottom mathematical support for the cryptographic system based on the operational characteristics of mathematical problems such as large integer decomposition, ideal operation, discrete logarithm and the like. At present, algebraic number theory is not applied to systemization and engineering in the technical field of NFC, and the existing safety, efficiency and functional bottlenecks of NFC cannot be solved by means of mathematical characteristics of the algebraic number theory. Disclosure of Invention Aiming at the prior art, the NFC encryption authentication system based on algebraic numerology is provided, and the safety, transmission efficiency and application value of the NFC system are improved. The NFC encryption authentication system based on algebraic numerology comprises an NFC encryption authentication module; The NFC encryption authentication module comprises: The algebraic number domain construction unit is used for constructing a secondary domain or a semicircle domain as an algebraic number domain K, defining algebraic integer rings on the number domain K, and determining in-ring addition, multiplication and ideal operation rules; The key generation unit selects a mutual element non-zero true ideal I, J from the algebraic integer ring, generates a public key PK=I.J and a private key SK=I -1 through ideal operation, and stores the public key and the private key in a device safety area; The data encryption unit is used for converting NFC data to be transmitted into byte streams, grouping and mapping the byte streams into element sequences in algebraic integer rings according to fixed byte lengths, encrypting the element sequences by adopting a public key PK through ideal multiplication to obtain encrypted ring element sequences and transmitting the encrypted ring element sequences through NFC antennas; And the data decryption unit is used for enabling the receiver to execute ideal multiplication inverse operation through the private key SK, restore the original ring element sequence, reversely decode according to a preset mapping rule to obtain the original NFC data, and complete identity authentication. Further, the algebraic number field K is specifically a quadratic number fieldWherein D is a positive integer without a square factor. Further, in the data encryption unit, the data mapping rule is that every 4 bytes correspond to an algebraic integer ring element, and less than 4 bytes adopt 0x00 complementary bits. Further, the system also comprises an NFC data transmission optimization module; the NFC data transmission optimization module comprises: A data grouping unit for grouping the high-capacity NFC data according to a fixed length of 32 bytes, adopting 0x00 complementary bit for less than 32 bytes at the tail, and recording grouping sequence and total number; the element mapping unit converts each group of data into algebraic integer elements in a quadratic algebraic digital domain K through a polynomial mapping function to finish compact coding; The channel coding unit constructs a4 multiplied by 4 chann