CN101217362B - An RFID Communication Security Mechanism Based on Dynamic Randomized DRNTRU Public Key Encryption System - Google Patents

Abstract

The invention discloses an RFID communication security mechanism established based on a dynamic randomized DRNTRU (Dynamic, Randomized Number Theory Research Unit) public key encryption system. The RFID system communication security mechanism established by using the dynamic randomization DRNTRU public key encryption system proposed by the present invention can not only effectively solve the security problem of the RFID system, but also the method is novel, simple and easy to implement, and does not need to exhaustively search for keys and labels Code TID (Tag Identifier), does not require key synchronization, only one-way authentication is required, it is very suitable for RFID systems that only have limited resources and require high-speed response.

Description

An RFID Communication Security Mechanism Based on Dynamic Randomized DRNTRU Public Key Encryption System

technical field

The invention belongs to the technical field of communication, and is particularly suitable for the identification technology of radio frequency tags.

Background technique

With the widespread application of RFID (Radio Frequency Identification), the security issues of RFID systems are becoming more and more prominent. The main security issues in RFID systems include confidentiality, traffic analysis and traceability, and personal privacy leakage. These issues have been seriously It hinders the further development of RFID and becomes one of the key problems to be solved urgently in the development of RFID system. Therefore, it has also attracted the attention and investment of many network security scholars in the industry, and various solutions and strategies have been proposed, such as using hash functions, symmetric keys, etc. The system requires the server to exhaustively search for tags in the back-end database. The identification code TID and key of the tag, some systems need the key synchronization between the server and the tag, and the algorithm to maintain the key synchronization between the server and the tag is extremely complicated and difficult to implement, so it will consume a lot of resources of the system, such as execution time and The storage space is not suitable for RFID systems that require high-speed response and only have limited resources. So far, the industry has still failed to propose a safe, efficient, practical, and low-cost solution to the communication security problem of RFID systems. The present invention proposes a dynamic randomized DRNTRU (Dynamic, Randomized Number Theory Research Unit) public key encryption system for the first time in the field of RFID system security, and proposes to introduce randomization parameters into the algorithm based on the NTRU public key encryption system to make it dynamic and randomized. The DRTRUN public key cryptosystem and apply it to RFID system. The RFID system communication security mechanism established by using the dynamic randomized DRNTRU public key encryption system not only effectively solves the security problem of RFID system communication, but also has the characteristics of novelty, simplicity, and easy implementation. It does not require exhaustive key search and key synchronization. Ideal for RFID systems with limited resources.

Contents of the invention

The purpose of the present invention is to provide a kind of RFID communication security mechanism based on dynamic randomization DRNTRU public key encryption system establishment, and this scheme can satisfy the reader (Reader) and label (Tag) in the mid-level and high-level radio frequency identification (RFID) technology. ) The requirements for the security mechanism of the wireless communication between.

In order to achieve the above object, the present invention is achieved by taking the following technical solutions:

A kind of RFID communication security mechanism based on the dynamic randomization DRNTRU public key encryption system, it is characterized in that when the RFID system is initial, the server uses the dynamic randomization DRNTRU public key encryption system to generate the public key h _key and the private key (f _key , F _p ), and assign a unique identification code TID to each tag, the server will store the identification code TID and the relevant information of the item with the tag in the tag and the back-end database at the same time, and store the public key h _key and private key (f _key , F _p ) are stored in the label and the back-end database respectively, and the communication authentication protocol steps of the RFID system are as follows:

(1) Reader (Reader)→Tag (Tag): The reader selects a random number R _r from the polynomial set L _m , sends an authentication request Query to the tag, and sends R _r to the tag at the same time;

再从多项式集合L_ω中选取一随机数ω，利用公钥h_key对C进行加密运算然后将(PID，R_t)发送给读写器，读写器再将(PID，R_t，R_r)转发给服务器；(2) Tag (Tag) → Reader (Reader) → Server (Server): After the tag receives the authentication request (Query, R _r ) sent by the reader, it first selects a random number from the polynomial set L _m The number R _t is calculated from

Then select a random number ω from the polynomial set L _ω , and use the public key h _key to encrypt C Then send (PID, R _t ) to the reader, and the reader forwards (PID, R _t , R _r ) to the server;

和

获得C，因为

对C进行R₁＝Z||C，再对读写器转发来的(R_t，R_r)进行

然后将两者进行异或运算：

如果结果为0，则认证通过，再截取g(C，0，63)，即可得到标识码TID；否则，认证失败，拒绝接受标识码TID并停止操作。(3) Server (Server): After receiving (PID, R _t , R _r ), the server first uses the private key (f _key , F _p ) to decode the PID:

and

get a C because

Perform R ₁ =Z||C on C, and then perform the (R _t , R _r ) forwarded by the reader

Then XOR the two together:

If the result is 0, the authentication is passed, and then g(C, 0, 63) is intercepted to obtain the identification code TID; otherwise, the authentication fails, the identification code TID is rejected and the operation is stopped.

变换，即可将随机化参数R_r，R_t引入NTRU加密系统，使NTRU加密系统成为动态随机化DRNTRU公钥加密系统。令：ID，R_r，R_t∈L_m，ω∈L_ω，选择NTRU的参数p＝3，则L_m{m∈R：m的系数在[-1，1]区间}，标识码TID为64bits的二进制数，用ID表示，仅占用ID的[ID₀，ID₁，...，ID₆₃]，其余的[ID₆₄，ID₆₅，...，ID_N-1]用于传输随机数R_r，R_t，定义：令v，u，w∈L_m，将v，u，w用向量表示，其长度为N，The dynamic randomized DRNTRU public key encryption system of the present invention is based on the NTRU public key encryption system, and the randomization parameters R _r and R _t are introduced into the NTRU encryption system. The specific method is to modify the original encryption algorithm The plaintext m of is modified, and it is

Transformation, the randomization parameters R _r , R _t can be introduced into the NTRU encryption system, making the NTRU encryption system a dynamic randomized DRNTRU public key encryption system. Order: ID, R _r , R _t ∈ L _m , ω ∈ L _ω , select NTRU parameter p=3, then L _m {m ∈ R: the coefficient of m is in the interval [-1, 1]}, the identification code TID It is a binary number of 64bits, represented by ID, only occupies ID [ID ₀ , ID ₁ , ..., ID ₆₃ ], and the rest [ID ₆₄ , ID ₆₅ , ..., ID _N-1 ] is used for transmission Random number R _r , R _t , definition: Let v, u, w∈L _m , express v, u, w with vector, its length is N,

v=[v ₀ , v ₁ , . . . , v ₆₃ , v ₆₄ , v ₆₅ , . . . , v _N-1 ],

u=[u ₀ , u ₁ , . . . , u ₆₃ , u ₆₄ , u ₆₅ , . . . , u _N-1 ],

w=[w ₀ , w ₁ , . . . , w ₆₃ , w ₆₄ , w ₆₅ , . . . , w _N-1 ],

||Join operation: w=v||u=[v ₀ , v ₁ ,..., v ₆₃ , u ₆₄ , u ₆₅ ,..., u _N-1 ],

g(w, i, j) interception operation: g(w, i, j)=[w _i , w _i+1 , . . . , w _j ].

The features of the present invention are:

1. The dynamic randomization DRNTRU public key encryption system is proposed for the first time. Since the RFID system has special requirements for security issues such as anti-tracking, anti-traffic analysis, and privacy protection, the existing NTRU public key encryption system cannot meet the special needs of anti-tracking, anti-traffic analysis, and privacy protection for the RFID system. The NTRU public key encryption system must have the function of dynamic and random changes. This scheme is based on the NTRU public key encryption system, and introduces randomization parameters into the encryption algorithm, making it a new public key encryption system with dynamic and random changing functions - dynamic randomization DRNTRU public key encryption system. This encryption method not only has the characteristics of easy key generation of NTRU public key encryption system, rapid encryption and decryption, short key and high security performance, low performance requirements for bandwidth, processor and memory, and less system resource occupation, but also has the advantages of New features that change dynamically and randomly.

2. For the first time, it is proposed to use the dynamic randomized DRNTRU public key encryption system to establish the security mechanism of the RFID system, and apply the dynamic randomized DRNTRU public key encryption system to the RFID system. The RFID system communication security mechanism thus established can effectively solve the problem of RFID Special security issues that the system has. In addition, this scheme realizes the one-way authentication of the communication protocol of the RFID system. Compared with the two-way authentication, the one-way authentication is simpler and faster, and is more suitable for the RFID system that requires high-speed response. Since this method only uses the plaintext m in the DRNTRU encryption algorithm to realize the ID and Simultaneous transmission reduces transmission time and reduces bandwidth. The whole system only uses a pair of public key and private key, no need to exhaustively search the key in the back-end database, no need for key synchronization, which reduces the complexity of key storage and key management systems, saving a lot of time and space in the system . Because only the server has the private key, it can unlock the ciphertext information of a tag, so only one-way authentication is required for the tag. And because the server can directly obtain the encrypted identification code TID through authentication and decryption, there is no need to exhaustively search the identification code TID in the back-end database, and it is easy to implement in tags of RFID systems that require high speed and only have limited resources.

The beneficial effects of the present invention are:

Using the RFID system communication security mechanism established by the dynamic randomized DRNTRU public key encryption system proposed by the present invention, the entire system only needs a pair of public key and private key, all tags are encrypted with the public key, and the server uses the private key to decrypt. The DRNTRU public key encryption system encrypts the ID (TID) and the ciphertext PID generated each time is dynamically and randomly changed, so it can effectively resist traffic analysis and tracking attacks, and because each identification code TID is different, using DRNTRU public key After encrypted with the key, the ID in the communication transmits the PID in a changing ciphertext, so it can ensure that the PID information read by each label and each authentication is different, so the confidentiality of the transmitted information can be realized, and the denial of service attack, re- Unleash attacks, active attacks, etc., to meet the special requirements of the RFID system communication security mechanism.

The RFID system communication security mechanism established by the dynamic randomized DRNTRU public key encryption system proposed by the present invention can effectively solve the problem that the RFID system can realize the confidentiality of transmission information, resist denial of service attacks, replay attacks, active attacks, and resist traffic analysis and Attacks such as tracking, and do not need to exhaustively search the key and tag TID, do not need to update the key, the key storage and management are simple, novel, simple and easy to implement, therefore, the present invention effectively solves the communication security problem of the RFID system at the same time It also has the characteristics of fast response speed, less required resources, and easy implementation, and is very suitable for establishing a communication security mechanism for RFID systems.

The table below lists the security performance comparison between the existing security protocol and the security protocol of the present invention.

Table 1 Comparison of security performance of various methods

Description of drawings

Fig. 1 is a schematic diagram of the communication authentication protocol of the RFID system according to the present invention.

Detailed ways

1. Establish a dynamic randomized DRNTRU public key encryption system

1NTRU public key encryption system

The encryption of the NTRU public key encryption system uses a hybrid system based on polynomial algebra and logarithmic p and q reduction modulus, while decryption uses a non-hybrid system based on probability theory. The security of NTRU is based on the interaction of polynomials, mixed operations of different moduli, and the mathematical problem of finding extremely short vectors from a very large dimensional lattice in number theory. Since the algorithm only uses simple modular multiplication and modular inversion operations, it has the advantages of easy key generation, fast encryption and decryption, short key and high security performance, and low performance requirements for bandwidth, processor, and memory. Occupy the system With few resources and other characteristics, NTRU has attracted great attention in the field of cryptography, and has been developed and improved rapidly, and has achieved good results in practical applications.

An NTRU public-key encryption system is based on three integer parameters (N, p, q) and four polynomial sets L _f , L _g , L _ω , L _m whose highest order coefficient is N-1. p and q are not necessarily prime numbers, but gcd(p, q)=1 is required, and q is far greater than p. NTRU is built on the integer coefficient polynomial ring R=Y[X]/(X ^M -1), an element A∈R can be expressed as a polynomial or a vector:

来表示环R上的乘法，这个乘法可以表示为一个循环卷积：

use

To represent the multiplication on the ring R, this multiplication can be expressed as a circular convolution:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&equiv;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}$

Among them, the polynomial set L _f , L _g , L _ω , and L _m meet the following requirements: L _m = {m∈R: the coefficient of m is located in the interval [-(p-1)/2, (p-1)/2]}

Definition: L(d ₁ , d ₂ )={F∈R: F has d ₁ coefficient as 1, d ₂ coefficients as -1, and the remaining coefficients as 0}, and then select three positive integers d _f , d _g , d _ω , let the polynomial sets L _f , L _g , L _ω respectively satisfy: L _f ＝L(d _f , d _f -1), L _g ＝L(d _g , d _g ), L _ω ＝L(d _ω ，d _ω )

1.1 Key Generation

其中F_p和F_q可以使用扩展的欧几里德算法来计算。然后计算公钥：

多项式h_key就是NTRU公钥加密系统的公钥，而多项式f_key即为NTRU的私钥，同时将F_p与f_key一起保存，共同用作私钥。When the NTRU public key encryption system generates a key, it first randomly selects two polynomials f _key ∈ L _f , g ∈ L _g . It is required that the inverse F _p and F _q of f _key with respect to modulus p and modulus q both exist, that is to say, satisfy:

where F _p and F _q can be calculated using the extended Euclidean algorithm. Then calculate the public key:

The polynomial h _key is the public key of the NTRU public key encryption system, and the polynomial f _key is the private key of NTRU. At the same time, F _p and f _key are stored together as the private key.

1.2 encryption

e就是S发给R的密文。During communication, assuming that the sender S wants to send a message m to the receiver R, S first selects the message m to be sent from the plaintext set L _m . Then randomly select a polynomial ω from L _ω , and use R's public key h _key to calculate:

e is the ciphertext sent by S to R.

1.3 Decryption

计算，即可重新得到S发来的明文m。When the receiver R receives the ciphertext message e sent by S, R uses its own private key (f _key , F _p ) to decrypt it. R first has to calculate: Select the coefficient of a in [-q/2, q/2], and then perform a

By calculating, the plaintext m sent by S can be obtained again.

The decryption principle is:

$\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; \&equiv;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; key</span>}}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; \&equiv;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; key</span>}}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; p\&omega;</span>}<span\; class="notranslate">\; \&CircleTimes;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; key</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; key</span>}}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>$

$=f_{\mathrm{key}}\&CircleTimes;\mathrm{p\&omega;}\&CircleTimes;f_q\&CircleTimes;g+f_{\mathrm{key}}\&CircleTimes;m\left(\mathrm{mod}q\right)$ (∵ $h_{\mathrm{key}}\&equiv;f_q\&CircleTimes;g\left(\mathrm{mod}q\right)$ )

$=\mathrm{p\&omega;}\&CircleTimes;g+f_{\mathrm{key}}\&CircleTimes;m\left(\mathrm{mod}q\right)$ (∵ $f_p\&CircleTimes;f_{\mathrm{key}}\&equiv;1\left(\mathrm{mod}p\right)$ )

由于对NTRU参数选择地严格限制，几乎总是可以保证它的所有系数都在[-q/2，q/2]内，所以对它的系数进行模q后，多项式仍然保持不变，因而也就恢复了原多项式：

再把a模p后就得到了多项式

再与F_p相乘，就又重新得到了消息m。Consider the last polynomial

Due to the strict restrictions on the selection of NTRU parameters, it can almost always be guaranteed that all its coefficients are in [-q/2, q/2], so after modulo q on its coefficients, the polynomial remains unchanged, and thus The original polynomial is restored:

Then modulo a to p to get the polynomial

Multiplying it with F _p again gives the message m again.

2 Dynamic randomization DRNTRU public key encryption system

可知：当对一个固定的消息m加密后得到的密文都始终相同，因而无法满足RFID系统的安全要求，必须使其具备动态、随机变化功能，因而本发明以NTRU公钥加密系统为基础，将随机化参数引入该算法，使NTRU算法成为具有动态的、随机变化能力的动态随机化DRNTRU公钥加密系统。Since the security mechanism of the RFID system not only requires the confidentiality of the transmitted information, but also resists attacks such as denial of service and replaying information, it must also be able to resist traffic analysis, tracking attacks, and solve special security issues of the RFID system such as privacy. Therefore, it must be ensured that the identification code TID information read by each tag in each authentication must not only be communicated in ciphertext, but also be transmitted in dynamic and randomly changing ciphertext. In the NTRU public key encryption system, by the encryption formula

It can be seen that the ciphertext obtained after encrypting a fixed message m is always the same, so it cannot meet the security requirements of the RFID system, and it must be equipped with dynamic and random changing functions. Therefore, the present invention is based on the NTRU public key encryption system. The randomization parameters are introduced into the algorithm, so that the NTRU algorithm becomes a dynamic randomized DRNTRU public key encryption system with the ability of dynamic and random changes.

In the present invention, let: ID, R _r , R _t , Z∈L _m , ω∈L _ω , for the convenience of description, the vector representation of ID, R _r , R _t , Z is used here. Select the parameter p=3 of NTRU, then L _m {m∈R: the coefficient of m is in the [-1, 1] interval}, the identification code TID is a binary number of 64 bits, which can be represented by ID. Since the identification code TID is 64 bits, therefore It only occupies [ID ₀ , ID ₁ , . . . , ID ₆₃ ] of the ID, and the rest [ID ₆₄ , _{ID 65 ,} . R _r , R _t represent the random numbers used in communication authentication, which can be transmitted using [ID ₆₄ , ID ₆₅ , ..., ID _N-1 ] bits, so that random numbers can be successfully introduced into the NTRU encryption algorithm without To increase communication time and bandwidth, set Z=[0, . . . , 0].

Definition: let v, u, w∈L _m , express v, u, w with a vector whose length is N,

v=[v ₀ , v ₁ , ..., v ₆₃ , v ₆₄ , v ₆₅ , ..., v _N-1 ] and u=[u ₀ , u ₁ , ..., u ₆₃ , u ₆₄ , _u65 ,..., _uN-1 ]

w=[w ₀ , w ₁ , . . . , w ₆₃ , w ₆₄ , w ₆₅ , . . . , w _N-1 ]

·||Join operation: w=v||u=[v ₀ , v ₁ ,..., v ₆₃ , u ₆₄ , u ₆₅ ,..., u _N-1 ]

g(w, i, j) interception operation: g(w, i, j)=[w _i , w _i+1 , . . . , w _j ]

：为异或运算·

: XOR operation

·Other variables and operations used in the authentication process are consistent with the NTRU public key encryption system.

的明文m进行了修改处理，将其进行

变换，即可将随机化参数R_r，R_t引入本加密系统，使NTRU算法成为具有动态的、随机变化能力的动态随机化DRNTRU公钥加密系统。The specific method of introducing randomization parameters into the NTRU encryption system is to modify the original encryption algorithm

The plaintext m of has been modified, and it will be

In other words, the randomization parameters R _r and R _t can be introduced into the encryption system, so that the NTRU algorithm can become a dynamic randomization DRNTRU public key encryption system with dynamic and random changing capabilities.

Notes:

1. Due to ID, R _r , R _t ∈ L _m , both polynomial representation and vector representation can be used in NTRU public key encryption system. In order to be consistent with NTRU representation, the present invention still uses polynomial representation, only in connection operation and interception For the convenience of expression, it is treated as a vector during operation, so ID, R _r , R _t , Z are not represented by the common expression method of bold lowercase vector.

2. The present invention refers to random polynomials and random vectors as random numbers.

2. Establish an RFID communication security mechanism based on a dynamic randomized DRNTRU public key encryption system

2.1 Initial condition setting

At the beginning of the RFID system, the server uses the DRNTRU public key encryption system to generate the public key h _key and private key (f _key , F _p ), and assigns a unique identification code TID to each tag (which can be completed by the manufacturer), and the server will The identification code TID and the relevant information of the item (the item with the tag) are stored in the tag and the back-end database at the same time, and the public key h _key and the private key (f _key , F _p ) are stored in the tag and the back-end database respectively. The public key h _key and private key (f _key , F _p ) are generated by the server when the system is established, and the server keeps the private key (f _key , F _p ) secretly, and distributes the public key h _key to each At the same time, the identification code TID is stored in each corresponding tag through a secure channel, so the identification code TID and the private key (f _key , F _p ) are considered safe and confidential in this system.

2.2 Authentication steps

The communication authentication protocol of the RFID system is shown in Figure 1, and the authentication steps are as follows:

1. Reader→Tag: The reader selects a random number R _r from the polynomial set L _m , sends an authentication request Query to the tag, and sends R _r to the tag at the same time;

再从多项式集合L_ω中选取一随机数ω，利用公钥h_key对C进行加密运算

然后将(PID，R_t)发送给读写器，读写器再将(PID，R_t，R_r)转发给服务器；2. Tag→Reader→Server: After the tag receives the authentication request (Query, R _r ) sent by the reader, it first selects a random number R _t from the polynomial set L _m to calculate

Then select a random number ω from the polynomial set L _ω , and use the public key h _key to encrypt C

Then send (PID, R _t ) to the reader, and the reader forwards (PID, R _t , R _r ) to the server;

和

获得C，因为

对C进行R₁＝Z||C，再对读写器转发来的(R_t，R_r)进行

然后将两者进行异或运算：

如果结果为0，则认证通过，再截取g(C，0，63)，即可得到标识码TID(利用TID就可直接在后端数据库中读取该标识码TID对应的标签信息，如果后端数据库中没有该标识码TID，则也认为其为非法标签拒绝接受而停止操作)；否则，认证失败，拒绝接受标识码TID并停止操作。3.Server: After receiving (PID, R _t , R _r ), the server first uses the private key (f _key , F _p ) to decode the PID:

and

get a C because

Perform R ₁ =Z||C on C, and then perform the (R _t , R _r ) forwarded by the reader

Then XOR the two together:

If the result is 0, the authentication is passed, and then intercept g(C, 0, 63) to obtain the identification code TID (by using TID, you can directly read the label information corresponding to the identification code TID in the back-end database, if later If there is no such identification code TID in the terminal database, it is also considered as an illegal label and the operation is stopped); otherwise, the authentication fails, the identification code TID is rejected and the operation is stopped.

The variables and expressions described in the above-mentioned specific implementation are described below:

variable:

L _f , L _g , L _ω , L _m : It is a polynomial set with four integer coefficients whose highest order coefficient is N-1, and meets the following requirements: L _m = {m∈R: the coefficient of m is located in the interval [-( p-1)/2, (p-1)/2]}, where N, p, q are three integers, p, q do not have to be prime numbers, but require gcd(p, q) = 1, and q is much greater than p.

R: a polynomial ring with integer coefficients R=Y[X]/(X ^N -1).

A: It is an element A∈R, and its vector form can be expressed as:

R _r : the random number generated by the reader, R _r ∈ L _m .

R _t : the random number generated for the label, R _t ∈ L _m .

Z: N-dimensional zero vector, Z∈L _m .

ID: is the vector representation of the tag's identification code TID, ID∈L _m .

PID: is the ciphertext representation of the tag's identification code TID vector, PID∈L _m .

f _key : The private key generated by the DRTUN public key encryption system.

h _key : the public key generated by the DRTUN public key encryption system

F _p : the inverse F _p modulo p, which satisfies:

F _q : the inverse F _q with respect to modulo q, which satisfies:

definition:

Definition 1. If a and b are integers, then a and b are said to be congruent modulo n, which is denoted as a≡b(modn).

Definition 2. The non-negative number d is called the greatest common factor of a and b, which is denoted as d=gcd(a, b).

Definition 3: L(d ₁ , d ₂ )={F∈R: F has d ₁ coefficient as 1, d ₂ coefficients as -1, and the remaining coefficients as 0}, and then select three positive integers d _f , d _g , d _ω , suppose the polynomial sets L _f , L _g , L _ω respectively satisfy: L _f ＝L(d _f , d _f -1), L _g ＝L(d _g , d _g ), L _ω ＝L( d _ω ，d _ω )

Definition 4: let v, u, w ∈ L _m , express v, u, w with a vector whose length is N,

v=[v ₀ , v ₁ , ..., v ₆₃ , v ₆₄ , v ₆₅ , ..., v _N-1 ] and u=[u ₀ , u ₁ , ..., u ₆₃ , u ₆₄ , _u65 ,..., _uN-1 ]

w=[w ₀ , w ₁ , . . . , w ₆₃ , w ₆₄ , w ₆₅ , . . . , w _N-1 ]

Operation:

||: join operation w=v||u=[v ₀ , v ₁ ,..., v ₆₃ , u ₆₄ , u ₆₅ ,..., u _N-1 ]

g(w, i, j): for interception operation g(w, i, j)=[w _i , w _i+1 ,..., w _j ]

：为异或运算

: XOR operation

: Represents the multiplication on the ring R, which can be expressed as a circular convolution:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&equiv;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; mod</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}$

Claims (2)

1. An RFID secure communication method based on dynamic randomization DRNTRU public key encryption system is characterized in that: when the RFID system was initial, the server uses dynamic randomization DRNTRU public key encryption system to generate public key h _key and private key (f _key , F _p ), where the public key h _key and private key (f _key , F _p ) are generated as follows: When the NTRU public-key encryption system generates a key, it first randomly selects two polynomials f _key ∈ L _f , g ∈ L _g , and requires that the inverses F _p and F q of f _key with respect to modulus p and modulus _q exist, that is, satisfy:

where F _p and F _q can be calculated using the extended Euclidean algorithm, and then calculate the public key: The polynomial h _key is the public key of the NTRU public key encryption system, and the polynomial f _key is the private key of NTRU. At the same time, F _p and f _key are stored together and used as the private key (f _key , F _p ); After the public key h _key and private key (f _key , F _p ) are generated, a unique identification code TID is assigned to each tag, and the server stores the identification code TID and the relevant information of the item with the tag in both the tag and the tag. The back-end database stores the public key h _key and the private key (f _key , F _p ) in the tag and the back-end database respectively. The communication authentication protocol steps of the RFID system are as follows: (1) Reader (Reader)→Tag (Tag): The reader selects a random number R _r from the polynomial set L _m , sends an authentication request Query to the tag, and sends R _r to the tag at the same time; (2) Tag (Tag) → Reader (Reader) → Server (Server): After the tag receives the authentication request (Query, R _r ) sent by the reader, it first selects a random number from the polynomial set L _m The number R _t is calculated from

Then select a random number ω from the polynomial set L _ω , and use the public key h _key to encrypt C Then send (PID, R _t ) to the reader, and the reader forwards (PID, R _t , R _r ) to the server; (3) Server (Server): After receiving (PID, R _t , R _r ), the server first uses the private key (f _key , F _p ) to decode the PID:

and

get a C because

Perform R ₁ =Z||C on C, and then perform the (R _t , R _r ) forwarded by the reader

Then XOR the two together:

If the result is 0, the authentication is passed, then intercept g(C, 0, 63) to obtain the identification code TID; otherwise, the authentication fails, refuse to accept the identification code TID and stop the operation; The variables, definitions and operation symbols involved in the above scheme are described as follows: L _f , L _g , L _ω , L _m : a collection of four integer coefficient polynomials with the highest coefficient of N-1 p, q: two integers, p, q do not have to be prime numbers, but require gcd(p, q) = 1, and q is much larger than p R _r : the random number generated by the reader, R _r ∈ L _m R _t : random number generated for the label, R _t ∈ L _m Z: N-dimensional zero vector, Z∈L _m ID: is the vector representation of the tag's identification code TID, ID∈L _m PID: is the ciphertext representation of the tag's identification code TID vector, PID∈L _m f _key : the private key generated by the DRTUN public key encryption system h _key : the public key generated by the DRTUN public key encryption system F _p : the inverse F _p modulo p, which satisfies:

F _q : the inverse F _q with respect to modulo q, which satisfies:

||: join operation g(C, 0, 63): Indicates that 0 to 63 bits of the vector C are intercepted using the interception operation g(w, i, j) mod: modulo operation

XOR operation

Represents the multiplication on the ring R, which can be expressed as a circular convolution:

2. the RFID secure communication method based on dynamic randomization DRNTRU public key encryption system according to claim 1 is characterized in that: described dynamic randomization DRNTRU public key encryption system is based on NTRU public key encryption system, will The randomization parameters R _r , R _t are introduced into the NTRU encryption system, making the NTRU encryption system a dynamic randomized DRNTRU public key encryption system. The specific method of introducing the randomization parameters R _r , R _t into the NTRU encryption system is to modify the original encryption algorithm

The plaintext m of is modified, and it is

Transformation, where ID, R _r , R _t ∈ L _m , ω ∈ L _ω , select NTRU parameter p=3, then L _m = {m ∈ R: the coefficient of m is in the interval [-1, 1]}, identify The code TID is a binary number of 64 bits, represented by ID, which only occupies [ID ₀ , ID ₁ , ..., ID ₆₃ ] of Id, and the rest [ID ₆₄ , ID ₆₅ , ..., ID _N-1 ] Used to transmit random numbers R _r , R _t .

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