CN108833118B - Safety access method and system applying rational interpolation containing parameter Thiele type - Google Patents
Safety access method and system applying rational interpolation containing parameter Thiele type Download PDFInfo
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- CN108833118B CN108833118B CN201810828507.4A CN201810828507A CN108833118B CN 108833118 B CN108833118 B CN 108833118B CN 201810828507 A CN201810828507 A CN 201810828507A CN 108833118 B CN108833118 B CN 108833118B
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3234—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving additional secure or trusted devices, e.g. TPM, smartcard, USB or software token
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/08—Network architectures or network communication protocols for network security for authentication of entities
- H04L63/083—Network architectures or network communication protocols for network security for authentication of entities using passwords
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/08—Network architectures or network communication protocols for network security for authentication of entities
- H04L63/0853—Network architectures or network communication protocols for network security for authentication of entities using an additional device, e.g. smartcard, SIM or a different communication terminal
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3226—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using a predetermined code, e.g. password, passphrase or PIN
Abstract
The application discloses a security access method and a system applying a Thiele type continuous rational interpolation containing parameters. The secure access method comprises the following steps: inputting a digital password to the mobile phone; the mobile phone transmits the digital password to a server; the server verifies the mobile phone number and the digital password, and executes the following operations for the condition that the mobile phone number and the digital password are verified: the server takes each digit of the digital password as corresponding given interpolation data, randomly sets the parameter of the Thiele type rational interpolation by using the Thiele type rational interpolation containing the parameter, generates an image corresponding to the parameter, and sends the image to the mobile phone; and the unlocking device receives the image sent from the server as a standard image, scans the image of the mobile phone, and starts an unlocking action by the unlocking mechanism of the unlocking device when the standard image is consistent with the image scanned by the mobile phone.
Description
Technical Field
The present disclosure relates generally to the field of secure access to secure resources, and more particularly, to a secure access method and system using a rational interpolation including a parameter Thiele type.
Background
Typically, in a secure resource system such as doors, computers and other devices, the secure device will be unlocked when the identity and access rights of the user are verified at a verification means physically connected to the door, computer and other device. When a plurality of users are provided, if a uniform password is provided, the problem of leakage is easily caused; and if different passwords are provided for different users, a lot of inconvenience is brought. Therefore, the existing cryptographic technology cannot meet the above requirements, and brings inconvenience.
Disclosure of Invention
In view of the above-mentioned deficiencies or inadequacies in the prior art, it would be desirable to provide a secure access scheme that applies Thiele-type rational interpolation.
In a first aspect, an embodiment of the present application provides a secure access method applying a rational interpolation with parameter Thiele type, including the following steps:
inputting a digital password to the mobile phone;
the mobile phone transmits the digital password to a server;
the server verifies the mobile phone number and the digital password, and executes the following operations for the condition that the mobile phone number and the digital password are verified:
the server takes each digit of the digital password as corresponding given interpolation data, randomly sets the parameter of the Thiele type rational interpolation by using the Thiele type rational interpolation containing the parameter, generates an image corresponding to the parameter, and sends the image to the mobile phone;
and the unlocking device receives the image sent from the server as a standard image, scans the image of the mobile phone, and starts an unlocking action by the unlocking mechanism of the unlocking device when the standard image is consistent with the image scanned by the mobile phone.
The rational interpolation containing the parameter Thiele type is a rational interpolation containing a parameter unitary Thiele type.
The unitary Thiele type rational interpolation containing the parameters is a Thiele type continuous fraction rational interpolation containing single parameters.
The Thiele type continuous fraction rational interpolation containing the single parameter constructs the following Thiele type continuous fraction rational interpolation containing the single parameter lambda;
wherein
The unitary Thiele type rational interpolation containing parameters is single triple node double parameter Thiele type rational interpolation.
The single triple node double-parameter Thiele type rational interpolation constructs the following form of tangential touch rational interpolation containing double parameters alpha and beta
Wherein
The parameter-containing Thiele type rational interpolation is double-double node double-parameter Thiele type rational interpolation.
The double-double node double-parameter Thiele type rational interpolation is specifically to construct the following Thiele continuous fraction rational interpolation containing double parameters phi and delta
Wherein
The digital password is a unified digital password.
In a second aspect, an embodiment of the present application provides a secure access system applying Thiele-type rational interpolation, including:
the mobile phone terminal is configured to input a digital password and transmit the password to the server;
the server is configured to receive the digital password of the mobile phone terminal, verify the mobile phone number and the digital password, and execute the following operations when the mobile phone number and the digital password are verified:
the server takes each digit of the digital password as corresponding given interpolation data, randomly sets the parameter of the Thiele type rational interpolation by using the Thiele type rational interpolation containing the parameter, generates an image corresponding to the parameter, and sends the image to the mobile phone;
and the unlocking device is used for receiving the image sent from the server as a standard image, scanning the image of the mobile phone, and starting an unlocking action when the standard image is consistent with the image scanned by the mobile phone.
The secure access method applying Thiele type rational interpolation provided by the embodiment of the application can provide uniform digital passwords for a plurality of users. The server needs to verify the mobile phone numbers, for example, a company can input the mobile phone numbers of all users into a database of the server, and when the mobile phone number is the same as a certain number stored in the database, the mobile phone number can be verified. Therefore, even if the user leaks the password to someone other than the company, the user will not pass the authentication when the other person uses his/her mobile phone. In case that the user carelessly loses the mobile phone, the user can not pass the authentication because the user needs to input the digital password.
In addition, for the condition of passing the mobile phone number verification and the digital password verification, the parameters can be randomly set and the image corresponding to the set parameters is generated due to the adoption of the Thiele type rational interpolation containing the parameters, and the image is correspondingly randomly generated due to the random setting of the parameters. Compared with the simple number, the image is more difficult to decipher, so that the function of further encryption can be played, and the safety of access is ensured.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings in which:
FIG. 1 is a flow chart illustrating a method for secure access in an embodiment of the present application;
FIG. 2 is a block diagram of a secure access system in an embodiment of the present application;
fig. 3 shows that R is-0.8 when λ is ═ 0.8 in the embodiment of the present application2(x) The image of (a);
fig. 4 shows that when λ is 80 in the embodiment of the present application, R is2(x) The image of (2).
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the described embodiments are only a part, and not all, of the present invention. For convenience of description, only portions related to the invention are shown in the embodiments.
It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be further noted that, unless otherwise explicitly stated or limited, the terms "disposed" and "connected" are to be interpreted broadly, and may be, for example, a fixed connection, a detachable connection, or an integral connection; can be mechanically or electrically connected; the connection may be direct or indirect via an intermediate medium, and may be a communication between the two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The embodiment of the application provides a secure access method applying Thiele-type continued fraction rational interpolation, as shown in fig. 1, including the following steps:
inputting a digital password to the mobile phone;
the mobile phone transmits the digital password to a server;
the server verifies the mobile phone number and the digital password, and executes the following operations for the condition that the mobile phone number and the digital password are verified:
the server takes each digit of the digital password as corresponding given interpolation data, randomly sets the parameter of the Thiele type rational interpolation by using the Thiele type rational interpolation containing the parameter, generates an image corresponding to the parameter, and sends the image to the mobile phone;
and the unlocking device receives the image sent from the server as a standard image, scans the image of the mobile phone, and starts an unlocking action by the unlocking mechanism of the unlocking device when the standard image is consistent with the image scanned by the mobile phone.
The rational interpolation containing the parameter Thiele type is a rational interpolation containing a parameter unitary Thiele type.
The unitary Thiele type rational interpolation containing the parameters is a Thiele type continuous fraction rational interpolation containing single parameters.
The Thiele type continuous fraction rational interpolation containing the single parameter constructs the following Thiele type continuous fraction rational interpolation containing the single parameter lambda;
wherein
The unitary Thiele type rational interpolation containing parameters is single triple node double parameter Thiele type rational interpolation.
The single triple node double-parameter Thiele type rational interpolation constructs the following form of tangential touch rational interpolation containing double parameters alpha and beta
Wherein
The parameter-containing Thiele type rational interpolation is double-double node double-parameter Thiele type rational interpolation.
The double-double node double-parameter Thiele type rational interpolation is specifically to construct the following Thiele continuous fraction rational interpolation containing double parameters phi and delta
Wherein
In some cases, the digital code is a unified one. It is understood that the invention can be implemented for a number of different digital passwords as well for a digital password and is therefore also within the scope of protection of the present application.
In a second aspect, an embodiment of the present application provides a secure access system applying Thiele-type rational interpolation, as shown in fig. 2, including:
the mobile phone terminal 102 is configured to be used for the user 110 to input a digital password and transmit the password to the server;
a server 104 configured to receive the digital password of the mobile phone terminal through the network 103, authenticate the mobile phone number and the digital password, and perform the following operations for the case of authenticating the mobile phone number and the digital password:
the server takes each digit of the digital password as corresponding given interpolation data, randomly sets the parameter of the Thiele type rational interpolation by using the Thiele type rational interpolation containing the parameter, generates an image corresponding to the parameter, and sends the image to the mobile phone;
and the unlocking device 101 is used for receiving the image sent by the server as a standard image, scanning the image of the mobile phone, and starting an unlocking action when the standard image is consistent with the image scanned by the mobile phone.
In addition, it is worth noting that, in the interpolation method common in the prior art, on the premise of interpolation data giving, an interpolation function has uniqueness on interpolation data, cannot modify the shape of a curve or a curved surface without changing given data, cannot completely meet actual requirements, and can meet the situation that a contrast quotient does not exist or cannot reach points when a Thiele continuous fractional rational interpolation is calculated. For any given interpolation condition, aiming at different node distribution conditions, several unitary Thiele type rational interpolations containing parameters are constructed, an interpolation algorithm and an interpolation theorem are given, and the conditions that the condition that a difference quotient does not exist and an unreachable point can be processed in the continuous fractional interpolation are proved to exist.
The following is a detailed description of the theorem and the associated proof.
Rational interpolation of 1-parameter unitary Thiele type
In the interval [ a, b]In the above, the function value { (x) of n +1 mutually different nodes of the known function y ═ f (x)0,y0),(x1,y1),…,(xn,yn) Structure of
Wherein b isi(i-1, …, n) is the inverse quotient if biIf (i) is 1, …, n,) then equation (1) is a Thiele type rational interpolation.
The inverse quotient Table of the form of Table 1 can be constructed
TABLE 1 contrast quotient Table
1.1 Thiele-type continuous rational interpolation with single parameter
Consider any one (x) of the raw data pointsk,yk) (k is 0,1, …, n) as a dual node, and the multiplicity of other data points is kept unchanged, so that
When j is 1, …, k +1, j +1, …, n,
for a given i ═ k +1, k +2, …, n,
when j is k +2, k +3, …, n, for i is j, j +1, …, n,
thiele-type continuous rational interpolation with parameter lambda constructed as follows
Wherein
The table of the inverse quotient corresponding to the formula (6) is shown in Table 2
TABLE 2 single parameter contrast quotient Table
It is demonstrated that the parameter-containing Thiele continuous fraction interpolation function constructed by the formula (6) satisfies the interpolation condition
Rn (0)(xi)＝f(xi)＝yi,i＝0,1,L,n. (7)
And (3) proving that: when i is more than or equal to 0 and less than or equal to k,
(6) the formula is the classic Thiele continuous fractional interpolation, and R is easy to seen (0)(xi)＝f(xi)＝yi,i＝0,1,L,k.
When i is equal to k +1,
when n is more than or equal to i and more than or equal to k +2,
thus having Rn (0)(xi)＝f(xi)＝yi,i＝0,1,…,n.
1.2 Single triple node two parameter Thiele type rational interpolation
Consider the original dataAny one of the points (x)k,yk) (k is 0,1, …, n) as a triple node, the number of other data points is kept unchanged, the following form of tangential rational interpolation with parameters alpha, beta is constructed,
the following algorithm is constructed:
Step 1: value of initialization function
Step 2: when j is 1, …, k +1, j +1, …, n,
step 3: for a given i ═ k +1, k +2, …, n,
step 4: for a given i ═ k +1, k +2, …, n,
step 5: when j is k +2, k +3, …, n, for i is j, j +1, …, n,
step 6: constructing a tangential rational interpolation containing two parameters alpha, beta in the following form
Wherein
TABLE 3A TRIPLE NODE PARAMETER TABLE WITH DOUBLE-PARAMETERS
Rn (1)(xi)＝f(xi)＝yi,i＝0,1,…,n. (16)
And (3) proving that: when i is more than or equal to 0 and less than or equal to k,
the formula (14) is a classical Thiele continuous fraction interpolation, which is easy to see Rn (0)(xi)＝f(xi)＝yi,i＝0,1,…,k.
When i is equal to k +1,
when n is more than or equal to i and more than or equal to k +2,
thus having Rn (1)(xi)＝f(xi)＝yi,i＝0,1,L,n.
1.3 double node double parameter Thiele type rational interpolation
Consider any two nodes (x) in the raw data pointk,yk)((xs,ys),s>k, s, k ═ 0,1, …, n) are all madeFor a double node, the multiplicity of other data points is kept constant, and a tangential rational interpolation with parameters phi and delta in the form of
The following algorithm is constructed:
Step 1: value of initialization function
Step 2: when j is 1, …, k +1, j +1, …, n,
step 3: for a given i ═ k +1, k +2, …, n,
step 4: when j is k +2, k +3, …, s +1, j +1, …, n,
step 5: for a given i ═ s +1, s +2, …, n,
step 6: when j is s +2, s +3, …, n, for i is j, j +1, …, n,
step 7: constructing a Thiele continuous fraction rational interpolation containing two parameters phi and delta in the following form
Wherein
TABLE 4 two-fold node inverse quotient table with two parameters
The following theorem can be found by analogy with the demonstration in theorem 1
Theorem 3 for a given interpolated data { (x)0,y0),(x1,y1),…,(xn,yn) Satisfy the interpolation condition by the rational interpolation function determined by the expressions (24) - (25)
Rn (2)(xi)＝f(xi)＝yi,i＝0,1,…,n. (26)
2 example of numerical values
Several examples will be given in this section to illustrate the effectiveness of the method of this chapter, examples 1 to 3 being unary interpolation scenarios. Example 1 is Runge interpolation, and the error can be greatly reduced by using the method in this chapter. Example 2 is the case where the contrast quotient does not exist, example 3 is the case of interpolation with unreachable points, the shape of the curve can be changed by adjusting the parameters by example 3, and example 4 is the case of binary interpolation.
Example 1 for a function
Common high-order continuous rational interpolation has instability, the calculation is carried out by using a Thiele continuous rational interpolation containing parameters, and only the interpolation interval [ -1,0 ] is discussed due to the symmetry of functions]The situation is described.
TABLE 5 interpolation Table
From table 2, it can be obtained that the Thiele-type continuous rational interpolation containing parameters has better effect, and some novel Thiele-type continuous rational interpolation can be obtained by selecting parameters.
Example 2[27] the point interpolation data { (0,0), (1,1), (2,0.5), (3,3), (4, -0.5), (5,5) } is given, and rational interpolation satisfying the condition is found.
After calculating the difference quotient and knowing that the difference quotient does not exist, adjusting (3,3), (4, -0.5) the two nodes according to the method can construct a rational interpolation function,
is easy to see R1(x) If the interpolation condition is not met, the method in the chapter considers (0,0) as a double node, and the parameter c (c ≠ 0) is introduced
It is easy to prove that the interpolation condition is satisfied.
Example 3 given interpolation data is set as follows
TABLE 6 interpolation data Table
The corresponding Thiele type continuous fraction interpolation inverse difference quotient table is shown in Table 8
TABLE 7 inverse quotient Table
So that its Thiele-type continuous fraction interpolation is
Due to r (x)0) R (2) ≠ 0, so that (2,1) is an unreachable point of r (x). According to the algorithm in the chapter, the weight of the nodes (2,1) is increased, the contact-cut interpolation with the first derivative at the points (2,1) is constructed, the parameter lambda (lambda is not equal to 0) is introduced, the inverse difference quotient table shown in the upper table 4 is constructed, and the corresponding Thiele type contact-cut rational interpolation is obtained
After the verification, the user can verify that the user can not use the electronic device,
R2(xi)＝fi(i＝0,1,2)
when λ is-0.8
When λ is 80
When λ is-0.8, R2(x) When λ is 80, R is shown in fig. 12(x) As shown in fig. 2.
According to the results, through strategic adjustment of the repeated number of interpolation nodes, parameters are introduced in the construction process of Thiele type continuous fractional interpolation, several parameter-containing unitary Thiele type rational interpolations which are simple in calculation and have explicit mathematical expressions are constructed, and the interpolation algorithm, the interpolation theorem and the dual interpolation are researched. The new interpolation format is easy to apply and convenient for theoretical research, and the function can modify the function value of any point in the interpolation area by selecting proper parameters on the premise of not changing given interpolation data, thereby modifying the shape of a curve or a curved surface.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the invention as referred to in the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.
Claims (10)
1. A secure access method using rational interpolation with parameter Thiele type, comprising the steps of:
inputting a digital password to the mobile phone;
the mobile phone transmits the digital password to a server;
the server verifies the mobile phone number and the digital password, and executes the following operations for the condition that the mobile phone number and the digital password are verified:
the server takes each digit of the digital password as corresponding given interpolation data, randomly sets the parameter of the Thiele type rational interpolation by using the Thiele type rational interpolation containing the parameter, generates an image corresponding to the parameter, and sends the image to the mobile phone;
and the unlocking device receives the image sent from the server as a standard image, scans the image of the mobile phone, and starts an unlocking action by the unlocking mechanism of the unlocking device when the standard image is consistent with the image scanned by the mobile phone.
2. The method of claim 1, wherein the parametric Thiele-type rational interpolation is a parametric unitary Thiele-type rational interpolation.
3. The method of claim 2, wherein the parametric unitary Thiele-type rational interpolation is a single parametric Thiele-type continued fraction rational interpolation.
4. The security access method applying the Thiele-type rational interpolation with parameter as claimed in claim 3, wherein the Thiele-type continuous rational interpolation with single parameter constructs a Thiele-type continuous rational interpolation with single parameter λ of the following form;
wherein
5. The secure access method using parametric Thiele-type rational interpolation of claim 2, wherein the parametric univariate Thiele-type rational interpolation is a single triple-node two-parametric Thiele-type rational interpolation.
6. The method according to claim 5, wherein the single triple node double parameter Thiele type rational interpolation constructs a tangential touch rational interpolation with double parameters α, β of the following form
Wherein
7. The method of claim 2, wherein the parametric Thiele-type rational interpolation is a dual-node dual-parametric Thiele-type rational interpolation.
8. The method according to claim 7, wherein the double-dual node double-parameter Thiele type rational interpolation is a Thiele continuous fraction rational interpolation with double parameters phi and delta
Wherein
9. The method of any one of claims 1 to 8, wherein the digital code is a unified digital code.
10. A secure access system employing rational interpolation with parameter Thiele-type, comprising:
the mobile phone terminal is configured to input a digital password and transmit the password to the server;
the server is configured to receive the digital password of the mobile phone terminal, verify the mobile phone number and the digital password, and execute the following operations when the mobile phone number and the digital password are verified:
the server takes each digit of the digital password as corresponding given interpolation data, randomly sets the parameter of the Thiele type rational interpolation by using the Thiele type rational interpolation containing the parameter, generates an image corresponding to the parameter, and sends the image to the mobile phone;
and the unlocking device is used for receiving the image sent from the server as a standard image, scanning the image of the mobile phone, and starting an unlocking action when the standard image is consistent with the image scanned by the mobile phone.
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