CN113920548A - Reusable robust fuzzy extraction method based on fingerprints - Google Patents

Abstract

The invention belongs to the field of biological feature processing, and discloses a reusable robust fuzzy extraction method based on fingerprints, which comprises the following specific steps: 1. preprocessing a fingerprint image; 2. extracting characteristics; 3. constructing a plane rectangular coordinate system; 4. reusable robust key generation; 5. robust key recovery may be reused. The invention calculates the public parameter according to the fingerprint characteristics by extracting the fingerprint characteristics of the user and extracts the secret key from the fingerprint characteristics. The public parameters are then saved, but the user's biometric is not saved, and the key also does not need to be remembered. If the key needs to be used again, the same key can be recovered by the algorithm only by acquiring the biological characteristics of the same fingerprint and inputting the public parameters stored before. Compared with other schemes, the invention has faster speed and lower storage overhead.

Description

Reusable robust fuzzy extraction method based on fingerprints

Technical Field

The invention belongs to the field of biological feature processing, and particularly relates to a reusable robust fuzzy extraction method based on fingerprints.

Background

Among the various authentication approaches, biometrics provide good user-friendliness. However, it faces the problem of theft due to the unrenewability of the biological feature. The advent of the fuzzy extractor solved this problem well. The fuzzy extractor may extract evenly distributed keys from various random sources of noise (e.g., biometric features, physical unclonable functions, quantum bits, etc.). In most studies in this direction, the study of the blur extractor only stays at a theoretical level, does not consider how the extracted biometric should be encoded, and does not give a simulation case in combination with a specific biometric.

Disclosure of Invention

The invention aims to provide a reusable robust fuzzy extraction method based on fingerprints, and aims to solve the technical problems of existing secret key security and biological feature storage.

In order to solve the technical problems, the specific technical scheme of the reusable robust fuzzy extraction method based on the fingerprint comprises the following steps:

a reusable robust fuzzy extraction method based on fingerprints comprises the following steps:

step 1: preprocessing a fingerprint image;

step 2: extracting characteristics;

and step 3: constructing a plane rectangular coordinate system;

and 4, step 4: reusable robust key generation;

and 5: robust key recovery may be reused.

Further, the step 1 comprises the following specific steps:

step 1.1: segmentation of fingerprint regions from image background: averagely dividing the fingerprint image into n multiplied by n blocks, and then calculating the mean value and the variance value of the intensity in each block so as to divide a fingerprint area from the graph background;

step 1.2: enhancing the fingerprint image to generate a fingerprint skeleton diagram: two minutiae, namely an end point and a bifurcation point of the fingerprint, are extracted as features by adopting a Cross Number method.

Further, the step 2 comprises the following specific steps:

step 2.1: selecting a central point:

a Poincare index algorithm is adopted to obtain a central point, the area where the central point is located is used as a reference, and a plurality of minutiae are selected around the central point area;

step 2.2: selecting the detail nodes:

first, a minimum sampling radius R is defined_minThen, selecting a fingerprint ridge line end point which is outside the sampling radius and is closest to the central point as a reference point, taking the central point as a pole, starting from the central point, leading a ray to the end point as a polar axis to establish a polar coordinate system, taking the anticlockwise direction as positive, then the coordinate of the central point is (0, 0), and the coordinate of any thin node i is (rho)_i，θ_i) For any detail point, if ρ satisfies the following condition, it will be taken as a candidate detail point:

ρ＞R_min

at the moment, for all candidate detail points, N detail points with the shortest distance are selected according to the distance from the center point to be added into a selection queue;

step 2.3: sorting detail points:

sorting the detail points selected in the last step from small to large according to the theta values, and if two or more detail points with the theta values within a given angle threshold value delta exist, sorting the detail points with smaller rho values in the front; finally, a minutiae set m ═ m (m) is formed₁，...，m_n) Wherein N is the number of the selected effective minutiae; m is_i＝(ρ_i，θ_i)，ρ_iIs the distance from the center point, θ_iIs a deflection angle, theta, relative to the polar axis_i∈[0，2π]。

Further, step 3 comprises the following specific steps:

in the safety outline, an error correction algorithm is realized under a plane rectangular coordinate system based on the Chebyshev distance, and biological characteristics are expressed in the plane rectangular coordinate system, wherein each characteristic is a point in the coordinate system; wherein the X axis and the Y axis intersect at the origin O, and the unit distance a belongs to R⁺Defining points (…, -4a, -Sa, -2a, -a, 0, a, 2a, 3a, 4a,) on the X-axis and Y-axis, respectively, defining an interval on the coordinate axis (b, b + ka), wherein k ∈ {1, 2,. said } indicates a distance of several units in an interval, and therefore, k ∈ {1, 2,. said } indicates a distance of several units in an intervalka is the width of one space,

representing an interval starting point, wherein the number of intervals on one coordinate axis is represented by v; the representation of an area on the plane of the coordinate system is defined as follows: let (m, n),

will be provided with

And

the square enclosed by the four points is called a region I_m，nAn area is defined by the coordinates of the center of the square that makes up the area_m，n＝(m，n)。

Further, the step 4 comprises the following specific steps:

step 4.1: generating a stem summary:

firstly, inputting all n detail points into a safety outline scheme to obtain an outline s, wherein the s is used for trying to recover the original detail points in a subsequent key recovery algorithm;

step 4.2: key extraction:

in order to ensure the randomness of the key, combining a biological characteristic B and a current timestamp T, connecting B and T, inputting the connected B and T into a Hash function, and averagely dividing the obtained Hash value into two parts, wherein the former part is used as a key R, and the latter part is used as a verifier v;

step 4.3: and (3) constructing common parameters:

assuming that m (m is less than or equal to n) is the worst case of the number of recoverable minutiae, randomly taking m minutiae out of n different minutiae in disorder each time and combining the m minutiae into a group to obtain

A subset B₁，B₂，...，B_Z，

Step 4.4: and (3) encryption of the hash value:

and SKE.Enc is an encryption algorithm of a symmetric key encryption method, wherein (R, v) is used as a plaintext message, and B is used as a plaintext message₁，B₂，...，B_ZPerforming encryption operation on (R, v) as an encryption key to obtain a corresponding ciphertext c₁，c₂，...，c_Z，

Let C be ═ C₁，c₂，...，c_Z) P ═ s, v, C is saved as a public help string, and the remaining data are destroyed.

Further, the step 5 comprises the following specific steps:

step 5.1: and (3) recovering fingerprint characteristic points:

B′＝(b′₁，…，b′_n) Firstly, combining the outline s to restore the original minutiae point for the fingerprint minutiae point of the same finger collected for the second time, inputting B' and s into a restoration algorithm of a safe outline to obtain a restored minutiae point sequence

Step 5.2: decryption key:

by using the method of combination number, randomly selecting m detail nodes out of order from the n recovered detail nodes at each time and combining the m detail nodes into a group to obtain a subset

If any one exists

Then pair c can be realized_iDecryption by authentication

Whether v is equal, if so, successfully recovering the key

Further, the algorithm of the security profile comprises: step a: a registration phase and a step b: and (5) a verification stage.

Further, the step a comprises the following specific steps:

step a.1 initialization phase:

constructing a coordinate system C based on the step 3_a，k，vV intervals are arranged on each coordinate axis, so that v × v regions are formed;

inside each region, the maximum acceptable chebyshev distance t ═ ka/2, also referred to as the biometric threshold;

in the fingerprint minutiae set m ═ (m ═ m₁，...，m_n) For each minutia m_i＝(ρ_i，θ_i) And converting the polar coordinates into rectangular coordinates, wherein the process is as follows:

so as to obtain the biological characteristic information vector B ═ B₁，...，b_n)；

Step a.2: ss (b) → s stage:

biometric information vector for user B ═ B₁，...，b_n) Wherein b is_i＝(x_i，y_i) Is a rectangular coordinate system C_a，k，vA point of (1);

finding a point x ═ (p, q) in a given coordinate system C_a，k，vThe latter belonging region I_m，nAs can be seen from step 3, the interval width on each coordinate axis is ka,

the method is equally applicable to points on the boundary of a region or to intersections of 4 regions, e.g. b_i(ka, ka) if b_iOn the boundary perpendicular to the x-axis, then b is_iBelonging to the left area closest thereto; if b is_iOn the boundary parallel to the x-axis, then b_iBelonging to the descending area closest to the descending area; b_iAt the intersection of 4 regions, judging according to the two rules, and determining all b_i∈(b₁，...，b_n) According to each b_iIn the region I_m，nIs provided with

I_m，n＝b_i+s_i

Wherein s is_iIs a vector represented by a coordinate point pair in a coordinate system C, representing a point b_iIf I is to be reached_m，nIs required to follow vector s_iMoving all s_iAnd establishing a parameter (a, k, v) forming set s ═ a, k, v, s of the plane rectangular coordinate system₁，...，s_n) Returned as a sketch and exposed publicly.

Further, the step B adopts the same characteristic extraction method for the input fingerprint image to extract the biological characteristic information vector B', and comprises the following specific steps:

step b.1: rec (B', s) → stage B:

the input is a coded user biological information vector B ═ B₁′，...，b_n') and a safety sketch s, where b_i' (x, y) is the coordinate system C_a，k，vPoint (b), the recovery algorithm is as follows:

firstly, a plane rectangular coordinate system C is reconstructed through parameters (a, k, v)_a，k，v

For all b_i′∈(b₁′，...，b_n') and s_i∈(s₁，...，s_n) Calculating

For all

Finding inclusion according to formula

Region I of_m，n，

Computing

d_i＝I_m，n-s_i

Return vector D ═ D₁，...，d_n) And the recovery is finished; if dis (B, B') is less than or equal to t, D ═ B is considered, namely the biological characteristics collected in the registration stage can be completely recovered.

Further, the recovery process of the coordinate point includes the following specific steps:

the interval width ka is 8, so the threshold t is 8/2 is 4, and the point b is₁(2, 6) is the original biometric; b₁In the region I_4，4In the safety margin generation algorithm, first, a sketch s is calculated (4, 4)₁＝I_4，4-b₁(4-2, 4-6) ═ 2, -2), keeping public parameter s₁Original biometric information b₁The storage is not needed;

in the recovery algorithm, the resampled biometric b is input₁′＝(-1，3)，b₁And b₁The Chebyshev distance between' is dis (b)₁，b₁') 3 < t; first of all, calculate

Then obtain

Is in the region I_4，4And finally d is calculated₁＝I_4，4-s₁(4-2, 4- (-2)) ═ 2, 6), to give b₁＝d₁By, the recovery is complete.

The reusable robust fuzzy extraction method based on the fingerprint has the following advantages that: the invention does not need to save the biological characteristics of the user, effectively protects the safety of the biological characteristics, and provides stable secret key generation and recovery capability through the fuzzy extractor designed by the invention. In experiments, a complete set of solutions is provided by successfully combining the fuzzy extractor with the fingerprint features, starting from fingerprint feature extraction and encoding to no recovery of key generation. Meanwhile, experiments show that the scheme of the invention has higher practicability in the overhead of the storage space.

Drawings

FIG. 1 is a flow chart of a reusable robust fuzzy extraction method based on fingerprints according to the present invention;

FIG. 2(a) is a schematic diagram of an image of a fingerprint according to the present invention;

FIG. 2(b) is a schematic diagram of a clipped fingerprint region according to the present invention;

FIG. 2(c) is a diagram of a fingerprint skeleton according to the present invention;

FIG. 2(d) is a schematic diagram of the minutiae points of the fingerprint of the present invention;

FIG. 3 is a diagram illustrating the simulated effect of the fingerprint center according to the present invention;

FIG. 4(a) is a graph of simulation effect of selecting a sampling radius according to the present invention;

FIG. 4(b) is a diagram of the selected minutiae simulation effect of the present invention;

FIG. 5 is a schematic diagram of a rectangular coordinate system constructed according to the present invention;

FIG. 6 is a flow chart of feature extraction and representation of the present invention;

FIG. 7 is a flow chart of a key generation phase of the present invention;

FIG. 8 is a flow chart of a key recovery phase of the present invention;

FIG. 9 is a schematic diagram of a coordinate recovery process of the present invention;

FIG. 10(a) is a schematic diagram of a fingerprint image during enrollment in accordance with the present invention;

FIG. 10(b) is a diagram illustrating fingerprint minutiae during an enrollment process of the present invention;

FIG. 10(c) is a diagram of a fingerprint minutiae simulation effect during enrollment in accordance with the present invention;

FIG. 11(a) is a schematic view of a fingerprint image at a testing stage according to the present invention;

FIG. 11(b) is a schematic view of a fingerprint minutiae point at a testing stage according to the present invention;

FIG. 11(c) is a diagram of the effect of the fingerprint minutiae simulation during the testing phase of the present invention.

Detailed Description

In order to better understand the purpose, structure and function of the present invention, a reusable robust fuzzy extraction method based on fingerprints according to the present invention is further described in detail below with reference to the accompanying drawings.

As shown in fig. 1, a reusable robust fuzzy extraction method based on fingerprints of the present invention includes the following steps:

step 1, preprocessing a fingerprint image.

First the fingerprint area needs to be segmented from the image background. The fingerprint image is divided into n × n blocks on average, and then the mean and variance values of intensities in each block are calculated to divide the fingerprint region from the graphic background. And performing enhancement processing on the fingerprint image to generate a fingerprint skeleton image. Here we use Cross Number method to extract the end points of fingerprint, and the two kinds of minutiae of bifurcation point are used as features. The fingerprint processing procedure and the labeled minutiae are shown in FIGS. 2(a) -2(d), wherein FIG. 2(a) is a fingerprint image taken; FIG. 2(b) is a clipped fingerprint region; FIG. 2(c) is a fingerprint skeleton diagram; figure 2(d) shows fingerprint minutiae.

And 2, extracting the characteristics.

Since the acquired fingerprint image is affected by external factors such as noise, the extracted minutiae include a large number of pseudo minutiae (e.g., edge portions of the fingerprint image and blurred portions in the image), and therefore the extracted feature points need to be selected. Meanwhile, in order to match the input of the fuzzy extractor, the selected feature points need to be represented in a proper form. Step 2, which is the implementation of the present invention, is described in further detail with reference to fig. 6.

Step 2.1 selection of Central Point

The center point is defined as a pixel point corresponding to the maximum curvature value in the curvature field of the image, namely, the point with the maximum change of the ridge line direction in the image is usually positioned at the progressive center of the fingerprint ridge line, and the peripheral ridge line is approximately in a semicircular trend. Currently, the most common method for finding the center point is the Poincare index algorithm, although this method may not be accurate enough (e.g. a center area of a fingerprint is obtained instead of a specific point), but does not affect our method. Because we do not use it as a reference point directly for feature extraction or fingerprint alignment, but rather select several minutiae points around the region of the center point as a reference. Fig. 3 is a diagram showing the simulated effect of the fingerprint center according to the present invention.

Step 2.2 selection of minutiae points

Step 2.2, which is carried out in accordance with the present invention, is described in further detail with reference to fig. 4(a) -4 (b). Wherein FIG. 4(a) is a drawing to select a sampling radius R_minEstablishing a polar coordinate system according to the ridge line end point closest to the ridge line end point; fig. 4(b) shows selected minutiae points.

Meanwhile, if the distance between the detail point and the central point is too close, a measurement error may be generated, and the detail point is screened. When too many minutiae are selected, the verification time is increased, but too few minutiae weaken the uniqueness of the fingerprint, so that an appropriate number of minutiae should be acquired to represent the characteristics of the entire fingerprint.

Here, a minimum sampling radius R is first defined_min. Then, the end point of the fingerprint ridge line which is outside the sampling radius and is closest to the central point is selected as a reference point. Taking a central point as a pole, starting from the central point, leading out a ray to the end point as a polar axis to establish a polar coordinate system, taking the anticlockwise direction as positive, then the coordinate of the central point is (0, 0), and the coordinate of any minutiae point i is (rho)_i，θ_i). For any minutiae point, if ρ satisfies the following condition, it will be a candidate minutiae point.

ρ＞R_min

At this time for all candidate minutiae m_dAnd selecting N detail nodes closest to the central point according to the distance from the central point to the central point, and adding the N detail nodes into the selection queue.

Step 2.3 minutiae ordering

Sorting the detail points selected in the last step from small to large according to the value of theta, and if the detail points are storedWhere two or more minutiae values theta are within a given angular threshold value delta, then the minutiae points with smaller p are ranked first. Finally, a minutiae set m ═ m (m) is formed₁，...，m_n) And N is the number of the selected effective minutiae. m is_i＝(ρ_i，θ_i)，ρ_iIs the distance from the center point, θ_iIs the angle of deflection relative to the polar axis. Theta_i∈[0，2π]。

And 3, constructing a plane rectangular coordinate system.

In our proposed safety outline, the error correction algorithm will be implemented based on the chebyshev distance under the rectangular plane coordinate system, which is different from the traditional method based on the error correction code (RS code, BCH code). Meanwhile, the biological features are expressed in a rectangular plane coordinate system, and each feature is a point in the coordinate system.

Step 3, which is the implementation of the present invention, is described in further detail with reference to fig. 5.

Wherein the X axis and the Y axis intersect at the origin O, and the unit distance a belongs to R⁺Points (…, -4a, -3a, -2a, -a, 0, a, 2a, 3a, 4a,) are defined on the X-axis and Y-axis, respectively. Defining an interval on the coordinate axis (b, b + ka), where k e {1, 2. } denotes the span of several unit distances in an interval, so ka is the width of an interval, and b ═ ka is the sum of the intervals

Indicating the start of the interval. The number of intervals on one axis is denoted by v.

Next, the representation of an area on the plane of the coordinate system is defined. Let us assume that (m, n),

will be provided with

And

the square enclosed by the four points is called a region I_m，nAn area is defined by the coordinates of the center of the square forming the area_m，n(m, n). For example, when k is 2, the points (2a, 2a), (2a, 4a), (4a, 2a), (4a, 4a) form an area I_3a，3a＝(3a，3a)。

Step 4 may reuse robust key generation.

Step 4, which is the implementation of the present invention, is described in further detail with reference to fig. 7.

Step 4.1 generating a synopsis

Firstly, inputting all n detail points into a safety outline scheme to obtain an outline s, wherein the outline s is used for trying to recover the original detail points in a subsequent key recovery algorithm.

Step 4.2 Key extraction

To guarantee the randomness of the key, we combine the biometric B with the current timestamp T. And B and T are connected and then input into a hash function, and the obtained hash value is averagely divided into two parts, wherein the former part is used as a secret key R, and the latter part is used as a verifier v.

Step 4.3 construction of common parameters

Let m (m ≦ n) be the worst case for the number of minutiae that can be recovered. Randomly taking m detail points out of n different detail points at a time and combining the m detail points into a group to obtain

A subset B₁，B₂，...，B_Z，

Step 4.4 encrypt hash value

Enc is an encryption algorithm of a symmetric key encryption method, and (R, v) are used as plaintext messages, and B is used as plaintext messages₁，B₂，...，B_ZPerforming encryption operation on (R, v) as an encryption key to obtain a corresponding ciphertext c₁，c₂，...，c_Z，

Let C be ═ C₁，c₂，...，c_Z). Finally, we save P ═ (s, v, C) as a public help string, and the rest of the data can be destroyed.

Step 5 may reuse robust key recovery.

Step 5, which is the implementation of the present invention, is described in further detail with reference to fig. 8.

Step 5.1 recovery of fingerprint feature points

B′＝(b′₁，…，b′_n) Is the fingerprint minutiae of the same finger acquired a second time. Firstly, attempting to recover an original minutiae point by combining a skeleton s, inputting B' and s into a recovery algorithm of a safety skeleton to obtain a recovered minutiae sequence

Step 5.2 decryption Key

There may be some failure in the recovery of the minutiae, so the method of borrowing the number of combinations is also needed, and any m minutiae out of order are combined into one group from n recovered minutiae at a time, so as to obtain the subset

If any one exists

Then pair c can be realized_iDecryption, passing verification

Whether v is equal, if so, successfully recovering the key

The security skeleton algorithm in the above step comprises the following steps:

step 1 registration phase

The safety outline includes two algorithms: SS and Rec. First we will show the process of system initialization, followed by the introduction of the proposed security sketch.

Step 1.1 initialization phase

Constructing a coordinate system C based on the step 3 of the stage_a，k，vThere are v intervals on each coordinate axis, thereby constituting v × v regions. Inside each region, the maximum acceptable chebyshev distance t ═ ka/2, we also refer to t as the biometric threshold.

In the fingerprint minutiae set m ═ (m ═ m₁，...，m_n) For each minutia m_i＝(ρ_i，θ_i) And converting the polar coordinates into rectangular coordinates, wherein the process is as follows:

so as to obtain the biological characteristic information vector B ═ B₁，...，b_n)。

Step 1.2 SS (B) → s stage

Biometric information vector for user B ═ B₁，...，b_n) Wherein b is_i＝(x_i，y_i) Is a rectangular coordinate system C_a，k，vPoint (2).

First, how to find a point x ═ p, q in a given coordinate system C is described_a，k，vThe latter belonging region I_m，n(m, n). From step 3 above, the interval width on each coordinate axis is ka.

The method is equally applicable to points on the boundary of a region or to intersections of 4 regions, e.g. b_i(ka, ka). If b is_iOn the boundary perpendicular to the x-axis, then b_iTo the left area nearest thereto(ii) a If b is_iOn the boundary parallel to the x-axis, then b_iBelonging to the descending area closest to the descending area; b_iAnd judging according to the two rules when the region is positioned at the intersection of the 4 regions.

For all b_i∈(b₁，...，b_n) According to each b_iIn the region I_m，nIs provided with

I_m，n＝b_i+s_i

Wherein s is_iIs a vector represented by a coordinate point pair in a coordinate system C, representing a point b_iIf I is to be reached_m，nIs required to follow vector s_iMoving all s_iAnd establishing a parameter (a, k, v) forming set s ═ a, k, v, s of the plane rectangular coordinate system₁，...，s_n) Returned as a sketch and may be exposed.

Step 2 verification phase

And extracting a biological characteristic information vector B' by adopting the same characteristic extraction method for the input fingerprint image.

Step 2.1 Rec (B', s) → stage B

The input is a coded user biological information vector B ═ B₁′，...，b_n') and a safety sketch s, where b_i' (x, y) is the coordinate system C_a，k，vPoint (b), the recovery algorithm is as follows.

Firstly, a plane rectangular coordinate system C is reconstructed through parameters (a, k, v)_a，k，v

For all b_i′∈(b₁′，...，b_n') and s_i∈(s₁，...，s_n) Calculating

For all

Finding inclusion according to formula

Region I of_m，n。

Computing

d_i＝I_m，n-s_i

Return vector D ═ D₁，...，d_n) And the recovery is completed. If dis (B, B') ≦ t, we consider D ═ B, i.e. the biometric collected during the enrollment phase can be fully recovered.

Referring to fig. 9, the recovering process of the coordinate point according to the present invention will be described in detail.

In the coordinate system of fig. 9, it can be seen that the interval width ka is 8. Therefore, the threshold value t 8/2 is 4. Point b₁(2, 6) are raw biometrics (e.g., fingerprint end points or bifurcation points). b₁In the region I_4，4(4, 4). In the algorithm for generating the safety outline, first, a sketch s is calculated₁＝I_4，4-b₁(4-2, 4-6) ═ 2, -2), keeping public parameter s₁Original biometric information b₁No need for storage.

In the recovery algorithm, the resampled biometric b is input₁' -1, 3. Albeit b₁And b₁' in different regions, but with a Chebyshev distance between them is dis (b)₁，b₁') 3 < t. So we first calculate

Then obtain

Is in the region I_4，4. Finally calculate d₁＝I_4，4-s₁(4-2, 4- (-2)) ═ 2, 6), to give b₁＝d₁By, the recovery is complete.

The effects of the present invention can be further illustrated by the following simulations:

1. simulation conditions are as follows:

the hardware environment simulated by the invention is as follows: the computer system Windows 10, the processors Intel i5-8265U, the memory 8GB, the hard disk 512 GB. Fingerprint image to be processed: the FVC2002 DR1_ a database includes 100 fingers, each finger having 8 different live scan fingerprint images, with an image size of 296x 560. For each finger, the fingerprint shown in (a) of fig. 10 was selected as the fingerprint image in the enrollment process, and the fingerprint shown in (a) of fig. 11 was selected as the fingerprint image in the testing process, and 100 sets of experiments were performed in total.

2. Simulation content and result analysis:

the hash function used in the experiment was SHA-256, with an output hash value of 256 bits in length. The symmetric key encryption scheme used is AES, the key length is 128 bits, and the packet length is 128 bits.

In this experiment, the number N of feature points we selected is 15, and the sampling radius R _ min is 40px (px represents a picture pixel). Fig. 10(a) is a fingerprint image (simply referred to as a registration image) used in the blur extractor Gen algorithm, and fig. 11(a) is a fingerprint image (simply referred to as a verification image) used in the Rep algorithm.

(1) Gen (b) → (R, P) stage:

(1.1) as shown in fig. 10(B), minutiae points B of the registered fingerprint image are extracted as (B)₁，...，b_n) And converts the polar coordinates to rectangular coordinates. And selecting parameters a as 10, k as 2 and v as 8, and establishing a rectangular coordinate system. Minutiae point b_1-15The coordinates of (a) are shown in table 1.

TABLE 1 minutiae points b of training fingerprint images_1-15Coordinates of the object

(1.2) selecting the time stamp T of the user registration, connecting the biological characteristic B, and generating the secret key R and the authenticator v.

T＝1622521128

B||T＝ 51055124231544334473662-247-565-2468-2852-2634-4940-7015-39-4313-401622521128

Hash(B||k)＝46408bc21d8ffbcbd1dd2248d56600b0160f13b30b7d0daa561742270f2ac2 08

R＝46408bc21d8ffbcbd1dd2248d56600b0

v＝160f13b30b7d0daa561742270f2ac208

(1.3) as shown in FIG. 10(c), the area to which each minutiae belongs is determined. Minutiae point b_1-15To which region I belongs_m，nAs shown in table 1. These minutiae points and the areas to which they belong are also shown in table 2. Calculating sketch s ═ a, k, v, s₁，..，s₁₅) Where a is 10, k is 2, and v is 8. s_1-15As shown in table 3.

TABLE 2 regions corresponding to each minutiae point of a training fingerprint image

TABLE 3 vector s_1-15Coordinates of (2)

(1.4) the number of feature points n in B is 15, and now optionally m from B is 13, such a common definition

Seed result, i.e. B₁～B₃₀₀₃We use the hash value in (1.2), i.e. (R, v), as the encrypted content, B₁～B₃₀₀₃Performing encryption operation as a key to obtain a ciphertext c₁～c₃₀₀₃Let C be (C)₁，c₂，...，c₃₀₀₃) Save public help string P ═ (s, v, C).

(2) Rep (B', P) → R stage:

(2.1) as shown in fig. 11(B), minutiae B ' ═ B ' of the test fingerprint image is extracted '₁，…，b′₁₅) And converting the polar coordinates to rectangular coordinates. The same rectangular coordinate system is established according to the public help string P with the parameters a 10, k 2 and v 8. Thin node b'_1-15The coordinates of (a) are shown in table 4.

TABLE 4 minutiae b 'of test fingerprint image'_1-15Coordinates of the object

(2.2) calculation of

The coordinates are shown in table 5 below. These minutiae points and the areas of interest are shown in fig. 11(b), 11 (c).

TABLE 5

Coordinates of the object

(2.3) calculating the finally restored coordinate d_i。d_1-15The coordinates are shown in table 6 below.

TABLE 6 initial minutiae points d of the final restoration_1-15Coordinates of the object

(2.4) set of minutiae of order restoration

The number n of feature points in (1) is 15, which is now the same as

Where m is 13 minutiae in a group, such that all together

In a seed stage of

The public help string saved in the registration phase is C ═ C₁，c₂，...，c₃₀₀₃) In which several encryption results are stored, then can be used

To c₁～c₃₀₀₃Decryption, since it exists as long as the number of recovered details is greater than m

Can be aligned with c_iDecryption, i.e.

(2.5) decrypted by comparison using the verifier v held in the public helper string

If v is equal, the recovery process is complete and the key is used

And (6) successfully recovering. Resulting in the recovered key R.

According to the test flow, if R is successfully recovered, recording as a successful experiment, and outputting ^ T as a failed experiment. We tested two cases of the selected minutiae n 15 and n 20, respectively, and recorded the experimental storage overhead and the fault resolution (FRR).

TABLE 7 false reject Rate of the present invention

The length of the biometric feature is calculated as follows: the coordinates of each minutia are represented by 8 bytes, where we take the average 6. Thus the length (in bytes) of each biometric is L ═ N × 8 × 8 (bit).

For comparison, some experimental data of Canetti et al are as follows. It can be seen that our solution has the advantage of significant memory overhead when it comes to having longer keys and biometric data.

TABLE 8 storage overhead for Canetti scheme

Table 9 storage overhead of the present invention

Simulation experiment results show that the safety of the biological characteristics and the secret key is effectively protected through the fuzzy extractor. Here, a fuzzy extractor is successfully combined with biometrics. By taking fingerprints as an example, a set of complete schemes is provided from feature extraction and coding to construction of a safe sketch and a reusable robust fuzzy extractor. We also theoretically analyzed its safety. Finally, simulation implementation is carried out, and the scheme has lower storage overhead.

It is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (10)

1. A reusable robust fuzzy extraction method based on fingerprints is characterized by comprising the following steps:

step 1: preprocessing a fingerprint image;

step 2: extracting characteristics;

and step 3: constructing a plane rectangular coordinate system;

and 4, step 4: reusable robust key generation;

and 5: robust key recovery may be reused.

2. The reusable robust fuzzy extraction method based on fingerprint according to claim 1, characterized by that, step 1 includes the following specific steps:

step 1.1: segmentation of fingerprint regions from image background: averagely dividing the fingerprint image into n multiplied by n blocks, and then calculating the mean value and the variance value of the intensity in each block so as to divide a fingerprint area from the graph background;

step 1.2: enhancing the fingerprint image to generate a fingerprint skeleton diagram: two minutiae, namely an end point and a bifurcation point of the fingerprint, are extracted as features by adopting a cross number method.

3. The reusable robust fuzzy extraction method based on fingerprint as claimed in claim 2, characterized by that, step 2 includes the following specific steps:

step 2.1: selecting a central point:

a Poincare index algorithm is adopted to obtain a central point, the area where the central point is located is used as a reference, and a plurality of detail points are selected around the central point area;

step 2.2: selecting the detail nodes:

first, a minimum sampling radius R is defined_minThen, selecting a fingerprint ridge line end point which is outside the sampling radius and is closest to the central point as a reference point, taking the central point as a pole, starting from the central point, leading a ray to the end point as a polar axis to establish a polar coordinate system, taking the anticlockwise direction as positive, then the coordinate of the central point is (0, 0), and the coordinate of any thin node i is (rho)_i，θ_i) For any detail point, if ρ satisfies the following condition, it will be taken as a candidate detail point:

ρ＞R_min

at the moment, for all candidate detail points, N detail points with the shortest distance are selected according to the distance from the center point to be added into a selection queue;

step 2.3: sorting detail points:

sorting the detail points selected in the last step from small to large according to the theta values, and if two or more detail points with the theta values within a given angle threshold value delta exist, sorting the detail points with smaller rho values in the front; finally, a minutiae set m ═ m (m) is formed₁，...，m_n) Wherein N is the number of the selected effective minutiae; m is_i＝(ρ_i，θ_i)，ρ_iIs the distance from the center point, θ_iAs angle of deflection relative to the polar axis, theta_i∈[0，2π]。

4. The reusable robust fuzzy extraction method based on fingerprint as claimed in claim 3, characterized by that, step 3 comprises the following specific steps:

in the safety outline, an error correction algorithm is realized based on the Chebyshev distance under a planar rectangular coordinate system, and biological characteristics are represented in the planar rectangular coordinate system, wherein each characteristic is a point in the coordinate system; wherein the X axis and the Y axis intersect at the origin O, and the unit distance a belongs to R⁺Defining points (. -, -4a, -3a, -2a, -a, 0, a, 2a, 3a, 4 a. -) on the X-axis and Y-axis, respectively, and defining an interval (b, b + ka) on the coordinate axis, where k ∈ {1, 2. - } is the tableShown spanning several unit distances in a space, so ka is the width of a space,

representing an interval starting point, wherein the number of intervals on one coordinate axis is represented by v;

the representation of an area on the plane of the coordinate system is defined as follows: let (m, n),

will be provided with

And

the square enclosed by the four points is called a region I_m，nAn area is defined by the coordinates of the center of the square that makes up the area_m，n＝(m，n)。

5. The reusable robust fuzzy extraction method based on fingerprint as claimed in claim 4, characterized by that, step 4 includes the following specific steps:

step 4.1: generating a stem summary:

firstly, inputting all n detail points into a safety outline scheme to obtain an outline s, wherein the s is used for trying to recover the original detail points in a subsequent key recovery algorithm;

step 4.2: key extraction:

in order to ensure the randomness of the key, combining the biological characteristic B and the current timestamp T, connecting B and T, inputting the connected B and T into a hash function, and averagely dividing the obtained hash value into two parts, wherein the former part is used as the key R, and the latter part is used as a verifier v;

step 4.3: and (3) constructing common parameters:

suppose m(m is less than or equal to n) is the worst condition of the number of the detail nodes capable of being recovered, and m detail nodes which are randomly taken out of order are combined into a group from n different detail nodes each time to obtain the result

A subset B₁，B₂，...，B_Z，

Step 4.4: and (3) encryption of the hash value:

and SKE.Enc is an encryption algorithm of a symmetric key encryption method, wherein (R, v) is used as a plaintext message, and B is used as a plaintext message₁，B₂，...，B_ZPerforming encryption operation on (R, v) as an encryption key to obtain a corresponding ciphertext c₁，c₂，...，c_Z，

Let C be ═ C₁，c₂，...，c_Z) P ═ s, v, C is saved as a public help string, and the remaining data are destroyed.

6. The reusable robust fuzzy extraction method based on fingerprint as claimed in claim 5, characterized by that, step 5 includes the following specific steps:

step 5.1: and (3) recovering fingerprint characteristic points:

B′＝(b′₁，…，b′_n) Firstly, combining the skeleton s to restore the original minutiae points for the fingerprint minutiae points of the same finger collected for the second time, inputting B' and s into a restoration algorithm of a safety skeleton to obtain a restored minutiae point sequence

Step 5.2: decryption key:

by means of the combination number, m detail nodes are randomly selected and combined into a group in disorder from n recovered detail nodes at each time,

obtaining a subset

If any one exists

Decryption of ci can be achieved, with verification

Whether v is equal, if so, successfully recovering the key

7. The reusable robust fuzzy extraction method based on fingerprints according to claim 6, characterized in that said algorithm of security profile comprises: step a: a registration phase and a step b: and (5) a verification stage.

8. The reusable robust fuzzy extraction method based on fingerprint as claimed in claim 7, characterized by that, step a includes the following specific steps:

step a.1 initialization phase:

constructing a coordinate system C based on the step 3_a，k，vV intervals are arranged on each coordinate axis, so that v × v regions are formed;

inside each region, the maximum acceptable chebyshev distance t ═ ka/2, also referred to as the biometric threshold;

in the fingerprint minutiae set m ═ (m ═ m₁，...，m_n) For each minutia m_i＝(ρ_i，θ_i) And converting the polar coordinates into rectangular coordinates, wherein the process is as follows:

so as to obtain the biological characteristic information vector B ═ B₁，...，b_n)；

Step a.2: ss (b) → s stage:

biometric information vector for user B ═ B₁，...，b_n) Wherein b is_i＝(x_i，y_i) Is a rectangular coordinate system C_a，k，vA point of (1);

finding a point x ═ (p, q) in a given coordinate system C_a，k，vThe latter belonging region I_m，nAs can be seen from step 3, the interval width on each coordinate axis is ka,

the method is equally applicable to points on the boundary of a region or to intersections of 4 regions, e.g. b_i(ka, ka) if b_iOn the boundary perpendicular to the x-axis, then b_iBelonging to the left area closest thereto; if b is_iOn the boundary parallel to the x-axis, then b_iBelonging to the lower area closest to the lower area; b_iAt the intersection of 4 regions, judging according to the two rules, and determining all b_i∈(b₁，...，b_n) According to each b_iIn the region I_m，nIs provided with

I_m，n＝b_i+s_i

Wherein s is_iIs a vector represented by a coordinate point pair in a coordinate system C, representing a point b_iIf I is to be reached_m，nIs required to follow vector s_iMove, all s_iAnd establishing a parameter (a, k, v) forming set s ═ a, k, v, s of the plane rectangular coordinate system₁，...，s_n) Returned as a sketch and exposed publicly.

9. The reusable robust fuzzy extraction method based on fingerprint as claimed in claim 8, wherein step B uses the same feature extraction method for the input fingerprint image to extract the biometric information vector B', comprising the following specific steps:

step b.1: rec (B', s) → stage B:

the input is a coded user biological information vector B ═ B₁′，...，b_n') and a safety sketch s, where b_i' (x, y) is the coordinate system C_a，k，vPoint (b), the recovery algorithm is as follows:

firstly, a plane rectangular coordinate system C is reconstructed through parameters (a, k, v)_a，k，v

For all b_i′∈(b₁′，...，b_n') and s_i∈(s₁，...，s_n) Calculating

For all

Finding inclusion according to formula

Region I of_m，n，

Computing

d_i＝I_m，n-s_i

Return vector D ═ D₁，...，d_n) And the recovery is finished; if dis (B, B') is less than or equal to t, D is considered to be B, namely the biological characteristics collected in the registration stage can be completely recovered.

10. The reusable robust fuzzy extraction method based on fingerprint as claimed in claim 9, characterized in that, the recovery process of the coordinate point includes the following specific steps:

the interval width ka is 8, so the threshold t is 8/2 is 4, and the point b is₁(2, 6) is the original biometric; b₁In the region I_4，4In the safety margin generation algorithm, first, a sketch s is calculated (4, 4)₁＝I_4，4-b₁(4-2, 4-6) ═ 2, -2), keeping public parameter s₁Original biometric information b₁The storage is not needed;

in the recovery algorithm, the resampled biometric b is input₁′＝(-1，3)，b₁And b₁The Chebyshev distance between' is dis (b)₁，b₁') 3 < t; first of all, calculate

Then obtain

Is in the region I_4，4And finally d is calculated₁＝I_4，4-s₁(4-2, 4- (-2)) ═ 2, 6), to give b₁＝d₁By, the recovery is complete.

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