CN102495886A - Method for searching fingerprint database based on quantum algorithm - Google Patents

Abstract

The invention relates to a method for searching a fingerprint database based on a quantum algorithm; the matching method comprises the following steps of: (1) collecting and preprocessing fingerprints, extracting detail minutiae, selecting reference points, and transferring an input fingerprint and a set of the detail minutiae in N template fingerprints to polar coordinates based on respective reference points; (2) obtaining a total matching number of all the template fingerprints and the input fingerprint at a time according to quantum parallelism principle, and storing the total matching number in a matching score database; (3) improving Oracle operators in a Grover algorithm so that the Grover algorithm comprises two databases, and finally carrying out one-to-one correspondence on the N states obtained in index registers and the positions of the all obtained matching score databases; and (4) rotating average values of all the states in the index registers, and measuring the index registers, and finally obtaining the researched target fingerprint. According to the method, the efficiency and the accuracy of fingerprint searching in the non-structured fingerprint database are improved by using the quantum algorithm.

Description

Fingerprint database searching method based on quantum algorithm

Technical field

The invention belongs to biometrics identification technology, relate in particular to a kind of fingerprint database searching method based on quantum algorithm.

Background technology

The affirmation of personal identification and authority identification are important link in the life, especially along with the arriving of network times, people for security require increasingly high.But more and more the complicated passwords setting also becomes the big worry of pendulum in face of the people, and in order to realize higher security, using more complicated and password more easily is present popular selection.And everyone fingerprint lines has nothing in common with each other on pattern, breakpoint and point of crossing, that is to say, is unique, and constant throughout one's life.Rely on this uniqueness and stability, just can be mapped a people with his fingerprint, through with his fingerprint and the fingerprint of preserving in advance compare, thereby verify his true identity.

The classical minutiae point fingerprint matching algorithm principle of correcting based on crestal line is described below:

At first to fingerprint gather, the extraction of pre-service and details.Next confirm the fingerprint that will mate whether singular point is arranged, just central point shown in Figure 1A and the trigpoint shown in Figure 1B.A kind of situation is that singular point is arranged, and just chooses near the nearest crestal line singular point, and whether judgement needs the corresponding respectively crestal line of two pieces of fingerprints of coupling similar.If similar, the singular point of then choosing just as two pieces of fingerprint corresponding reference points, is used for ensuing coupling step.Another kind is a singular point not, and this point that just needs to seek other is point as a reference.Define two point set M and N, one of them point set N representes L minutiae point extracting from the fingerprint image of input, and another point set M representes H minutiae point extracting from template.Then these two some set just are expressed as respectively:

$M=\{(x_1^M,y_1^M,{\mathrm{\θ}}_1^M),...,(x_H^M,y_H^M,{\mathrm{\θ}}_H^M)\}---\left(1\right)$

$N=\{(x_1^N,y_1^N,{\mathrm{\θ}}_1^N),...,(x_L^N,y_L^N,{\mathrm{\θ}}_L^N)\}---\left(2\right)$

Wherein

and

write down three information of i and j unique point among point set M and the N respectively: X coordinate, Y coordinate and direction.

Will concentrate in template details point set and input minutiae point then respectively selects a reference point as the initial point in the corresponding polar coordinate system, so that be transformed into minutiae point in the polar coordinate system.Because in advance and do not know the corresponding relation of template point set and input point set, so will consider that all possible reference point is right.

To the concentrated every bit M of template point _i=(the every bit N that 1≤i≤H) and input point are concentrated _i=(1≤i≤L), definition Rotate [i] [j] is with M _iAnd N _jBe used as reference point to the time the anglec of rotation from the input picture to the template image.If M _iAnd N _jCan be by as a pair of corresponding point, promptly they distinguish corresponding crestal line similarity to a certain degree, and then Rotate [i] [j] will get 0 and spend to a value between 360 degree, otherwise definition Rotate [i] [j] value is 400, with expression M _iAnd N _jNot a pair of corresponding point.

Next judge the similarity of crestal line, represent minutiae point M with T _iCorresponding crestal line, t representes minutiae point N _iCorresponding crestal line.Coupling t and T, calculate the difference between these two crestal lines with following formula:

$\mathrm{Diff}\_\mathrm{dist}=\frac{1}{S}{\mathrm{\Σ}}_{i=0}^S|T\left(d_i\right)-t\left(d_i\right)|---\left(3\right)$

$\mathrm{Diff}\_\mathrm{ang}=\frac{1}{S}{\mathrm{\Σ}}_{i=0}^S|T\left({\mathrm{\α}}_i\right)-t\left({\mathrm{\α}}_i\right)|---\left(4\right)$

Wherein S is the some number in the crestal line that writes down, T (d _i) and t (d _i) represent the distance from the some i on crestal line T and the t to corresponding minutiae point, T (α respectively _i) and t (α _i) the expression straight line that connects some i and corresponding minutiae point on crestal line T and the t is with the previous sampled point angle of the line of corresponding minutiae point therewith respectively.If Diff_dist＜W _dWhile Diff_ang＜W _α, W _dAnd W _αBe certain threshold value of choosing, then M _iAnd N _jIt is right to be taken as corresponding minutiae point, and the computing method of Rotate [i] [j] are as follows:

Rotate[i][j]＝β_in-β_temp (5)

Wherein β _ in and β _ temp are respectively N _jAnd M _iAngle with the line same level direction of first sampled point.

The front has obtained the RP of the details point set of template and input, next just with all the other unique points among template point set N and the input point set M with RP N _iAnd M _iFor initial point is transformed under the polar coordinates.The former notes the template minutiae point coordinate of conversion, template RP coordinate, the representation of template minutiae point in polar coordinates; The latter notes the coordinate of input minutiae point, input RP coordinate, and the representation of input minutiae point in polar coordinates, and draw the anglec of rotation that the input details reference is put relative template details reference point.

Set an initial value and be 0 matching fractional match-score, judge that the condition that y input fingerprint minutiae and x template fingerprint minutiae point are mated is: given three threshold values, r _a, e _a, θ _a, two details satisfy the following relationship formula:

|r _yi-r _xj|≤r _a

|e _yi-e _xj|≤e _a (6)

|θ _yi-θ _xj|≤θ _a

And the value of match-score added 1.Concrete coupling step is as shown in Figure 2.

In carrying out the fingerprint matching process, because fingerprint quantity is very big in the fingerprint database, so there is following shortcoming in classical finger print matching method:

(1) classical matching algorithm can only be from N template fingerprint storehouse, to search one by one; Till the template fingerprint that finds and import fingerprint matching; This algorithm on average need be sought N/2 time, will demonstrate the low problem of search rate for the matching algorithm of this classics of situation of large scale database.

(2) since classical fingerprint matching algorithm to carry out in the matching process be search one by one, will make that like this coupling chance of success is 1/2, brought the little problem of matching precision.

Is the problem of a search particular solution in unstructured database with the Grover algorithm application in fingerprint matching.Do not add improved Grover algorithm from initial state

beginning, make it be in balanced stack attitude with the Hadamard conversion:

The quantum wire figure of Hadamard door is as shown in Figure 3.Quantum search algorithm is made up of the quantum subroutine that the G of application note repeatedly is called the Grover iteration; Grover searching algorithm (G) comprises four simple operators shown in Figure 4, and the quantum wire that does not add improved Grover iteration of these four simple operator compositions can be divided into following four steps:

The first, use Oracle O;

The second, use Hadamard conversion

The 3rd, executive condition phase shift on computers makes | and 0>in addition each calculates ground state obtains-1 phase shifts:

$|x>\→-{(-1)}^{{\mathrm{\δ}}_{x0}}|x>---\left(8\right)$

The 4th, use Hadamard conversion

If will not add improved Grover algorithm application in fingerprint search, following problem will occur:

(1) selected 2 ⁿIndividual template fingerprint, can not with the structure 2 ^kIndividual quantum register constitutes corresponding relation.

(2) do not add improved Oracle operator in calculating process, the possibility of result can detect and not be included in this template fingerprint database of fingerprint, causes makeing mistakes.

Therefore the present invention improves the Oracle operator in original Grover algorithm, and the Grover algorithm after the improvement combines with classical fingerprint matching algorithm, is applied in the fingerprint search problem, can improve arithmetic speed, increases search precision.

Summary of the invention

The objective of the invention is a kind ofly can overcome the low method with shortcoming such as low precision of classical fingerprint search speed.

For realizing above-mentioned purpose, the present invention adopts following technical scheme, and it comprises the steps:

Step 1 is utilized quantum concurrency principle, once seeks out the match-score value of the minutiae point matching algorithm of correcting based on crestal line in all classical fingerprint matching algorithms.

Step 2 is improved the Oracle operator in the quantum Grover algorithm, makes and obtains N state in the indexed registers.

Step 3 is rotated operation to the mean value of all states of indexed registers the inside, to its measure obtain the target fingerprint that will search for.

In step 1, when a pair of details of input fingerprint and template fingerprint satisfied certain condition, initial value was that 0 match-score adds 1, and what draw at last is that the logarithm of all details that satisfy condition is the match-score value.The principle of f (x) value when utilizing the quantum concurrency can calculate x for different value simultaneously can once seek out the match-score value of input fingerprint and all template fingerprints.

In step 2, the Oracle operator is improved to two databases, comprise four registers in the database one, first register is one and is initialized as | 0>n quantum bit indexed registers.

In step 3; Rotary manipulation mainly is to use Hadamard conversion

the vectorial application matrix of the probability amplitude of all states of quantum bit indexed registers is carried out unitary transformation; The searching scope of target quantum state is dwindled greatly, amplify to seek the probability amplitude of quantum state.

Adopt the present invention of technique scheme; The method that a kind of Grover algorithm after utilizing the quantum concurrency and improving combines with classical finger print matching method has been proposed; Can solve existing classical fingerprint matching algorithm under extensive fingerprint database background, the slow and low defective of matching precision of fingerprint matching speed.

Description of drawings

Figure 1A is the singular point of central point for fingerprint lines type;

Figure 1B is the singular point of trigpoint for fingerprint lines type;

Fig. 2 is the classical minutiae point fingerprint matching algorithm process flow diagram based on the crestal line rectification;

Fig. 3 is in its balance stack attitude and calculates f (0) simultaneously to f (2 for making all quantum states ^N-1) Hadamard door quantized transformation circuit;

Fig. 4 is the quantum wire that comprises the quantum Grover searching algorithm iteration of four operators;

Fig. 5 is the fingerprint database searching method schematic diagram based on quantum concurrency and quantum Grover algorithm;

Fig. 6 is for once asking for the process flow diagram of all match-score values based on quantum concurrency principle after improving.

Embodiment

The present invention is a kind of destructuring fingerprint database searching method based on quantum algorithm, and the whole schematic diagram of this inventive method is as shown in Figure 5, and the principle of work of system is described below:

The quantum concurrency is an essential characteristic of many quantum algorithms, and it can make quantum computer, and simultaneously computing function f (x) is in the value at many different x places, and its ultimate principle is:

If f (x): { 0,1} → { 0,1} is the function with 1 bit definitions territory and codomain.On quantum computer, an easy way calculating this function is: consider that initial state does | x, y>The quantum computer of two quantum bits, can carry out following computing to this state through the logic gate sequence

Here Expression mould 2 adds, and first register is called data register, and second is called destination register, mapping

Be defined as U _f, prove that easily it is the tenth of the twelve Earthly Branches.If y=0, then the end of a period state of second quantum bit is exactly f (x) value.If in the data register be the stack attitude

this can by the Hadamard gate action to | 0>on obtain.Then use U _fObtain:

Items different in the state that obtains comprise f (0) and f (1) simultaneously, thereby simultaneously two values of x have been calculated f (x).Utilize quantum computer to be in the ability of the stack attitude of different conditions, single f (x) circuit is used for calculating simultaneously the functional value of a plurality of x.

Affact n quantum bit simultaneously from entirely for n Hadamard door | 0 >, obtain:

$\frac{1}{\sqrt{2^n}}\underset{x}{\mathrm{\Σ}}|x>---\left(10\right)$

It is thus clear that the Hadamard conversion has produced all and has calculated the balance stack of ground state, and efficient is very high, has only used n Hadamard door just to produce 2 ⁿThe stack of individual state.

Utilize the overlay capability of quantum state, the circuit of the single match-score of asking for value is used for calculating simultaneously the match-score value of a plurality of x, and the concrete step of asking for is:

(1) preparation n+1 quantum bit state

is to have used the Hadamard conversion to preceding n position;

(2) the n+1 quantum bit state for preparing is connected to realization U _fQuantum wire, U _fJust calculated fingerprint is mated the circuit of number match-score value;

(3) obtain state and carry out a f calculating, obtain the match-score value of all input fingerprints and template fingerprint.

Once calculate and just can obtain all values, thereby accelerated counting yield.The process flow diagram of realizing is as shown in Figure 6.

Above through utilizing quantum concurrency principle once to obtain 2 ⁿIndividual match-score value, with this 2 ⁿIndividual match-score value is set up a matching fractional database.Utilize quantum Grover fast search algorithm that the matching fractional database is searched for below, obtain and import the target fingerprint of fingerprint matching.

Do not add improved Grover algorithm and can be applied in the modern communications for the detection technique of sending sequence, but the data in this database be with unordered full stored in form of arranging in database, so just can when application Oracle operator, suppose 2 ⁿIndividual quantum register and 2 ⁿIndividual possible transmission sequence constitutes corresponding relation, next just can utilize effective algorithm to detect minimum decision value, thereby draw the transmission sequence.And in the fingerprint search problem that will solve, selected 2 ⁿIndividual template fingerprint, can not with the structure 2 ⁿIndividual quantum register constitutes corresponding relation because extract be used to judge be this 2 ⁿThe details of individual fingerprint; The details of each fingerprint is all different; It is not the bit sequence of fingerprint details number in the template fingerprint database that the full arrangement that maximum minutias is counted out is certain to comprise in a large number; So if the Oracle operator that sends burst in the modern communications of asking for that will be in the past is used for the research that this paper does, just may connect to measure and be not included in this template fingerprint database of fingerprint, cause makeing mistakes.

In sum, need improve for this Oracle operator that is used for the quantum Grover algorithm of unstructured database, thereby make it be applicable to the situation of asking for particular value in the unstructured data storehouse.

Template fingerprint adds up to N=2 ⁿ, therefrom extract one piece of fingerprint as the input fingerprint, then this fingerprint of neutralization identical fingerprint in template fingerprint storehouse has only one piece, and the fingerprint in the template fingerprint storehouse is not with any obvious form ordering.In each the match-score string of binary characters that obtains; Maximal value length is the l bit; The string of binary characters of the minutiae point sum of input fingerprint is expressed as s, and N template fingerprint is labeled as respectively from 0 to N-1, respectively with import the resulting match-score number of fingerprint and can be expressed as d ₀..., d _N-1Construct two databases:

Comprise following four registers in the database one.

(1) one is initialized as | 0 n quantum bit indexed registers.

For the situation of single quantum bit, quantum ground state does | 0 and | 1 >, and quantum bit not only has | 0>and | 1>these two states, can drop on simultaneously | 0>and | 1>between continuous state, the linear combination of these two states just is called the stack attitude, for example:

The same n quantum bit for the sub-bit di sopra hypothesis of volume, the ground state of quantized system does

Totally 2 ⁿIndividual, just the back d in the database two that will construct ₀..., d _N-1N subscript, this N value is carried out addressing as index x, because the state of quantum bit can be in the stack attitude of these ground state, so x is in the stack of multiple value, n Hadamard door affacted this initial state simultaneously does | 0>N quantum bit on, use Represent the collateral action of this n Hadamard door, then can obtain

$\frac{1}{\sqrt{2^n}}\underset{x}{\mathrm{\Σ}}|x>---\left(12\right)$

Because the index x that obtains is in the stack of multiple value, then a secondary index just can index a plurality of values in the database two, thereby accelerates search speed.

(2) one are initialized as | s >, and in The whole calculations, keep the l quantum bit register of this state.

(3) one are initialized as | 0 l quantum bit data register.

(4) 1 quantum bit registers that are initialized as

.

Comprise N=2 in the database two ⁿIndividual register, each unit is made up of the l quantum bit, preserves the N=2 that previous calculations obtains ⁿIndividual match-score value d ₀..., d _N-1, be exactly the detected coupling fingerprint of wanting then corresponding to template fingerprint with the same number of match-score value of input fingerprint details.

Realize the realization of the key of quantum search algorithm at Oracle, it must overturn and in internal memory, locate the phase place of s index.If database one is in state:

$|x>|s>|0>\frac{|0>-|1>}{\sqrt{2}}---\left(13\right)$

The indexed registers of this moment is in state | x>, this state is the stack of each ground state, and data register is in state | 0>, the content d in x the register in the database two then _xBe added to data register:

Wherein

Expression step-by-step mould 2 adds, and that is to say that the data register state of this moment does | d _x>Then the state of database one is changed at this moment

$|x>|s>{|d}_x>\frac{|0>-|1>}{\sqrt{2}}---\left(14\right)$

At this time, the state of the l quantum bit register of database one does | s>, the state of data register does | d _x>, these two registers are compared, if identical, just use bit reversal to the i.e. 1 quantum bit register of the 4th register of database one, otherwise remain unchanged.Having operated last result is:

$|x>|s>|d_x>\frac{|0>-|1>}{\sqrt{2}}\→\left\{\begin{array}{c}-|x>|s>|d_x>\frac{|0>-|1>}{\sqrt{2}},d_x=s\\ |x>|s>|d_x>\frac{|0>-|1>}{\sqrt{2}},d_x\≠s\end{array}\right.---\left(15\right)$

Then again with the content d in x the register in the database two _xBe added to data register:

Can find out that the data register in the database one this moment returns to state | 0>Confirm the position of s in database with quantum search algorithm; Here only to use inferior is added to the operation of data register with the content in the database two, and the classical mode of contrast just needs N such operation with it.After several steps, last effect is if d above the process _x=s, then the state of indexed registers is from | x>Change to-| x>, otherwise keep register constant.The first step Oracle operator of Grover algorithm is accomplished like this.The overall function of Oracle be keep database one second and third, four registers are unaffected; And with first register be that indexed registers is not tangled; Final indexed registers obtains N state, carries out the matching fractional database location that the position and the front of this N state are set up corresponding one by one.

To N the state that obtains in the indexed registers; Use Hadamard conversion

the vectorial application matrix D of the probability amplitude of all states of indexed registers is carried out unitary transformation; Rotate the mean value of all states; The searching scope of target quantum state is dwindled greatly; Amplify to seek the probability amplitude of quantum state, D is defined as:

$\mathrm{Dpq}=\left\{\begin{array}{c}\frac{2}{N},p\≠q\\ -1+\frac{2}{N},p=q\end{array}\right.---\left(16\right)$

Being expressed as matrix form is exactly:

$\left|\begin{array}{ccccc}-1+\frac{2}{N}& & & & \\ & -1+\frac{2}{N}& & \frac{2}{N}& \\ & & ...& & \\ & \frac{2}{N}& & -1+\frac{2}{N}& \\ & & & & -1+\frac{2}{N}\end{array}\right|---\left(17\right)$

At last indexed registers is measured the position that just can obtain the target quantum state, thereby search the position of target fingerprint.

Claims (7)

1. the fingerprint database searching method based on quantum algorithm is characterized in that, comprises following step:

(1) the Hadamard conversion is used in the preceding n position of n+1 position quantum bit state ; Through the collateral action of n door, obtain the balance stack

that ground state is calculated in all n positions

(2) with the state of the n+1 quantum bit for preparing

Connect quantum wire U _fOn, U _fUtilize quantum concurrency principle to come calculated fingerprint to mate total match-score value, finally obtain F is the function that is used for calculating the match-score value, | f (x)>Balance stack attitude to all preceding n position quantum ground state

Carry out a f and calculated the N=2 that once calculates ⁿIndividual template fingerprint and the match-score value of importing fingerprint | f (x)>

(3) two databases of structure, database one comprises four registers, database two comprises N=2 ⁿIndividual register, four registers of database one are one respectively and are initialized as | 0>N quantum bit indexed registers, one be initialized as | s>And in The whole calculations, keep the l quantum bit register, one of this state to be initialized as | 0>L quantum bit data register, one be initialized as

1 quantum bit register, l is the bit number of each match-score string of binary characters maximal value length, s is the string of binary characters of the minutiae point sum of input fingerprint, N template fingerprint is labeled as respectively from 0 to N-1; Database two is preserved all input fingerprint and the resulting N=2 of template fingerprint ⁿIndividual match-score value is expressed as d ₀..., d _N-1, each unit is made up of the l quantum bit;

(4) with x content of registers d of database two _xBe added to the data register of database one, computing method are:

$|0>\→|0\⊕d_x>;---\left(1\right)$

(5) l quantum bit register and the data register to database one compares, if identical, just use the 1 quantum bit register of bit reversal to database one, otherwise remains unchanged.

(6) once more with x content of registers d of database two _xBe added in the data register being operating as of front logarithm data register

Obtain state | d _x>So, carrying out once such operation again, this step data register returns to state | 0>, last indexed registers obtains N state.

(7) N the state that obtains used Hadamard conversion

the vectorial application matrix D of the probability amplitude of all states of indexed registers is carried out unitary transformation; Rotate the mean value of all states; The searching scope of target quantum state is dwindled greatly; Amplify to seek the probability amplitude of quantum state; At last indexed registers is measured the position that just can obtain the target quantum state; Thereby search the position of target fingerprint, matrix D is:

$\left|\begin{array}{ccccc}-1+\frac{2}{N}& & & & \\ & -1+\frac{2}{N}& & \frac{2}{N}& \\ & & ...& & \\ & \frac{2}{N}& & -1+\frac{2}{N}& \\ & & & & -1+\frac{2}{N}\end{array}\right|---\left(2\right)$

2. a kind of fingerprint database searching method as claimed in claim 1 based on quantum algorithm; The method of the bit reversal that step (5) is related; It is characterized in that the identical d of being if x match-score value in the database two and the minutia of input fingerprint are counted _x=s, the state of database one by

Convert into

If it is different then the state of database one is constant.

3. a kind of fingerprint database searching method based on quantum algorithm as claimed in claim 1, the method for the bit reversal that step (5) is related is characterized in that the state of indexed registers obtains-1 phase shifts at last.

4. a kind of fingerprint database searching method based on quantum algorithm as claimed in claim 1, step (4) is characterized in that x content of registers d of database two to the described any indexing means of step (6) _xBeing added to data register is to carry out addressing through index x, just the N=2 through obtaining ⁿIndividual template fingerprint and the match-score value d that imports fingerprint ₀..., d _N-1N subscript carry out index.

5. a kind of fingerprint database searching method based on quantum algorithm as claimed in claim 1, the described any indexing means of step (4) or step (6) is characterized in that x content of registers match-score value d _xBeing added to what carry out in the data register is that mould 2 adds.

6. like the described method of claim 1 to 5; The position of N the quantum state that comprises in the final indexed registers that obtains is with corresponding one by one with N the resulting N of a template fingerprint match-score value position by the input fingerprint, searches for the position that the position that obtains the target quantum state also just searches target fingerprint.

7. like the described any indexing means of claim 1 to 5,2 ⁿIndividual template fingerprint and the match-score value d that imports fingerprint ₀, d ₁... d _x..., d _N-1All subscripts be that index x is the stack that is in multiple value.

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