IMPROVED FUZZY VAULT SCHEME FOR FINGERPRINT

VERIFICATION

Orencik, T. B. Pedersen, E. Savas¸ and M. Keskinoz

Faculty of Engineering & Natural Sciences, Sabanci University, Istanbul, 34956, Turkey

Keywords:

Fuzzy Vault, Template Protection, Biometrics, Fingerprint, Privacy.

Abstract:

Fuzzy vault is a well-known technique to address the privacy concerns in biometric identiﬁcation applications.

We revisit the fuzzy vault scheme to address implementation, efﬁciency, and security issues encountered in

its realization. We use the ﬁngerprint data as a case study. We compare the performances of two different

methods used in the implementation of fuzzy vault, namely brute force and Reed Solomon decoding. We

show that the locations of fake (chaff) points in the vault leak information on the genuine points and propose

a new chaff point placement technique that makes distinguishing genuine points impossible. We also propose

a novel method for creation of chaff points that decreases the success rate of the brute force attack from 100%

to less than 3.5%. While this paper lays out a complete guideline as to how the fuzzy vault is implemented in

an efﬁcient and secure way, it also points out that more research is needed to thwart the proposed attacks by

presenting ideas for future research.

1 INTRODUCTION

Identiﬁcation for access control and other purposes

can be achieved by utilizing three factors: 1) what you

know (e.g. passwords), 2) what you have (e.g. smart-

cards), and 3) what you are (biometric data identify-

ing a person). Either these factors can be used alone

or any combination of the three can be used together

to increase security and compensate the weaknesses

of one factor. While passwords can be forgotten and

smartcards can be stolen, a biometric is inseparable

from an individual and always accessible providing

comparably high level of security. In addition, it can

easily be combined with other factors to increase se-

curity further. Biometric identiﬁcation, on the other

hand, also suffers from two major drawbacks: 1) the

noisy nature of biometrics measurement process and

2) privacy issues due to the fact that biometric data re-

veals private information about the individuals which

is not intended to be revealed otherwise.

(Juels and Sudan, 2002) proposed the so-called

fuzzy vault scheme to overcome these two drawbacks

associated with biometrics usage in identiﬁcation.

The main idea is to exploit the relationship between

error correction and secret sharing — the biometric

data together with a secret deﬁnes a codeword from

an appropriate error correction code. Given the ﬁn-

gerprint, the codeword can be corrected, and the se-

cret is extracted. However, the secret does not re-

veal anything about the biometric data. If the secret is

compromised, one can always choose another secret

to combine with the same biometric.

A successful application of fuzzy vault to ﬁnger-

print biometrics is due to (Uludag et al., 2005) that ba-

sically uses the brute force approach. Different from

Clancy’s work they used alignment helper data which

decreases the error rates, and also a Cyclic Redun-

dancy Check (CRC) embedded in a coefﬁcient of the

secret polynomial is used to guarantee that the correct

polynomial is found.

In this paper, we focus on several issues involv-

ing fuzzy vault implementation for biometrics usage.

The ﬁrst issue is to compare the computational efﬁ-

ciencies of the aforementioned two methods, namely

brute-force and RS decoding methods. Another issue

we deal with is to analyze some security drawbacks of

the fuzzy vault scheme and propose solutions to those

weaknesses as outlined below:

• The locations of the points in the vault may reveal

some information as to which points are genuine

depending on the chaff point generation. We pro-

pose a method in Section 4.1 that makes distin-

guishing genuine points impossible.

• Mihailescu (Mihailescu, 2007) pointed out that

the fuzzy vault scheme is vulnerable to brute force

attack. We propose a new method in Section 4.2 to

Örencik C., B. Pedersen T., SavaÈ

Z E. and Keskinoz M. (2008).

IMPROVED FUZZY VAULT SCHEME FOR FINGERPRINT VERIFICATION.

In Proceedings of the International Conference on Security and Cryptography, pages 37-43

DOI: 10.5220/0001917600370043

 SciTePress

decrease the success rate of this attack from 100%

to less than 3.5%. This countermeasure proves to

be useful in certain settings.

• We study the effects of distances between chaff

points and between a chaff and a genuine point on

the security of the fuzzy vault.

• We also study limitations on the vault size and

its effects on the security and performance of the

fuzzy vault.

The rest of the paper is organized as follows. Sec-

tion 2 gives a review of the fuzzy vault scheme and

explains the most important details of the brute force

and Reed Solomon decoding algorithms (Roth, 2006)

used for reconstructing the secret polynomial hidden

in the fuzzy vault. Section 3 provides comparative

analysis for the performance of two techniques used

in polynomial reconstruction. Section 4 outlines two

proposed modiﬁcations to the enrollment stage to in-

crease the security of the fuzzy vault and summarizes

the security analysis of the scheme against brute force

attack. Section 5 explores the effects of the vault and

threshold sizes on the performance and security of the

fuzzy vault using experimental data. It also provides

a timing comparison between brute force and RS de-

coding methods. Section 6 is devoted to the summary

of the paper and proposes a new idea for future work.

2 REVIEW OF FUZZY VAULT

In this section we give a brief outline for the tech-

niques used in the application of fuzzy vault scheme

to ﬁngerprint biometrics. The identiﬁcation process

using the fuzzy vault consists of two major stages: the

enrollment and veriﬁcation. In the enrollment stage,

the fuzzy vault is created by embedding a secret poly-

nomial after the ﬁngerprint of the user is obtained.

The fuzzy vault hides the ﬁngerprint and the secret

polynomial, which can be revealed if the same ﬁnger

is used in veriﬁcation. The veriﬁcation stage contains

two phases: 1) the alignment of the measured ﬁnger-

print to the points in the fuzzy vault, and 2) the re-

construction of the secret polynomial. The enrollment

and alignment stages are the same for both brute force

and RS decoding methods that differ in the polyno-

mial reconstruction phase. The details of enrollment

and allignment stages are provided in (Juels and Su-

dan, 2002), (Clancy et al., 2003), therefore only the

polynomial reconstruction stage is described brieﬂy

in the following two sections.

2.1 Brute Force Approach

To reconstruct the secret polynomial using brute force

approach requires trying all the combinations of size k

given m matching minutiae points. Note that some of

the m matching minutiae points are the ones that ac-

tually match random chaff points in the fuzzy vault.

When k minutiae points that match the real minu-

tiae points are found during the exhaustive search, the

scheme is said to be successful.

In brute force approach, ﬁrst k pairs of (x

) are

chosen randomly from the veriﬁcation list and the

polynomial on which the selected k pairs lie is cal-

culated using Lagrange interpolation method. Then

whether µ of the remaining vault points satisﬁes y

p(x

) is tested. If more points that lie on the same

polynomial are found, the ﬁngerprint is veriﬁed; oth-

erwise rejected. If insufﬁcient number of pairs satisfy

= p(x

) condition, another random k pairs are taken

as input and the process is repeated. The maximum

number of trials is set to a high value, after which the

program rejects the ﬁngerprint if no polynomial sat-

isfying the condition is found. The drawback of the

brute force approach is high computation complexity

when the tested ﬁngerprint is too noisy.

2.2 Reed Solomon Decoding Approach

When we construct the fuzzy vault we evaluate the

secret polynomial for all n minutiae points, i.e. y

p(x

) for i = 1,... n. This can be put into a matrix-

vector formulation as follows:



... y





... p

k−1



where the matrix G is the generator matrix (Roth,

2006).

It is crucial to notice that the generator matrix

changes for each user, which differ from the conven-

tional application of RS encoding method. Since the

enrollment stage essentially utilizes the RS encoding,

the reconstruction of the secret polynomial in the ver-

iﬁcation stage can be achieved by employing an RS-

Decoder.

Utilizing error correcting codes for the implemen-

tation of fuzzy vault is ﬁrst proposed by (Juels and

Sudan, 2002). The authors state that after matching

minutiae points are obtained, use of Reed-Solomon

(RS) decoder is a more efﬁcient approach than the

brute force. The Reed-Solomon decoders have an

error correction capability of τ =

m−k

errors. The

best choice to implement RS decoder is to use the

Berlekamp-Massey (BM) algorithm as explained also

in (Clancy et al., 2003) since it is fast, easy to imple-

ment and widely studied.

SECRYPT 2008 - International Conference on Security and Cryptography

The RS decoding with BM algorithm takes two

vectors (v = [x

,...,x

] and y = [y

,...,y

])

as explained previously and returns the error locater

polynomial (ELP). Since ELP shows the locations of

all errors, the rest of the data must be correct.

Finally, the secret polynomial can be recon-

structed by using the Lagrange interpolation method

with the correct minutia points if the number of errors

does not exceed τ. Otherwise, the function returns a

wrong polynomial of degree k − 1. Again we check

if more points that lie on the same polynomial exist.

Otherwise, the function is called with fewer number

of pairs. This process is repeated several times with

some of the different random pairs being removed

from the list. If the algorithm still returns a wrong

polynomial as output after several attempts, then the

ﬁngerprint is rejected.

3 COMPUTATION COMPLEXITY

OF POLYNOMIAL

RECONSTRUCTION

In (Clancy et al., 2003), Clancy et al. argue that us-

ing the RS decoder is a better approach than the brute

force method if the attacker cannot eliminate some of

the chaff points from the veriﬁcation list. But the au-

thors do not provide a comparison between the two

approaches. In this paper we try to clarify as to which

method is optimal depending on the parameters of m

and k where m is the number of matched points and k

is one more than the degree of the secret polynomial.

For comparing the two approaches, we calculate

the number of operations in the secret polynomial

reconstruction phase for both methods. For sake of

simplicity, we ignore addition and assignment opera-

tions and only count multiplication and inverse oper-

ations in F

since the latter two operations dominate

the computation.

3.1 Complexity of RS Decoder

The Reed Solomon decoder has four steps as ex-

plained in (Roth, 2006) and complexity of each step

and the total complexity is given in Table 1. We as-

sume that Step 3 always returns an error locater poly-

nomial; i.e. the measured ﬁngerprint always leads to

matchings to chaff points.

From the perspective of complexity comparison,

the main difference between the brute force and the

RS decoding approaches is that, RS decoder can dis-

tinguish a genuine ﬁngerprint in only one trial if the

number of incorrect matchings is less than the error

Table 1: Operational Complexity of RS Decoding Method.

Step Multiplication Inv.

1. Constructing H 3m

− 2mk m

2. Syndrome Computation m(m− k) -

3. Finding Error Locations m(k

/3+ 2) -

4. Polynomial Construction k

Total 4m

+ m(k

/3) m

−m(3k+2) + k

correcting capability of the RS code τ. On the other

hand, the brute force approach may have to perform

excessively many trials to complete the veriﬁcation

process.

3.2 Complexity of Brute Force Method

Complexity of the brute force method is given in Ta-

ble 2. Selecting k random points out of m matched

points (i.e. Step 1 in the table) involves a randomized

algorithm, whose complexity we estimate as equiva-

lent to k multiplication operations. The variable l in

the last row of Table 2 stands for the number of trials

needed on average, which naturally increases with the

error in the tested ﬁngerprint. Without knowing the

number of trials l in the brute force method it is not

easy to compare two methods. Comparison is only

possible with experiments on real and synthetic data,

which we achieve in Section 5.

Table 2: Operational Complexity of Brute Force Method.

Phase Multiplication Inv.

1. Choosing k random points k -

2. Polynomial Construction k

3. Veriﬁcation of the result 5m -

Total l(k

+ 5m+ k) -

4 NEW ENROLLMENT STAGE

In this section, we explain two proposed modiﬁca-

tions to the enrollment stage in order to strengthen the

fuzzy vault against possible attacks.

4.1 Distribution of Chaff Points

Creation of random chaff points is crucial since they

should be uniformly distributed in the minutiae space

so that an attacker, having access to the vault, should

not be able to distinguish between genuine minutiae

points and random chaff points (Kholmatov et al.,

2006). If the chaff points were created with the con-

dition that every point in the vault should be at least

IMPROVED FUZZY VAULT SCHEME FOR FINGERPRINT VERIFICATION

t Euclidean distance apart to supply a uniform distri-

bution as proposed by (Juels and Sudan, 2002), the

fuzzy vault could leak some information about the lo-

cation of genuine points. We have no control over the

locations of genuine points, as some of them might

be very close to each other as exempliﬁed in Figure 1

where chaff points are represented as circles and gen-

uine points as circles with crosses. If an attacker inter-

cepts a fuzzy vault, he can locate some of the genuine

points correctly by checking the distances between

the points; i.e. if the distance between two points is

closer than the threshold t, then these points are gen-

uine.

0 100 200 300 400 500

100

150

200

250

300

350

400

450

500

Figure 1: Fuzzy vault as implemented described in (Juels

and Sudan, 2002) where genuine points are marked.

0 100 200 300 400 500

100

150

200

250

300

350

400

450

500

Figure 2: Fuzzy vault with chaff points being placed ac-

cording to a new scheme.

As a remedy, we generate the chaff points with

the condition that every chaff point in the vault should

be at least t Euclidean distance apart from a genuine

point and should be at leastt

′

Euclidean distance apart

from any other chaff point. Note that t

′

< t since hav-

ing chaff points far from the genuine points are de-

sirable and have a positive effect on false reject rate

(FRR) as demonstrated in Section 5. Smaller thresh-

old t

′

, on the other hand, for inter-chaff point dis-

tance is necessary to imitate the distribution of gen-

uine points where close genuine points occasionally

occur in the vault. While t value depends on the ﬁn-

gerprint image size and the total number of points in

the vault, t

′

should be chosen depending on the dis-

tribution of genuine points. For ﬁnger print image

of 500 pixels, Figure 2 shows the fuzzy vault con-

structed with the new chaff point placement strategy,

where the threshold values t and t

′

are chosen as 18

and 8, respectively. As seen in Figure 2, the distri-

bution of chaff points in the fuzzy vault closely re-

sembles the distribution of genuine points, hence an

attacker cannot easily distinguish the genuine points

from the chaff points.

4.2 A Novel Method for Chaff Point

Placement

Note that there are C points in the vault where n

of them are genuine and the secret polynomial has

degree k − 1. Mihailescu proved that in less than

8Ck(C/n)

operations

, the intruder can recover the

secret polynomial (Mihailescu, 2007). The idea of the

attack relies on the established fact (Juels and Sudan,

2002) that when there are more than D vault points on

a polynomial of degree k − 1 for D ∈ (k − 1, n), this

polynomial is the secret polynomial with a very high

probability.

Our proposed method to improve the security in-

volves the idea that, by choosing the chaff points at

random, but in a more cleverway, we can embed some

other (randomly chosen) polynomials of degree k− 1

other than the secret polynomial in the vault. If we

guarantee that the number of chaff points that lie on

these (fake) polynomials, is around n - the same num-

ber of genuine points on the secret polynomial on av-

erage - the attacker cannot distinguish the secret poly-

nomial from the fake ones. Otherwise the attacker

who succeeds to construct a polynomial can discard it

if there are fewer points. One way of choosing non-

random points is described below:

1. Place the genuine points in the vault

2. Keep the unassigned chaff points in a pool

3. Keep a list of fake polynomials which is initially

empty

4. Repeat until the pool is empty

(a) Pick a random number r close to n

(b) For the ﬁrst fake polynomial, take random k− 1

points from the vault and take one random point

By operation it is meant that atomic arithmetic opera-

tions such as additions and multiplications.

SECRYPT 2008 - International Conference on Security and Cryptography

from the pool. For others take random k points

from the vault.

degree polynomialthat passes

through the selected points. Add the polyno-

mial to the list if it is not already in it.

(d) Check the vault if there are any other points that

lie on the polynomial. Decrement r by the num-

ber of points on this polynomial.

(e) Pick r points from the pool (or the remaining

points if their number is less than r) and eval-

uate these points on the fake polynomial and

place the resulting values in the fuzzy vault.

With the proposed chaff placement method, we al-

low each polynomial intersect with other polynomials

in at least k vault points which increases the maximum

number of polynomials we can embed into the vault.

Note that any two polynomials cannot intersect with

each other in more than k−1 points. As a result of our

experiments in our setting described above, we are

able to hide around 30 fake polynomials in the vault.

Therefore, this method decreases the probability of

ﬁnding the secret polynomial using Mihailescu’s at-

tack from 100% to approximately 3.3% after the brute

force attack is applied. Due to the fact that most of the

identiﬁcation applications allow only limited number

of trials, the proposed method enhance the security

considerably. Moreover, the method does not affect

the false accept or false reject rates since the match-

ing algorithm considers only the x coordinates of the

points and this method changes only the y coordi-

nates.

4.3 Security Analysis

The attacks on the fuzzy vault scheme, mostly assume

the interception of a vault from a database. The basic

attack is the brute force attack over a single vault. The

analysis in this work based on the work of Mihailescu

(Mihailescu, 2007), shows that this attack is not com-

putationally infeasible, therefore fuzzy vault scheme

is insecure without additional security.

If an attacker intercepts a vault, but has no other

information about the locations of the genuine points,

the best method to recover the secret polynomial is

the brute force trials (Clancy et al., 2003)(Mihailescu,

2007). Mihailescu providesa strong brute force attack

in (Mihailescu, 2007), which ﬁnds the secret polyno-

mial in less than 8(Ck)(C/n)

operations where C is

the number of points in the vault, n is the number of

genuine points in the vault and the degree of the secret

polynomial is k− 1.

In our tests n parameter is on the average 35

and k is constant 10. For C = 300, which gives a

better FRR, breaking the system requires 8 × 300×

10 × (300/35)

≈ 2

operations. For C = 350,

which gives a worse FRR, the system provides a bet-

ter security; breaking the system requires this time

8× 350 × 10× (350/35)

≈ 2

operations.

Without the use of the proposed method in section

4.2, the secret polynomial is found with probability

1 after this attack. However, our proposed method

decrease the probability to approximately 0.03 since

the polynomial found as a result of brute force attack

is not guaranteed to be the secret polynomial.

5 TEST RESULTS

We implement polynomial reconstruction phase using

two previously discussed approaches: 1) brute force

method and 2) RS decoding.

For the implementations, we use a database of

180 people where there are two ﬁngerprint images

for each ﬁnger, totaling 360 ﬁngerprints. The ﬁrst

180 ﬁngerprint images are used for enrollment and

the second 180 images are used for veriﬁcation of the

corresponding ﬁngerprints. Later, all ﬁngerprints are

cross-tested for false accept rates. In the experimental

setting bitmap images of 500× 500 pixels are created

for each ﬁngerprint.

All computations and tests are performed on a

computer with 1.7 GHz Intel Celeron M processor

and 448MB of RAM. The codes are developed in ei-

ther Matlab or C++ (Microsoft Visual Studio) depend-

ing on the nature of the problem.

We basically investigate two issues; ﬁrstly, the ef-

fects of the vault and threshold sizes on the perfor-

mance and security of the fuzzy vault, and secondly

time efﬁciencies of two methods used in the polyno-

mial reconstruction phase of the veriﬁcation stage.

5.1 Effects of Vault and Threshold Sizes

The false reject rates (FRR) and false accept rates

(FAR) are calculated in four settings where different

values for vault size and minimum distance threshold

are used for our database of ﬁngerprints. We use vault

sizes of 300 and 350 points and minimum distance

thresholds of (t = 15) and (t = 18). The minimum

distance between any two chaff points is taken as 8.

We calculate the FAR and FRR results for both the

brute force and the RS decoding methods.

The FAR rates turn out to be 0% in all settings

after cross testing all ﬁngerprint images with different

ﬁngers in four settings.

Table 3 shows the FRRs for different vault sizes

and threshold values. The results clearly demonstrate

IMPROVED FUZZY VAULT SCHEME FOR FINGERPRINT VERIFICATION

Table 3: FRR for four different settings.

Vault Size

Threshold (t) 300 350

15 6.5% 9%

18 1.5% 4.5%

that as the minimum distance between two points in-

creases, the possibility of a genuine point matching to

a chaff point decreases resulting in lower FRRs. Al-

though the two values of threshold used in the exper-

iments have the same security level, increasing it fur-

ther may become impossible after certain point since

we cannot place as many points as we desired. Sim-

ilarly, when more chaff points are added to the vault,

the possibility of a genuine point matching to a chaff

point increases. Larger vault size results in higher se-

curity. The security impact of vault size was analyzed

in Section 4.3.

5.2 Timing Results for Polynomial

Reconstruction Phase

As explained before, veriﬁcation phase is the main

part where two approaches are compared in terms

of timing and success performance. The “Number

Theory Library” (NTL) (Shoup, 2008) is used for

all the operations in the polynomial reconstruction.

For both approaches, the polynomial reconstruction

algorithms take two vectors x = {x

,...,x

} and

y = {y

,...,y

} where y

= P(x

) for the points

matched to a genuine point and y

6= P(x

) for the

points matched to a chaff point.

We ﬁrst compare the timing results of the two ap-

proaches using our database of real ﬁngerprints. In

case of true ﬁngerprints we ﬁnd that for 15% of the

data, the RS decoding approach is faster. For forgery

data, RS decoding method is naturally always faster

since concluding that a ﬁngerprint is a forgery takes

1000 trials in our experiments.

Considering that the database used in the exper-

iments may not fully represent all cases, especially

the ones with high levels of noise in measurement

process, we use synthetic data to control the number

matched points in the alignment process. We generate

synthetic ﬁngerprints and corresponding fuzzy vaults

of 350 total points, where the number of matched

points are in the range of [21,35]. Timing results

of the experiment for changing number of matched

points are shown in Figure 3(a). As clearly observed

in the ﬁgure, the brute force method takes much

longer when the number of matching points are low

due to excessive number of trials to ﬁnd the correct

matching points. As the number of matching points

increases, the brute force becomes faster. We also

provide the same graphic for number of operations in

Figure 3(b), that we obtain in our theoretical analysis.

The similarity of two ﬁgures show that the experimen-

tal results are in line with the theoretical analysis

22 24 26 28 30 32 34

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

x 10

# genuine out of 35 points matched

time (ms)

time RS

time BF

(a) Timing complexities of two methods with varying

number of matched points.

22 24 26 28 30 32 34

x 10

# genuine out of 35 matched points

# of operations

opr RS

opr BF

(b) Operational complexities of two methods with

varying number of matched points.

Figure 3: Comparison of complexities of two methods.

The experiments demonstrate that the optimal

method changes depending on the number of genuine

points matched. The brute force approach is faster if

the matching is very good (i.e. most of the minutiae

points are matched to genuine points) since it will re-

quire very few trials to ﬁnd the polynomial. On the

other hand, the RS decoder is very fast to reject a

forgery since brute force will require excessive num-

ber of trials to decide on a reject. Also for a weak

matching of a valid ﬁngerprint, the RS decoder is

again faster.

6 CONCLUSIONS AND FUTURE

WORK

In this paper, we addressed the implementation, se-

curity, and performance issues of fuzzy vault for bio-

metric identiﬁcation. We ﬁrst provided a guideline

that brieﬂy explains the implementation steps of de-

SECRYPT 2008 - International Conference on Security and Cryptography

coding using two methods: brute force and Reed-

Solomon (RS). We then compared the efﬁciencies of

the two methods. The results shows that for weak

matching, the RS decoding method is more efﬁcient;

but for good matching, the brute force method works

faster. For the success rate of veriﬁcation, they both

give the same false accept rate (FAR) and false reject

rate (FRR).

We proposed a new chaff point placement method

to prevent some inferences on the location of gen-

uine points. By adjusting the distance between points

(genuine-to-chaff and chaff-to-chaff) we showed that

it is possible to increase security and performance of

the fuzzy vault implementation.

We explored the effects and limitations of the

vault size on the security and performance of the

fuzzy vault. The higher number of chaff points in

the vault is demonstrated to strengthen the method

against the most successful attack. However, plac-

ing more chaff points takes more time and becomes

impossible after certain number and has an adverse

effect on the FRR rate.

We proposed to embed a number of fake polyno-

mials in the fuzzy vault along with the secret polyno-

mial to reduce the success rate of the attacker. We suc-

ceeded in placing only limited number of fake poly-

nomials in the vault. We believe that further research

will reveal more efﬁcient methods to place higher

number of fake polynomials in the vault, that will fur-

ther increase the security.

Other than the brute force attack, there is another

attack that can be applied in the presence of two vaults

that belong to the same biometric (Kholmatov and

Yanikoglu, 2008). The correlation attack basically

utilizes two vaults of the same ﬁngerprint to reveal

most of the minutiae points by cross-matching the two

vaults. The correlation attack takes advantage of the

fact that minutiae point locations are almost the same

in two vaults and increasing the vault size has only

limited effect on the security. A more effective solu-

tion will be keeping a distorted version of the biomet-

ric that preserves the invariants of the biometric im-

age. For instance, Sutcu et al. (Sutcu et al., 2005)

proposed a method that uses Gaussian function for

distortion of the biometric. We plan to use a special

hash function that gives similar outputs for inputs that

differ by a few bits. By keeping the hash values of the

ﬁngerprint minutiae values and performing matching

in the hash space, we can avoid the correlation at-

tacks. The effectiveness of this method remains to

be analyzed which we plan to pursue as future work.

ACKNOWLEDGEMENTS

We would like to thank Eren Camlikaya for his ﬁn-

gerprint image processing codes. We also would like

to thank TUBITAK (The Scientiﬁc and Technical Re-

search Council of Turkey) for the M.Sc. fellowship

supports granted to Cengiz Orencik.

REFERENCES

Clancy, C., Kiyavash, N., and Lin, D. (2003). Secure

smartcard - based ﬁngerprint authentication. In ACM

Workshop on biometric methods and applications,

(WBMA).

Juels and Sudan, M. (2002). Fuzzy vault scheme. In

IEEE International Symposium on Information The-

ory, page 408.

Kholmatov, A. and Yanikoglu, B. (2008). Realization of

correlation attack against fuzzy vault. In Security,

Forensics, Steganography and Watermarking of Mul-

timedia Contents X, Electronic Imaging, San Jose CA,

USA.

Kholmatov, A., Yanikoglu, B. A., Savas, E., and Levi, A.

(2006). Secret sharing using biometric traits. In Bio-

metric Technology For Human Identiﬁcation III, vol-

ume 62022006, Orlando, Florida USA. In Proceed-

ings of SPIE.

Mihailescu, P. (2007). The fuzzy vault for ﬁn-

gerprints is vulnerable to brute force attack.

http://arxiv.org/abs/0708.2974v1.

Roth, R. M. (2006). Introduction to Coding Theory. Cam-

bridge University Press.

Shoup, V. (2008). Ntl: A library for doing number theory.

Sutcu, Y., Sencar, H. T., and Memon, N. (2005). A se-

cure biometric authentication scheme based on robost

hashing. In Proceedings of the 7th workshop on mul-

timedia and security, NY, USA.

Uludag, U., Pankanti, S., and Jain, A. (2005). Fuzzy vault

for ﬁngerprints. In Proceeding of International Con-

ference on Audio- and Video-Based Biometric Person

Authentication, pages 310–319.

IMPROVED FUZZY VAULT SCHEME FOR FINGERPRINT VERIFICATION