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by Bolle et al. [2] when it was observed that the empir-

ical false reject rate (FRR) was signiﬁcantly better than

predicted by their theoretical model. This fact implied

that the bits of an iris code are not equally susceptible

to ‘‘ﬂip’’, given different environmental conditions that

affect the quality of the captured iris images. Hollings-

worth et al. demonstrated that by eliminating (mask-

ing) inconsistent bits, one could dramatically improve

the FRR of an iris template.

Although the work of Hollingsworth et al. improves

the FRR by identifying and removing fragile bits, our

preliminar y results show that it may be possible, based

on bit instability, to further reduce the number of iris

code bits needed for recognition. Our results show that

this can also be done without an increase in the false

accept rate (FAR). By using GRIT (Genetically Reﬁned

Iris Templates), iris code templates can be reﬁned and

transformed into templates that use a signiﬁcantly

smaller number of iris code bits for iris recognition.

GRIT is a system that uses the concepts of bit inconsis-

tency [1] and simulated evolution [3–6] in an effort to

evolve iris code templates that use fewer iris code bits.

Bit Inconsistency

In [1], Hollingsworth et al. selected a dataset of 1251

images that were mostly unoccluded by eyelids or

lashes. If an individual iris code bit was mostly one

particular bit value and ‘‘ﬂipped’’ to the other bit value

some threshold percentage of the time, the bit was

considered fragile (inconsistent). For their analysis, a

bit was considered fragile if it ﬂipped more than 40%

of the time. The ir results indicated that on average,

15% of the bits had probability greater than 40% of

ﬂipping and 85% of the bits had probability less than

40% of ﬂipping. The implication of these rates indi-

cates that the FRR of systems using Daugman-style [7]

iris recognition system s could be dramatically reduced

by focusing only on consistent bits. With this modiﬁed

strategy, iris images would be analyzed to create an iris

template that would mask out inconsistent bits. This

mask would be combined with the typical masks used

to eliminate eyelids and eyelashes.

Genetically Refined Iris Templates

(GRIT)

GRIT is a system for evolving iris tem plates that have a

decreased FRR; use a smaller number of iris code bits;

and do not have an increased FAR. GRIT is composed

of two components: a preprocessor and a Geneti c

Algorithm (GA) [3–6]. The GRIT preprocessor uses

the concept of bit instability to eliminate fragile bits as

well as develop a probability distribution function to

be used by the GA to further reduce the number of iris

code bits needed for recognition. GAs belong to a class

of search techniques based on simulated evolution [5]

and have been successfully used to solve a wide range

of complex real-world search, optimization, and

machine-learning problems.

The GRIT Preprocessor

In order to describe the GRIT preprocessor, let I ={i

, ..., i

n1

} and M ={m

, m

, ..., m

n1

} be sets of iris

codes along with their associated bit masks. The pre-

processor, as shown in Fig. 1, works as follows. Given a

set of iris codes a nd masks it sets i to the ﬁrst iris code,

, in the set of iris codes and m to the associated mask

of i

, m

. Next a hyper iris code and a hyper mask are

created. The hyper iris code, v, simply records the

number of iris codes in I that have the same value for

each corresponding bit in i. The hyper mask, w,

records the number of iris codes in I (along with

their masks in M) that used a particular mask bit

(associated with the best offset resulting in the best

hamming ratio [7]) when comparing those iris codes

with i, given m.

Given v and w, the relative worth of ﬂipping a bit in

i can be computed. The hyper gain, g, represents the

number of iris codes in I that i will become closer to

Iris Template Extraction Via Bit Inconsistency and GRIT.

Figure 1 The GRIT Preprocessor.

860

Iris Template Extraction Via Bit Inconsistency and GRIT

(with respect to hamming ratio) by ﬂipping a par ticu-

lar bit. Those bits in i that have an associated positive

gain can be ﬂipped, because they will make the result-

ing iris template, i

, closer to a greater number of iris

codes in I. Those bits in i that have an associated gain

of zero represent bits that have a 50% inconsistency

rate, and therefore, can be ‘‘turned off

’’ (or masked)

by setting the associated bit in m to zero. The GRIT

preprocessor returns a modiﬁed iris code, i

, and mask,

, that has a lower FRR w ith respect to I than the iris

template consisting of i and m. The hyper gain, g, is also

returned and used as a probability distribution func-

tion (heuristic) to guide the mutation operator of the

GRIT genetic search method. Figure 1 provides a pseu-

do-code example of the GRIT preprocessor.

The GRIT GA

The GRIT GA takes as input i

, m

,g,I,M,andd,

where d represents the number of bits to mutate in

creating an offspring template. The GRIT GA begins

by creating P-1 mutants of m

, where P represents the

population size of the GA. These mutants along with i

make up the initial population of candidate bit masks.

In creating the initial population, each of the mutants

is created by mutating 100d bits of m

as follows. Two

bit positions are select ed at random and their asso-

ciated gains (using g) are compared. The bit that has

the highes t gain is then mutated (ﬂipped). This is how

the Mutate method of the GRIT GA operates.

Each candidate bit mask in the initial population is

evaluated using the following evaluation function:

Fði

; c

mask

; I; M; tÞ¼

bði

; c

mask

; i

; m

; tÞ

þ Rði

; c

mask

; I; M; t Þ;

where c

mask

represents a candidate mask,

bði

; c

mask

; i

; m

; tÞ represents the number of iris code

bits used in the comparison between the candidate

iris template and the jth iris code in I, and

Rði

; c

mask

; I; M; t Þ represents the penalty if any of the

iris codes in I is rejected by the template, (i

, c

mask

), by

have a hamming ratio greater than a user-speciﬁed

threshold, t. The penalty is simply the summation of

the amount by which the rejected iris codes exceed the

threshold plus a constant value, a.

After each candidate mask has been evaluated and

assigned a ﬁtness by the evaluation function F, the

counter, t, is set to |P| and the GA begins its evolution-

ary process. When the user-speciﬁed number of iris

template evaluations has not been reached, the GA

creates an offspring iris template mask by (1) selecting

two individuals from the current population as par-

ents; (2) crossing over [8] the parents to form an

‘‘embryo’’ by taking 50% of the bits from one parent

and 50% of the bits from the other parent; and

(3) mu tating the ‘‘embryo’’. The offspring is then eval-

uated and replaces the worst-ﬁt individual in the pop-

ulation (regardless of whether the worst-ﬁt indiv idual

has a better ﬁtness than the offspring). This process is

repeated until the user-speciﬁed number of evaluations

(Max_Evaluations) has been met. After the evolution-

ary process, the iris template with the lowest ﬁtness in

the population is then returned as the best solution

evolved by the GA. Figure 2 provides a pseudo-code

version of the GRIT GA.

The parent selection method works as follows:

(1) randomly select two individuals from the popula-

tion (excluding the worst-ﬁt individual) and return the

individual with the lower ﬁtness as the ﬁrst parent

(mom); (2) repeat this process to get a second parent

(dad). This parent selection method is commonly re-

ferred to as tournament selection [5].

Preliminary Results

For this work, the iris images were segmented using the

algorithm proposed by Thornton et al. [9], which ﬁnds

Iris Template Extraction Via Bit Inconsistency and GRIT.

Figure 2 GRIT (Genetically Refined Iris

Templates).

Iris Template Extraction Via Bit Inconsistency and GRIT

861

Iris Template Extraction Via Bit Inconsistency and GRIT. Table 1 The Hyper Gains of Subjects Before Revising the

Templates

Subject Hyper Gain

862

Iris Template Extraction Via Bit Inconsistency and GRIT

nonconcentric circles for both pupil and iris bound-

aries with high accuracy. Eyelids and eyelashes were

manually segmented. Given the iris images with occlu-

sion masks, iris codes are generated by convolving

them with a one-dimensional log Gabor ﬁlter row by

row. As in the Daugman’s algorithm [7, 10], the phase

information at each pixel is quantized into two bits,

and then Hamming distances are calculated by com-

paring these bits.

GRIT was used to develop iris templates for a total

of seven subjects taken from the ICE 2006 dataset [11]:

4, 5, 38, 51, 67, 75, and 93. For these subjects, the ﬁrst

10 iris codes in their respective sets were used to

develop an iris template. The other 20 iris codes were

used as a FRR test set. Each resulting iris template was

checked with all of the other instances of the ICE 2006

dataset to determine its FAR.

The GRIT GA used a population size of 20 candi-

date bit masks and evolved an additional 4820 while

keeping the best 19 candidate bit masks ever found at

all times. The value of d, the number of bits to mutate

in creating an offspring, was set to 100, and the penalty

Iris Template Extraction Via Bit Inconsistency and GRIT. Table 2 The Hyper Gains of Subjects After Revising the

Templates

Subject Hyper Gain

Iris Template Extraction Via Bit Inconsistency and GRIT

863

constant, a, used in the penalty function, R, was set to

43,920, because the dimensions of the iris codes and

masks used were 613602 bits.

Table 1 presents the hyper gains developed by the

GRIT preprocessor for each of the seven subjects.

In Table 1, for each visualization, the values associated

with higher magnitudes (farthest away from zero) are

more consistent (less fragile) than those bits with lower

magnitudes. The red areas of a given subject represent

the bits of the initial iris code template that were

ﬂipped in an effor t to reduce the FRR of the 10 training

instances. The green areas in the hyper gains represent

those bits of the iris code mask that have been removed

(‘‘turned off’’). The larger solid green regions that

appear at the top of each of the hyper gains in Table 1

represent the initial masked bits. Table 2 presents the

hyper gains after the iris template, (im), has been

revised to form ( i

). Notice that the visualizations

show that there are a number of bits w ith hyper gain

values close to zero that may be removed.

In Table 3, a comparison of the original masks, the

masks developed by the GRIT preprocessor, and the

Iris Template Extraction Via Bit Inconsistency and GRIT. Table 3 Preliminary GRIT Results

Subject Mask Type FRR Bits Used Visualized Masks

4 Original 0.0 (0.07) 31196

GRIT-PP 0.0 (0.07) 30545

GRIT-GA 0.0 (0.03) 20382

5 Original 0.0 (0.00) 32250

GRIT-PP 0.0 (0.00) 31635

GRIT-GA 0.0 (0.00) 21200

38 Original 0.6 (0.67) 30371

GRIT-PP 0.0 (0.00) 29667

GRIT-GA 0.0 (0.00) 19173

51 Original 0.2 (0.13) 31456

GRIT-PP 0.0 (0.00) 30743

GRIT-GA 0.0 (0.00) 20169

67 Original 0.1 (0.03) 31206

GRIT-PP 0.0 (0.00) 30455

GRIT-GA 0.0 (0.00) 19766

75 Original 0.4 (0.37) 32724

GRIT-PP 0.0 (0.03) 31831

GRIT-GA 0.0 (0.03) 21759

93 Original 0.0 (0.07) 33070

GRIT-PP 0.0 (0.00) 32365

GRIT-GA 0.0 (0.00) 21728

864

Iris Template Extraction Via Bit Inconsistency and GRIT

masks evolved by the GRIT GA are compared for each of

the seven subjects. For each of the masks, the FRR on the

training set of 10 instances is presented. For each of the

masks, the number in parenthesis represents the FRR of

the templates, compared with the 30 instances of I. In the

next column, the average number of bits used in the

comparisons with instances in the ICE dataset is pre-

sented. The ﬁnal column in Table 3 shows a visualiza-

tion of the original mask, the modiﬁe d mask developed

by the GRIT preprocessor, and the mask evolved by the

GRIT GA. The FARs for all of the templates were zero.

In Table 3, notice that except for Subjects 4 and 75,

the GRIT preprocessor was able to develop a modiﬁed

iris code template and mask that reduced the FRR

to zero. For Subject 4, the GRIT GA was able to reduce

the FRR on the test set. This suggests that long runs

of the GA may reduce the test set FRR further.

Also, notice in Table 3 that the GRIT preproc essor is

able to reduce the number of iris code bits needed to be

used for recognition; however, the GRIT GA is able to

reduce this number even further. The resulting iris codes

bits needed are reduced by approximately 30% for each of

the seven subjects.

Summary

In this article, GRIT, a novel approach toward devel-

oping iris templates, has been described. GRIT uses the

concepts of bit inconsistency and genetic search to

evolve iris templates that use a reduced number of

iris code bits for iris recognition. The preliminary

results show that the combination of bit inconsistency

and genetic search provides a powerful hybrid for

developing iris templates. Our results show that the

reduction in the iris code bits needed does not result in

an increase in FRR and FAR.

References

1. Hollingsworth, K., Bowyer, K., Flynn, P.: All iris code bits are not

created equal. In: 2007 IEEE Conference on Biometrics: Theory,

Applications, and Systems, September (2007)

2. Bolle, R.M., Pankanti, S., Connell, J.H., Ratha, N.: Iris individu-

ality: A partial iris model. In: Proceedings of the 17th Interna-

tional Conference on Pattern Recognition, vol. 2, pp. 927–930

(2004)

3. Davis, L.: Handbook of Genetic Algorithms. New York, Van

Nostrand Reinhold (1991)

4. Dozier, G., Homaifar, A., Tunstel, E., Battle, D.: An Introduction

to Evolutionary Computation (Chapter 17). In: Zilouchian, A.,

Jamshidi, M. (eds.) Intelligent Control Systems Using Soft Com-

puting Methodologies, pp. 365–380. Boca Raton, FL, CRC press

(2001)

5. Fogel, D.B.: Evolutionary computation: Toward a new philoso-

phy of machine intelligence, 2nd edn. Las Alomitas, IEEE Press

(2000)

6. Goldberg, D.E.: Genetic Algorithms in Search, Optimization &

Machine Learning. Addison-Wesley Publishing Company, Inc.,

Reading, Massachusetts (1989)

7. Daugman, J.: How iris recognition works. IEEE Trans. Circ. Syst.

Video Technol. 14(1), 21–30 (2004)

8. Syswerda, G.: Uniform Crossover in Genetic Algorithms. In:

David S. (eds.) Proceedings of the Third International Confer-

ence on Genetic Algorithms (ICGA-89), pp. 2–9. San Francisco,

CA, Morgan Kaufmann (1989)

9. Thornton, S.M., Kumar, V.: Robust iris recognition using advanced

correlation techniques. Proceedings of the International Confer-

ence On Image Analysis and Recognition, pp. 1098–1105 (2005)

10. Daugman, J.: High conﬁdence visual recognition of persons by a

test of statistical independence. IEEE Trans. Pattern Anal.

15(11), 1148–1161 (1993)

11. Iris Challenge Evaluation. National Institute of Standards and

Technology, http://iris.nist.gov/ICE/, (2006)

Iris Template Protection

PATRIZIO CAMPISI,EMANUELE MAIORANA,

LESSANDRO NER I

University of Roma TRE, Rome, Italy

Synonym

Iris template security

Definition

▶ Template protection is a crucial requirement when

designing a biometric based authentication system. It

refers to techniques used to make the stored template

unaccessible to unauthorized users. From a template,

information about the user can be revealed. Moreover,

identity theft can occur. Therefore, it is of dramatic

importance, if a template is compromised, to cancel,

to revoke, or to renew it. Template protection can be

performed using

▶ template distortion techniques,

Iris Template Protection

865

▶ biometric cryptosystems, and ▶ data hiding techni-

ques. Template protection techniques speciﬁcally

designed and applied to

▶ iris images are hereafter

summarized.

Introduction

Template protection is a key issue that has to be

addressed when a biometric based authentication sys-

tem is designed. It is highly desirable to keep secret a

template both for security and for privacy reasons, and

in case a template is compromised it is necessary to

revoke, to cancel, or to renew it. Also, it is highly

recommended to obtain from the same biometric dif-

ferent templates in order to avoid unauth orized track-

ing across different databases. In the recent past several

techniques have been proposed to secure biometric

templates and to provide the desirable cancelability

and renewability properties. In the following limi-

tations of classical cryptography, when applied within

the biometric framework, are highlighted. Moreover,

recently introduced techniques like template distor-

tions, biometric cryptosystems, and data hiding tech-

niques are brieﬂy discussed ﬁrst in general and later

with speciﬁc application to iris template protection.

Cryptography [1] allows secure transmission of

data over a reliable but insecure channel. The privacy

of the message and its integrity are ensured, and the

authenticity of the sender is guaranteed. However,

cryptographic systems rely on the use of keys which

must be stored and released on a password based

authentication protocol. Therefore, the security of a

cryptographic system relies on how robust is the pass-

word storage system to brute force attacks. However,

template encryption cannot solve the biometric tem-

plate protection problem. In fact, at the aut hentication

stage, when a genuine biometrics is presented to the

system, the match must be performed in the template

domain, after decryption. However, this implies that

there is no more security on the biometric templates.

The match in the encrypted domain could solve this

problem. However, because of the intrinsic noisy na-

ture of biometric data, the match in the encrypted

domain would inevitably bring to a failure because

small differences between data would bring to sig-

niﬁcant differences between their encrypted versions.

Some activities are ﬂourishing to deﬁne signal

processing operations in the encrypted domain,

which could allow, for example, to perform operations

on encrypted biometric templates on not trusted

machines. However, this activity is still in its infancy

and does not provide tools within the biometric frame-

work yet.

Among the possible approaches recently proposed

to address the issue of template protection, techniques

based on intentional template distortions on the origi-

nal biometrics have been introduced in [ 2]. Speciﬁcal-

ly, the distortion can take place either in the biometric

domain, that is, before feature extraction or in the

feature domain. Moroever, the distor tion can be per-

formed using either an invertible or a non invertible

transform on the base of a user key which must be

known at the authentication stage . On ly the distorted

data are stored in the database. This implies that, even

if the database is compromised, the biometric data

cannot be retrieved unless, when dealing with invert-

ible transforms, user dependent keys are revealed.

Moreover, different templates can be generated from

the same original data, simply by changing the para-

meters of the employed transforms. The described

technique allows obtaining both cancelability and

renewability.

In the recent past, some efforts have been devoted

to design biometric cryptosystems (see [3] for a review)

where a classical password based authentication ap-

proach is replaced by biometric based authentica-

tion. Biometric cryptosystems can be used for either

securing the keys obtained when using traditional

cryptographic schemes or for providing the whole

authentication system. A possible classiﬁcation of the

operating modes of a biometric cryptosystem is given

in [3] where key release, key binding,andkey generation

modes are identiﬁed. Speciﬁcally, in the key release

mode the crypto graphic key is stored together with

the biometric template and the other necessary infor-

mation about the user. After a successful biome tric

matching, the key is releas ed. However, this approach

has several drawbacks, since it requires access to the

stored template and then the one bit output of the

biometric matcher can be overridden by using Trojan

horse attacks. In the key binding mode the key is bound

to the biometric template in such a way that both of

them are inaccessible to an attacker and the key is

released when a valid biometric is presented. It is

worth pointing out that no match between the tem-

plates nee ds to be performed. Among the key binding

approaches it is worth citing the fuzzy commitment

866

Iris Template Protection

and the fuzzy vault scheme. In the key generation mode

the key is obtained from the biometric data and no

other user intervention besides the donation of the

required biometrics is needed. Both the key binding

and the key generation modes are more secure than

the key release mode . However, they are more difﬁcult

to implement because of the variability of the biomet-

ric data.

Data hiding techniques [4] complement encryp-

tion. In fact, encryption can be applied to ensure

privacy, to protect the integrity, and to authenticate a

biometric template. However, among the possible

drawbacks, encryption does not provide any protec-

tion once the content is decrypted. On the other hand,

data hiding techniques can be used to insert additional

information, namely the watermark, into a digital ob-

ject. Within the biomet ric fram ework, data hiding can

be applied for copy protection, ﬁngerprinting, data

authentication, and timestamping in such a way that

after the expiration date the template is useless. It is

worth pointing out that some security requirements

are also needed when dealing with data hiding techni-

ques. In fact, according to the application, we should

be able to face unauthorized embedding, unauthorized

extraction, and unauthorized removal of the watermark.

Recently some efforts are being devoted to the integra-

tion between watermarking and cryptography. Howev-

er, much more research activity is still needed before

deployment. In the following, after a quick overview

on iris template generation, the most signiﬁcant

approaches for iris template protection are discribed.

Iris Template Generation

An iris image is preprocessed to select the actual iris

region to use for feature extraction, thus removing

unwanted elements such as eyelid, eyelashes, pupil,

reﬂections, and all the other noise components. Then

an iris normalization process takes place, since the

extracted iris regions, both from different people and

from the same people, can differ because illumi nation

changes, variation of the eye-camera dista nce, elastic

deformations in the iris texture, and similar. These

effects can generate matching problems. In some

approaches a scale-invariant transform like the Four-

ier-Mellin is used. In some others, a mapping of the iris

image from raw cartesian coordinates to non concen-

tric polar coordinate system is used. After the normali-

zation stage, the features extraction procedure takes

place. This task can be accomplished using different

approaches such as multi-scale Gabor wavelet ﬁltering

and its variants, singular value decomposition, principal

component analysis, and so on.

Cancelable Iris Template

A cancelable iris biometric approach, namely S-Iris

Encoding, is proposed in [5]. The method is roughly

sketched in Fig. 1 and brieﬂy summarized in the fol-

lowing. Iris preprocessing is performed ﬁrst. Speciﬁ-

cally iris segmentation by means of the Canny edge

detector, to ﬁnd the edge map, followed by the Circular

Hough Transform, to detect the iris and pupils bound-

aries are carried out. Linear Hough transform is used

to discard eyelids and eyelashes. The normalization is

performed using the Daugman’s rubber sheet model

[6]. The iris feature extraction is performed by con-

volving the normalized 2D pattern rows, each

corresponding to a circular ring of the iris region, by

using 1D Log-Gabor ﬁlter. The magnitude of the so

obtained complex features are then collected in a vec-

tor

w that is further processed to obtain the S-Iris code

Iris Template Protection. Figure 1 S-Iris Encoding scheme [5].

Iris Template Protection

867

as described in the next steps. A set of m orthonormal

pseudorandom vectors f

?;i

g, with i ¼ 1; 2; ; m, are

then generated using a token. The inner products

¼ <w; r

?;i

>, with i ¼ 1; 2; ; m, are then evalu-

ated. The m bits of the S-Iris code

s ¼fs

j i ¼ 1; ; mg are computed as

0ifa

< m

 s

; a

> m

þ s

1ifm

 s

 a

 m

þ s

;



where m

and s

are the average and standard deviation

of a

respectively. This approach allows to discard those

inner products which are numerically small and which

therefore must be excluded in order to improve the

veriﬁcation rate. The authors of [5] point out that the

system authentication performance have a signiﬁcant

improvement over the solely biometric system.

Iris Template Protection using

Cryptosystems

Among the methods which can be classiﬁed as key

binding based approaches [3] we can cite the fuzzy

commitment scheme [7], based on the use of error

correction codes and the fuzzy vault scheme [8],

based on polynom ial based secret sharing .

Speciﬁcally, the fuzzy commitment scheme is

depicted in Fig. 2 in its general form. In the enrollment

stage, the biometric template

x is used to derive some

side information

s which is stored to be used in the

authentication stage. Then a randomly chosen code-

word

c is gen erated on the base of a token k. The

binding between the biometric meas urement

x and

the codeword

c is obtained as y ¼ x  c. Both y and

a hashed version of the token k are eventually stored. In

the authentication stage, the side information

s is re-

trieved and, together with the actual biometric mea-

surement, it is used to obtain the biometric templa te

. This latter usually differs from the template

obtained in the enrollment stage because of the intrin-

sic variability of biometrics. Then the codeword

obtained as

¼ x

 y. Finally k

is obtained by

decoding

. Its hashed version hðk

Þ is obtained and

compared with the stored hðkÞ. If the obtained values

are identical, the authentication is successful. It is

worth pointing out that this scheme provides both

template protection, since from the stored information

s; y; hðkÞÞ it is not possible to retrieve the template,

and template renewability, since by changing the token

k the template representation changes.

In [9] the fuzzy commitment scheme here de-

scribed is applied to iris protection. Iris preprocessing

consists in the edge map extraction followed by Circu-

lar Hough Transform to detect the iris and pupils

boundaries followed by Linear Hough transform to

discard eyelids and eyelashes. The normalization is

performed using the Daugman’s rubber sheet model.

The iris feature extraction is performed by convolving

the rows of the normalized 2D pattern by using 1D

Log-Gabor ﬁlter. The phase information from both

the real and the imaginary part is eventually quantized.

A reliable bits selection is then performed according

to the assumption that the more reliable bits are those

coming from the pixels closer to the pupil center,

Iris Template Protection. Figure 2 Fuzzy Commitment scheme.

868

Iris Template Protection

where eyelid and eyelashes are not likely to be found.

With respect to the general scheme in Figure 2,in[9 ],

the feature vector

x is split into two feature vectors x

and x

of the same length and two BCH encoder are

used. Speciﬁcally, two tokens k

and k

are employed

to generate two codewords

and c

obtained each

from one of the two employed BCH encoders. Eventu-

ally the secret data

¼ x

 c

and y

¼ x

 c

are

obtained. Therefore the stored information will be

given by ð

s; y

; y

; hðk

Þ; hðk

ÞÞ. The authentication

step is dual with respect to the enrolment stage. The

authors of [9] point out that the division strategy is

needed to balance the desired veriﬁcation accuracy and

the BCH code error correction capabi lity.

In [10] the authors use the fuzzy commitment

scheme for the protection of binary iris template,

namely the iriscode [6], by employing a cascade of

Reed Solomon codes and Hadamard codes to handle

the intra-variability of the biometric templates. This

choice has been driven by an exhaustive study of the

error patterns which can be encountered employing

iris codes. The authors propose a fuzzy commitment

architecture, where a two-layer error correction

method is performed. The outer layer uses a Hada-

mard code to correct random errors at the binary level

which are generated by CCD camera pixel noise, iris

distortion, or other image-capture effects which can

not be corrected by the initial preprocessing. The inner

layer uses a Reed Solomon code to correct burst errors

in the iriscode, due to und etected artefact like eyelashes

or specular reﬂections in the iris image. The proposed

architecture is tested on a proprietary database with

700 iris samples from 70 different eyes, with 10 samples

from each eye. It has been found out that an error

free key can be reproduced from an actual iriscode

with a 99:5% success rate. Iris orientation is of big

concern when unlocking the key in the fuzzy commit-

ment scheme. Multiple attempts have to be performed,

shifting the observed iris code by octect-bits, being

impossible to cyclically scroll the iris sample as in the

unprotected approach.

In [11] the application of the fuzzy commitment

scheme, for the protection of biometric data, is dis-

cussed. Speciﬁcally, a method for ﬁnding an upper

bound on the underlying error correction capability,

when using a fuzzy commitment scheme is provided.

The analysis is conducted by introducing a model for

the recognition process, composed of two binary sym-

metric channels, the matching and the non matching

channel. Speciﬁcally, the ﬁrst is used to model the

errors coming from the matching between templates

belonging to the same user. The latter is used to model

the errors coming from the matching between tem-

plates belonging to different users. An erasure mecha-

nism is introduced in the matching channel to manage

the template dimension variability due for example to

occlusions. Moreover, a practical implementation of

the fuzzy commitment for iris template protection is

proposed, employing as error correcting codes the

product of two Reed Muller codes, together with a

speciﬁc decoding process, derived from the min-sum

decoding algorithm. The proposed protection scheme

is tested on a public iris database. The authors show

that correction performance close to the theoretical

optimal decoding rate are obtained.

The fuzzy vault cryptographic scheme [8] consists

in placing a secret S in a vault and in securing it by

using a set of unordered data A ¼fa

; a

; ; a

which in our biometric context represents the biomet-

ric template. Speciﬁcally, a polynomial pðxÞ, whose

coefﬁcients are given by the secret S, is generated

and the polynomial projections pða

Þ, for all the

elements belonging to A, are evaluated. Then a

large number of chaff points, which do not lie on

the polynomial pðxÞ, are arbitarily chosen. Speciﬁcally,

M unique points fc

; c

; ; c

g are randomly set

with the constraint that c

6¼ a

, for j ¼ 1; 2; ; M

and i ¼ 1; 2; ; N. Then, anoth er set of M ran-

dom points fd

; d

; ; d

g, such that d

6¼ pðc

Þ,

j ¼ 1; 2; ; M, is chosen. The concatenation of the

two sets fða

; pða

ÞÞ; ða

; p ða

ÞÞ; ; ða

; pða

ÞÞg

and fðc

; d

Þ; ðc

; d

Þ; ; ðc

; d

Þg represents the

vault V which secures both the secret and the template.

When a user tries to unlock the vault, another set of

unordered data A

can be used. If the set A

substan-

tially overlaps with the set A then the user can identify

many points of the vault lying on the polynomial. If the

overlapping point number is sufﬁcient, the polynomial

can be identiﬁed by using Lagran ge interpolation, thus

identifying the secret. If the two sets are signiﬁcantly

different, the polynomial reconstruction is unfeasible.

Many implementations of the general principle here

sketched have been proposed in literature.

In [12], iris data are used for securing the vault. The

method is depicted in Fig. 3. Speciﬁcally, the feature

extraction is performed as follows. After having loca-

lized the iris region, it is transform ed into a polar

coordinate image and two regions not occluded by

Iris Template Protection

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