Efficient Cancelable Biometric Key Generation Scheme for Cryptography

International Journal of Network Security, Vol.11, No.2, PP.61–69, Sept. 2010 61

Efficient Cancellable Biometric Key GenerationScheme for Cryptography

Sunil V. K. Gaddam 1 and Manohar Lal 2

(Corresponding author: Sunil V. K. Gaddam)

Department of CSE, Meerut Institute of Engineering & Technology, Meerut, U. P., India1

School of Computer and Information Sciences, IGNOU, New Delhi, India2

(Email: [email protected])(Received June 24, 2008; revised and accepted Feb. 12, 2009)

Abstract

This paper puts forth a fresh methodology for the se-cure storage of fingerprint template by generating SecuredFeature Matrix and keys for cryptographic techniques ap-plied for data Encryption or Decryption with the aid ofcancellable biometric features. Conventional techniquesdepend on biometric features like face, fingerprint, handgeometry, iris, signature, keystroke, voice and the like forthe extraction of key information. If a Biometric Key ismissing or stolen, it is lost perpetually and possibly forevery application where the biometric is utilized, since abiometric is permanently linked with a user and cannot bealtered. In this paper we propose a technique to producecancellable key from fingerprint so as to surmount theseproblems. The flexibility and dependability of cryptog-raphy is enhanced with the utilization of cancellable bio-metric features. There are several biometric systems inexistence that deal with cryptography, but the proposedcancellable biometric system introduces a novel methodto generate Cryptographic Key. We have as well discussedabout the Security analysis of the projected CancellableBiometric System.Keywords: Biometrics, cancellable biometrics, cryptogra-phy, fingerprint, key generation, minutiae points, securityanalysis

1 Introduction

Progress of communication technologies in contemporarytimes has resulted in huge quantities of digital data in thepublicly shared media. This has necessitated the drasticdevelopment of cryptographic techniques. Cryptographyis considered to be one of the fundamental building blocksof computer security. Data can be encoded with the aidof cryptographic techniques in order to ensure that it ap-pears unintelligible to the public or third party and coher-ent only to the intended receivers of it (Data Confiden-tiality). DES, AES [1, 2, 4] and public key architectures

such as RSA [17] is a notable few among the widely uti-lized cryptographic techniques.

Regrettably cryptographic security is conditioned byan authentication step that characteristically depends onlong pseudo-random keys (of at least 128 bits in symmet-ric encryption), which are nearly impossible to keep inmind. The inability of human users to remember pow-erful cryptographic keys has been a feature restrainingthe security of systems for decades. Numerous historicalinstances illustrate that a person is capable of remember-ing only tiny passwords or keys, and even then have atendency to aspire for passwords or keys that are easilydeduced by dictionary attacks (e.g., see [8, 15, 18, 19, 23])or obtained using social engineering methods.

Typically we write down and store keys in an insecureplace that can possibly be communal among users, andthus is not capable of ensuring non-repudiation. More-over many people are intended towards using identicalkeys or password for a variety of applications and as a re-sult breaching one system lead to the breaching of manyothers. This makes the work of an attacker simple byshockingly reducing the general security of the data beingprotected. It is possible to solve this in a variety of ap-plications by producing powerful cryptographic keys frombiometric data, possibly in combination with the entry ofa password [10, 12, 24].

Biometrics provides a person with a distinct charac-teristic that is always prevalent. It is the technique ofauthenticating a person’s individuality from one or morebehavioral or physiological features. Diverse biometrictechniques that are under research include fingerprints,facial, palm prints, retinal and iris scans, and hand geom-etry, signature capture and vocal features.

Cryptography is merged with biometrics in Biometriccryptosystems, otherwise known as crypto-biometric sys-tems [25]. It is possible to carry out the integration of bio-metrics and cryptography broadly in two distinct steps.In case of biometrics-based key generation, a biometricmatching amid an input biometric signal and a registeredtemplate is utilized in the release of the secret key. The


biometric signals are immensely bounded to the keys incase of biometrics-based key generation.

A chief issue with regard to biometrics is that resettingis intricate. The uniformity of biometric data over timeis one of its huge merit and demerit at the same instant.In case of a missing credit card, it is possible to issue anew one but it is impossible to substitute the biometriccharacteristics and it is fully evident since it is not feasibleto provide a person with a fresh fingerprint when the oldone is stolen.

We have introduced the concept of “cancellable bio-metrics” [3] so as to simplify the problem. The procedureensures the planned, repeatable distortion of a biometricsignal on basis of a predefined transform. The distortionof biometric signal recurs in the same method at everypresentation, for enrollment and for every key generation.This approach facilitates the every incidence of enroll-ment to utilize a distinct transform thus making exposecross matching unachievable. Furthermore, once a vari-ant of the transformed biometric data is compromised itis enough to merely change the transform operation toproduce a new variant for re-enrollment, in effect, a newperson. Generally, the transforms utilized for distortionare chosen to be non-invertible. Thus it is not possibleto recover the original (undistorted) biometrics despiteknowing the transform method and the resulting trans-formed biometric data.

The organization of the paper is as follows: A brief re-view of the researches related to our proposed approach isgiven in Section 2. The proposed methodologies and thesteps are detailed in Section 3. In Section 4, the securityanalysis of the proposed algorithm is presented. The ex-perimental analysis and the results are given in Section 5and conclusions are summed up in Section 6.

2 Related Works

Our work is inspired from a number of previous worksrelated to cancellable biometrics and the generation ofcryptographic key from cancellable biometric features. Abrief review of some of the works is given below.

Cancellable biometrics proffers a greater level of pri-vacy by facilitating more that one template for the samebiometric data and thus the non-linkability of user’s datastored in diverse databases. The measurement of the suc-cess of a particular transformation and matching algo-rithm for fingerprints was described by Ang et al. [3].A key dependant geometric transform was employed onthe features obtained from a fingerprint, so as to pro-duce a key-dependent cancellable template for the finger-print. Besides, they have also studied the performanceof an authentication system that utilizes the cancellablefingerprint matching algorithm detection purposes. Ex-perimental evaluation of the system was carried out andthe results illustrated that it was possible to bring about agood performance when the matching algorithm remainsunaltered.

Hao et al. [12] presented a realistic and secure wayto incorporate the iris biometric into cryptographic ap-plications. They deliberated on the error patterns withiniris codes and developed a two-layer error correction tech-nique that merges Hadamard and Reed-Solomon codes.The key was produced from the iris image of the subjectthrough the auxiliary error correction data that do notdisclose the key and can be saved in a tamper-resistanttoken like a smart card. The evaluation of the methodol-ogy was performed with the aid of samples from 70 dif-ferent eyes, 10 samples being obtained from every eye. Itwas established that an error-free key can be reproducedreliably from genuine iris codes with a success rate of 99.5percent. It is possible to produce up to 140 bits of bio-metric key, more than adequate for 128-bit AES.

The application of handwritten signature to cryptog-raphy was analyzed by Freire-Santos et al. [10] on basis ofrecent works displaying the likelihood of key generation bymeans of biometrics. A cryptographic construction calledthe fuzzy vault was employed in the signature-based keygeneration scheme. The analysis and evaluation of theusability of distinctive signature features appropriate forthe fuzzy vault was carried out. Results of experimentalevaluation were reported. The reports also included theerror rates to release the secret data with the aid of bothrandom and skilled forgeries from the MCYT database.

An on-line signature-based biometric authenticationsystem, where non invertible transformations were ap-plied to the acquired signature functions ruling out thepossibility to derive the original biometrics from thestored templates at the same time maintaining the samerecognition performances of an unprotected system wasprojected by Maiorana et al. [21]. Precisely the proba-bility of producing cancellable templates from the sameoriginal data, thereby proffering an appropriate solutionto privacy concerns and security problems was intenselyexplored.

Teoh et al. [22] have presented a two-factor cancellableformulation that facilitates data distortion in a revoca-ble yet non-reversible manner by first converting the rawbiometric data into a fixed-length feature vector followedby the projection of the feature vector onto a sequence ofrandom subspaces that were obtained from a user-specificPseudorandom Number (PRN). The process was revoca-ble making the replacement of biometrics seem as easy asreplacing PRNs. This formulation was confirmed undernumerous scenarios (normal, stolen PRN, and compro-mised biometrics scenarios) with the aid of 2400 FacialRecognition Technology face images.

A cancellable biometric approach called PalmHashingwas projected by Tee et al. [7] in order to address the non-revocable biometric issue. This technique hashes palm-print templates with a set of pseudo-random keys to ac-quire a unique code known as the palmhash. It is possibleto store the palmhash code in portable devices such tokensand smartcards for authentication. Moreover, PalmHash-ing also provides numerous advantages over other modernday approaches including clear separation of the genuine-


imposter populations and zero EER occurrences. Theyoutlined the implementation facts besides emphasizing itscapabilities in security-critical applications.

A fuzzy commitment method working on lattice map-ping for cryptographic key generation from biometric datawas proposed by Zheng et al. [27]. Despite providing highentropy keys as output the method as well obscures theoriginal biometric data such that it becomes unfeasibleto recover the biometric data besides the stored informa-tion in the system being open to an attacker. Results ofsimulation illustrated that the method’s authenticationaccuracy was analogous to that of the renowned.

Jo et al. [14] presented a simple technique for the gen-eration of digital signatures and cryptography communi-cation with the aid of biometrics. It has been termednecessary to generate the signature in such a way that itbecomes possible to verify the same with a cryptographicalgorithm in existence like the RSA/ElGamal without al-tering its own security constraint and infrastructure. Itwas anticipated that the mechanism will be capable ofguaranteeing security on the binding of biometric infor-mation in the signature scheme on telecommunication en-vironments.

A framework for stable cryptographic key generationfrom unstable biometric data was projected by Chang etal. [5]. The chief difference between the proposed frame-work and the prior work is that here, user-dependenttransforms are employed to produce more compact anddistinguishable features. Thus a longer and highly sta-ble bit stream can probably be produced. Experimentswere carried out on one face database to demonstrate thepracticability of the framework.

Chen et al. [6] have presented a technique that makesuse of entropy oriented feature extraction procedure to-gether with Reed-Solomon error correcting codes that arecapable of generating deterministic bit-sequences from theoutput of an iterative one-way transform. The evaluationof the methodology was done with the 3D face data andwas illustrated to be capable of producing keys of suitablelength for 128-bit Advanced Encryption Standard (AES)in a reliable fashion.

3 Proposed Methodology

Recently, crypto-biometric systems have been studied forsolving the key management problem of cryptographicsystems and protecting templates in biometric systemsat the same time. In general, the identity theft problemis drastically exacerbated for the biometric systems, sincethe biometric data and the corresponding feature vectorsare non-renewable. To overcome this we generate a se-cured feature matrix from the fingerprint template andstrengthened this by AES Encryption/Decryption algo-rithm. Besides that, this paper discusses how keys canbe generated and demonstrates the technique using fin-gerprint images.

3.1 Key Generation from Fingerprint

This section confers the feature generation from finger-print biometric data. The stages are discussed below

• Extracting minutiae points from Fingerprint;

• Secured Feature Matrix generation;

• Key generation from Secured Feature Matrix.

3.1.1 Extracting Minutiae Points from Finger-print

For extracting minutiae points from fingerprint, a three-level approach is broadly used by researchers. These levelsare listed as follows

• Preprocessing.

• ROI selection Separation.

• Minutia extraction.

For the fingerprint image preprocessing, HistogramEqualization [26] and Filters [11] are used to do imageenhancement. Binarization is applied on the fingerprintimage. Locally adaptive threshold method [13] is used forthis process. Then Morphological operations [13, 20] areused to extract Region of Interest [ROI]. In a morpholog-ical operation, the value of each pixel in the output imageis based on a comparison of the equivalent pixel in theinput image with its neighbors. By selecting the size andshape of the neighborhood, we can construct a morpho-logical operation that is sensitive to specific shapes in theinput image.

1) PreprocessingHistogram Equalization. This method usually in-creases the local contrast of many images, especiallywhen the usable data of the image is representedby close contrast values. Through this adjustment,the intensities can be better distributed on the his-togram.

Perceptional information of the image is increasedthrough histogram equalization which permits pixelvalue to expand the distribution of an image. Theoriginal histogram of a fingerprint image has the bi-modal type, the histogram after the histogram equal-ization converts all the range from 0 to 255 and thevisualization effect is improved.

Gabor Filters. The Gabor filter is applied to thefingerprint image obtained by the previous step byspatially convolving the image with the filter.

A two-dimensional Gabor [11] filter consists of a si-nusoidal plane wave of a specific orientation and fre-quency, modulated by a Gaussian envelope. Gaborfilters are employed as they have frequency-selectiveand orientation-selective properties. These proper-ties permit the filter to be tuned to give maximal


Figure 1: Captured fingerprint and after histogram equal-ization

response to ridges at a specific orientation and fre-quency in the fingerprint image. So, a properly tunedGabor filter shall be used to effectively retain theridge structures while reducing noise. The even-symmetric Gabor filter is the real part of the Gaborfunction, which is yielded by a cosine wave modu-lated by a Gaussian.

A Gaussian function multiplied by a harmonic func-tion defines the impulse response of the linear fil-ter, the Gabor filter. Because of the multiplication-convolution property (Convolution theorem), theFourier transform of a Gabor filter’s impulse responseis the convolution of the Fourier transform of theharmonic function and the Fourier transform of theGaussian function.

g(x, y; λ, θ, ψ, σ, γ)

= exp(−x′2 + γ2y′2

2σ2)cos(2π

x′

λ+ ψ).

Where,

x′ = xcosθ + ysinθ,

and

y′ = −xsinθ + ycosθ.

In this equation, λ represents the wavelength of thecosine factor, θ represents the orientation of the nor-mal to the parallel stripes of a Gabor function, ψ isthe phase offset, and γ is the spatial aspect ratio, andspecifies the ellipticity of the support of the Gaborfunction.

2) ROI SelectionBinarization. Nearly all minutiae extraction algo-rithms function on binary images where there areonly two levels of interest: the black pixels that de-note ridges, and the white pixels that denote valleys.Binarization is the process that translates a grey levelimage into a binary image. This enhances the con-trast between the ridges and valleys in a fingerprintimage, and consequently makes it possible the ex-traction of minutiae.

Figure 2: After binarization

One practical property of the Gabor filter is that ithas a DC component of zero, which means the re-sultant filtered image has a mean pixel value of zero.Hence, straightforward binarization of the image canbe achieved using a global threshold of zero. Thebinarization process involves analyzing the grey-levelvalue of each pixel in the enhanced image, and, if thevalue is greater than the global threshold, then thepixel value is set to a binary value one; otherwise, itis set to zero. The result is a binary image holdingtwo levels of information, the foreground ridges andthe background valleys.

ROI Extraction by Morphological Opera-tions. We perform morphological opening on thegrayscale or binary image with the structuring ele-ment. We also performed morphological closing onthe grayscale or binary image resulting in closed im-age. The structuring element is a single structuringelement object, as opposed to an array of objects forboth open and close. Then as the result this ap-proach throws away those leftmost, rightmost, up-permost and bottommost blocks out of the bound soas to get the tightly bounded region just containingthe bound and inner area.

3) Minutiae ExtractionThe last image enhancement step normally per-formed is thinning. Thinning is a morphological op-eration that successively erodes away the foregroundpixels until they are one pixel wide. Ridge Thinningis to eliminate the redundant pixels of ridges till theridges are just one pixel wide [16] uses a Ridge Thin-ning algorithm, which is used for Minutiae points’extraction in our approach. The image is dividedinto two distinct subfields in a checkerboard pattern.In the first sub-iteration, delete pixel p from the firstsubfield if and only if the conditions G1, G2, and G3are all satisfied. In the second sub-iteration, deletepixel p from the second subfield if and only if theconditions G1, G2, and G3’ are all satisfied.

Condition G1:

XH(P ) = 1,


where

XH(P ) =4∑

i=1

bi =

1 if x2i−1 = 0 and(x2i = 1 or x2i+1 = 1)

0 otherwise

Here, x1, x2, . . ., x8, are the values of the eight neigh-bors of p, starting with the east neighbor and num-bered in counter-clockwise order.

Condition G2:

2 ≤ min{n1(p), n2(p)} ≤ 3,

where

n1(p) =4∑

k−1

X2k−1 ∨ x2k;

n2(p) =4∑

k−1

X2k ∨ x2k+1.

Condition G3:

(x2 ∨ x3 ∨ x8) ∧ x1 = 0.

Condition G4:

(x6 ∨ x7 ∨ x) ∧ x5 = 0.

The two sub-iterations together make up one itera-tion of the thinning algorithm.

3.2 Secured Feature Matrix Generation

The steps involved in the generation of Secured FeatureMatrix are discussed in this sub-section. We assumethat the extracted minutiae point’s co-ordinates are main-tained in a vector.

• Mp −→ Minutiae point set.

• Np −→ Size of Minutiae point set.

• Vk −→ Key Vector.

• Lk −→ Length of the AES key.

• p −→ (x, y) co-ordinate of a minutiae point.

The Extracted minutiae points are represented as

Pm = {pi} = 1, . . . , Np.

Initially the is transformed to a Key vector as follows

Vk = {xi : p(xi)} i = 1, . . . , Lk,

where

p(x) = PmbPm[i]modNpc i = 1, . . . , Lk.

Then the initial key vector (Vk) is converted into amatrix BKm of size

√(Lk)×

√(Lk).

Then the resultant matrix BKm is encrypted with theAES algorithm to form Secured Feature matrix SFm.

SFm = Evk(BKm).

The key used in the AES encryption is the generatedkey from the whole process. Once after the key is gen-erated, AES encryption progressed to generate a securedfeature matrix, but initially encryption process doesn’toccur in the key generation from the whole process.

The generated Secured feature matrix is irreversible,moreover it cannot be hacked by an attacker because ofthe strength of AES and the mathematical operations in-volved in the generation.

3.2.1 Key Generation from Secured Feature Ma-trix (SFm)

The key is generated as follows. The Secured FeatureMatrix is decrypted by AES Decryption to form the de-ciphered matrix.

Then the resultant matrix BKm is given as

BKm = Dvk(SFm),

where

BKm = (aij

√(Lk)×

√(Lk)).

Then an intermediate key vector is generated as follows

Iv = {Ki : p(k)} i = 1, . . . , Lk,

where

p(k) = |SMij |, SMij = BKmi : i + size,

j + size,−1 < i < sqrt(Lk)SMij ,

is an extracted matrix formed from the key matrix. Thenthe final key vector is formed as

FBKy ={

1, if lv[i] > mean(Iv)0, otherwise.

}

The extracted final key vector is more secured and itis non-reversible. That means the final key cannot betraced back from the template. This irreversible propertymakes the key unbreakable, because we processed throughminutiae points and secured feature matrix.

4 Security Analysis

Security of the proposed algorithm is strengthen by thesethree robust features

• Cancellable Transform;

• Feature Matrix Security Analysis;

• Irreversible Analysis.


4.1 Cancellable Transform

Cancellable transform [9] is used to generate a cancellabletemplate. The core intention of the cancellable transfor-mation is to provide cancellable skill a “non-invertible”transform. Normally, it decreases the discriminativepower of the original template. Therefore, the cancellabletemplates and the secure templates of an individual indifferent applications will be different. In turn, the crossmatching across databases will not be feasible. More-over, the secure template can be cancelled and reissuedby changing the cancellable transform parameters.

4.2 Feature Matrix Security Analysis

In our algorithm security is more strengthened by AESencryption. Once after the template is formed and minu-tia points are acquired, a feature matrix is generated byfollowing a sequence of steps. This feature matrix is thenencrypted using AES. Reinforced by AES, the feasibil-ity of decrypting the ciphered feature matrix is almostnegligible. Anticipating a worst-case scenario, that if ahacker succeeds in decrypting the AES encryption withan intend to obtain the feature matrix; the chances of re-organizing the minutia point and the templates are almostnil. Furthermore, there is no possibility of conjecturingthe steps we followed to generate the feature matrix andit is absolutely chanceless to restructure the template byany means.

The key thus formed cannot be traced back to the ori-gin i.e. to the template and moreover the key itself can-not be regenerated falsely using the template. This irre-versible aspect makes the key armored and reliable andeven resistant to brute force attacks. This shatter-proofproperty emanates from the very essence of preservingthe confidentiality of the battery of operations we followin transforming minutia points to a Feature matrix.

To decrypt the key we generated, the steps we followedto create it have to be performed in the reverse order.First the feature matrix encrypted using AES, have to bedeciphered, then the sequence of steps proceed for formingthe feature matrix should be executed from bottom-up.These operations will yield the minutia points acquiredfrom the template in the inception.

4.3 Irreversible Analysis

To enunciate the concept further tracing out the matrixusing the determinant or reorganizing shuffled data is to-tally infeasible just like attempting to generate an origi-nal document using a hashed bits after hashing functionis applied.

The security of our algorithm is strengthened by theinherent irreversible nature, by this tracing the minutiaepoints from the keys generated is practically impossible.The proposed algorithm is more suitable and specific fordata like the ones used for handling minutiae points ar-rived using the above process.

5 Experimental Results

The experimental analysis of our proposed approach ispresented in this section. Our approach is programmedin Matlab (Matlab 7.4). We have tested our proposedapproach with different fingerprint images. The minutiaepoints are extracted from the fingerprint images using thethree level approach presented in the paper. Initially, inthe preprocessing stage, histogram equalization and Ga-bor filtering are performed on the fingerprint images toenhance them. Secondly, the binarization is applied onthe fingerprint images and then the region of interest isdetermined. Subsequently minutiae points are extracted.Later, the secured feature matrix is generated based onthe co-ordinates of minutiae points. Eventually, the 256-bit key is generated from the secured feature matrix. Theinput image, extracted minutiae points and the interme-diate results of five different fingerprint images are shownin Figure 3. The 256-bit key generated from the five fin-gerprint images given in Figure 3 are depicted in Figure 4.

6 Conclusion

Biometrics-based Key Generation outperforms traditionalsystems in usability domain. Precisely it is not possiblefor a person to lose his/her biometrics, and the biometricsignal is intricate to falsify for steal. The proposed can-cellable biometric Crypto System is an all-new techniquefor the authentication that yields the synergistic controlof biometrics. The proposed system employs intentionaldistortion of fingerprint in a repeatable fashion and thefingerprint thus obtained is utilized in the cryptographickey generation. When the old finger print is “stolen” it ispossible to obtain a “new” fingerprint just by altering theparameters of the distortion process. Subsequently, en-hanced privacy for the user results as his true fingerprintis not utilized anywhere and diverse transformations fordistortions can be utilized for a variety of accounts.

A notable enhancement in terms of decrease in theconsumed time is attained with the elimination of moresteps that are redundant with the mixture of the pro-posed methodology. Integration of the projected tech-nique with the existing cryptographic methodologies isuncomplicated and as well decreases key-generation andkey-release issues in a remarkable manner. This method-ology can be further made efficient and sophisticated withthe combination of any of the evolving cryptographic sys-tems.

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Figure 3: (a) Input Fingerprint Image (b) Histogram equalized image (c) Gabor Filtered Image (d) Binarized Image(e) Region of Interest (ROI) (f) Fingerprint Image with minutiae points

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Figure 4: Generated 256-bit key

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Sunil VK Gaddam received his B. Tech. fromSri Venkateswara University (SVU), Tirupati, India, in1993, Post Graduate Diploma in Computer Engineering(PGDCE) from Jawaharlal Nehru Technological Univer-sity (JNTU), Hyderabad, India, in 1994, and M. Tech.(Computer Science) from Jawaharlal Nehru University(JNU), New Delhi, India, in 1997.


He has over 10 years of experience of teaching coursesin the discipline of Computer Science in various IndianUniversities. He is currently a Professor & Head in theDepartment of Computer Science & Engineering, MeerutInstitute of Engineering & Technology (MIET), Meerut,U.P. Earlier, he worked at RGMCET, Nandyal, A.P., asan Associate Professor, and at KSRMCE, Kadapa, A.P.,as an Assistant Professor. His areas of Interest includeComputer Networks, Network Security, Data Structuresand Operating Systems.

He also worked as Software Engineer for ExpertSoftware Consultancy (ESC), Noida, India, for overa year. He has a number of publications in Nationaland International Conferences and Journals. He or-ganized many National Conferences, Seminars andWorkshops for faculty as well as for students. He isalso the member of professional bodies like ISTE and CSI.

Manohar Lal is the Director, School of Computer &Information Sciences, Indira Gandhi National Open Uni-versity, New Delhi (India). He has teaching and researchexperience of more than 30 years at various Indian univer-sities including University of Delhi and Jawaharlal NehruUniversity (JNU), New Delhi.

Prof. Manohar Lal is a product of reputed Indian aca-demic institutions including IIT Kanpur, IIT Delhi andUniversity of Delhi. He completed his M. Tech in Com-puter Science and Engineering from IIT Kanpur and pur-sued his second Ph. D. in Computer Science and Engi-neering from IIT, Delhi. Earlier, he completed his mas-ter’s and Ph. D. programmes in Mathematics from Uni-versity of Delhi. During 1982-83, he visited North Car-olina State University for Post-Doctoral work. In contextof academic work, he has visited a number of countriesincluding U.S.A, U.K, Germany and France.

Prof. Lal has long research experience. Earlier, heworked in the area of ’Error-Correcting Codes’. Cur-rently, he is working in the areas of E-Learning, Automa-tion of Reasoning and Computer Networks.

Efficient Cancelable Biometric Key Generation Scheme for Cryptography

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