PalmHashing: a novel approach for dual-factor authentication

Abstract

Many systems require a reliable personal authentication infrastructure to recognise the identity of a claimant before granting access to him/her. Conventional secure measures include the possession of an identity card or special knowledge like password and personal identification numbers (PINs). These methods are insecure as they can be lost, forgotten and potentially be shared among a group of co-workers for a long time without change. The fact that biometric authentication is convenient and non-refutable makes it a popular approach for a personal identification system. Nevertheless, biometric methods suffer from some inherent limitations and security threats. A more practical approach is to combine two-factor or more authenticators to achieve a higher level of security. This paper proposes a novel dual-factor authenticator based on the iterated inner product between tokenised pseudo-random numbers and user-specific palmprint features. This process generates a set of user-specific compact code called PalmHash, which is highly tolerant of data offset. There is no deterministic way to get the user-specific code without having both PalmHash and the user palmprint feature. This offers strong protection against biometric fabrication. Furthermore, the proposed PalmHashing technique is able to produce zero equal error rate (EER) and yields clean separation of the genuine and imposter populations. Hence, the false acceptance rate (FAR) can be eliminated without suffering from the increased occurrence of the false rejection rate (FRR).

Appendices

Appendix

1.1 Subspace projection techniques

In this appendix, we provide a brief review of basic PCA, FDA and wavelet transformation theories. For a more detailed explanation, please refer to [19, 24, 25] for a comprehensive understanding on the topics.

1.2 Principal component analysis (PCA)

Let us consider a set of M palmprint images i ₁, i ₂,..., i _M . The average palm of the set is defined as:

$$ \ifmmode\expandafter\bar\else\expandafter\=\fi{i} = \frac{1} {M}{\sum\limits_{j = 1}^M {i_{j} } } $$

(4)

Each palmprint image differs from the average palm $\ifmmode\expandafter\bar\else\expandafter\=\fi{i}$ by the vector $\phi _{n} = i_{n} - \ifmmode\expandafter\bar\else\expandafter\=\fi{i}.$ A covariance matrix is constructed where:

$$ C = {\sum\limits_{j = 1}^M {\phi _{j} \phi ^{{\text{T}}}_{j} } } $$

(5)

Then, eigenvectors v _k and eigenvalues λ _k with symmetric matrix C are calculated. v _k determines the linear combination of M difference images with φ to form the eigenbases:

$$ b_{l} = {\sum\limits_{k = 1}^M {v_{{lk}} \phi _{k} } },\quad l = 1, \ldots ,\;M $$

(6)

From these eigenbases, K(<M) bases are selected to correspond to the K highest eigenvalues.

The set of palmprint images {i} is transformed into its eigenbase components (projected into the palm space) by the operation:

$$ \omega _{{nk}} = b_{k} {\left( {i_{n} - \ifmmode\expandafter\bar\else\expandafter\=\fi{i}} \right)} $$

(7)

where n=1,..., M and k=1, ..., K.

The weights obtained form a vector Ω _n =[ω _n1, ω _n2,..., ω _nK ], which describes the contribution of each eigenbase in representing the input palm image, treating the eigenbases as a basis set for the palm images.

1.3 Fisher discriminant analysis (FDA)

Consider a set of M palmprint images having c classes of images, with each class containing n set images, i ₁, i ₂,..., i _n . Let the mean of the images in each class and the total mean of all images be represented by $\ifmmode\expandafter\tilde\else\expandafter\~\fi{m}_{c}$ and m, respectively. The images in each class are centred as:

$$ \phi ^{c}_{n} = i^{c}_{n} - \ifmmode\expandafter\tilde\else\expandafter\~\fi{m}_{c} $$

(8)

and the class mean is centred as:

$$ \omega _{c} = \ifmmode\expandafter\tilde\else\expandafter\~\fi{m}_{c} - m $$

(9)

The centred images are then combined side by side into a data matrix. By using this data matrix, an orthonormal base U is obtained by calculating the full set of eigenvectors of the covariance matrix $\phi ^{{c{\text{T}}}}_{n} \phi ^{c}_{n}$ The centred images are then projected into this orthonormal base as follows:

$$ \ifmmode\expandafter\hat\else\expandafter\^\fi{\phi }^{c}_{n} = U^{{\text{T}}} \phi ^{c}_{n} $$

(10)

The centred means are also projected into the orthonormal base as:

$$ \ifmmode\expandafter\hat\else\expandafter\^\fi{\omega }_{c} = U^{{\text{T}}} \omega _{c} $$

(11)

Based on this information, the within-class scatter matrix S _W is calculated as:

$$ S_{{\text{W}}} = {\sum\limits_{j = 1}^c {{\sum\limits_{k = 1}^{n_{j} } {\widehat{{\phi ^{j}_{k} }}\widehat{{\phi ^{j}_{k} }}^{{\text{T}}} } }} } $$

(12)

and the between-class scatter matrix S _B is calculated as:

$$ S_{{\text{B}}} = {\sum\limits_{j = 1}^c {n_{j} \ifmmode\expandafter\tilde\else\expandafter\~\fi{\omega }_{j} \ifmmode\expandafter\tilde\else\expandafter\~\fi{\omega }^{{\text{T}}}_{j} } } $$

(13)

The generalised eigenvectors V and eigenvalues λ of the within-class and between-class scatter matrices are solved as follows:

$$ S_{{\text{B}}} V = \lambda S_{{\text{W}}} V $$

(14)

The eigenvectors are sorted according to their associated eigenvalues. The first c−1 eigenvectors are kept as the Fisher basis vectors, W. The rotated images α _M , where α _M =U ^T i _M , are projected into the Fisher base by:

$$ \ifmmode\expandafter\bar\else\expandafter\=\fi{\omega }_{{nk}} = W^{{\text{T}}} \alpha _{M} $$

(15)

where n=1,..., M and k=1,..., M−1.

The weights obtained is used to form a vector $\Upsilon _{n} = {\left[ {\ifmmode\expandafter\bar\else\expandafter\=\fi{\omega }_{{n1}} ,\;\ifmmode\expandafter\bar\else\expandafter\=\fi{\omega }_{{n2}} , \ldots ,\;\ifmmode\expandafter\bar\else\expandafter\=\fi{\omega }_{{nK}} } \right]}$ that describes the contribution of each Fisherpalm in representing the input palm image by treating Fisherpalms as a basis set for the palm images.

1.4 Wavelet transformation

The wavelet decomposition of a signal f(x) can be obtained by the convolution of a signal with a family of real orthonormal bases, ψ _a,b (x):

$$ {\left( {W_{\psi } f{\left( x \right)}} \right)}{\left( {a,\;b} \right)} = {\left| a \right|}^{{ - \frac{1} {2}}} {\int\limits_\mathbb{R} {f{\left( x \right)}\psi {\left( {\frac{{x - b}} {a}} \right)}} }{\text{d}}x\quad f{\left( x \right)} \in L^{2} {\left( \mathbb{R} \right)} $$

(16)

where a, b∈ℝ and a≠0 are the dilation and translation parameters, respectively. The basis function ψ _a,b (x) is obtained through the translation and dilation of a kernel function ψ(x), known as mother wavelet, as defined below:

$$ \psi _{{a,b}} {\left( x \right)} = 2^{{ - a \mathord{\left/ {\vphantom {a 2}} \right. \kern-\nulldelimiterspace} 2}} \psi {\left( {2^{{ - a}} x - b} \right)} $$

(17)

The mother wavelet ψ(x) can be constructed from a scaling function, ϕ(x). The scaling function ϕ(x) satisfies the following two-scale difference equation:

$$ \phi {\left( x \right)} = {\sqrt 2 }{\sum\limits_n {h{\left( n \right)}\phi {\left( {2x - n} \right)}} } $$

(18)

where h(n) is the impulse response of a discrete filter which has to meet several conditions for the set of basis wavelet functions to be orthonormal and unique. The scaling function ϕ(x) is related to the mother wavelet ψ(x) via:

$$ \psi {\left( x \right)} = {\sqrt 2 }{\sum\limits_n {g{\left( n \right)}\phi {\left( {2x - n} \right)}} } $$

(19)

The coefficients of the filter g(n) are conveniently extracted from filter h(n) from the following relation:

$$ g{\left( n \right)} = {\left( { - 1} \right)}^{n} h{\left( {l - n} \right)} $$

(20)

The discrete filters h(n) and g(n) are the quadrature mirror filters (QMF), and can be used to implement a wavelet transform instead of explicitly using a wavelet function.

For 2-D signal such as images, there exists an algorithm similar to the 1-D case for 2-D wavelets and scaling functions obtained from 1-D ones by the tensiorial product. This kind of 2-D WT leads to a decomposition of the approximation coefficients at level j−1 in four components: the approximations at level j and the details in three orientations (horizontal, vertical and diagonal):

$$ L_{j} {\left( {m,\;n} \right)} = {\left[ {H_{x} * {\left[ {H_{y} * L_{{j - 1}} } \right]}_{{ \downarrow 2,1}} } \right]}_{{ \downarrow 1,2}} {\left( {m,\;n} \right)} $$

(21)

$$ D_{{j{\text{vertical}}}} {\left( {m,\;n} \right)} = {\left[ {H_{x} * {\left[ {G_{y} * L_{{j - 1}} } \right]}_{{ \downarrow 2,1}} } \right]}_{{ \downarrow 1,2}} {\left( {m,\;n} \right)} $$

(22)

$$ D_{{j{\text{horizontal}}}} {\left( {m,\;n} \right)} = {\left[ {G_{x} * {\left[ {H_{y} * L_{{j - 1}} } \right]}_{{ \downarrow 2,1}} } \right]}_{{ \downarrow 1,2}} {\left( {m,\;n} \right)} $$

(23)

$$ D_{{j{\text{diagonal}}}} {\left( {m,\;n} \right)} = {\left[ {G_{x} * {\left[ {G_{y} * L_{{j - 1}} } \right]}_{{ \downarrow 2,1}} } \right]}_{{ \downarrow 1,2}} {\left( {m,\;n} \right)} $$

(24)

where, * denotes the convolution operator $\downarrow 2,1\;{\left( { \uparrow 2,1} \right)}$ subsampling along the rows (columns) and H and G are a low-pass and bandpass filter, respectively. Similarly, two levels of the wavelet decomposition are obtained by applying WT on the low-frequency band sequentially.

Originality and contribution

Traditional identity authenticators that use ID- or password-based techniques are not secure as IDs and passwords can be lost, forgotten and potentially be shared in a workgroup for a long time without change. Using biometric features is a reliable personal authentication method as it can positively link the system usage to the actual user. However, biometrics suffer from some inherent biometric threats and limitations. For example, biometric data cannot be re-issued once it is compromised; and the performance of the system requires a tradeoff between the FAR and FRR variable factors. There is suggestion to employ multimodal biometrics fusion to improve the overall performance as it can reduce FRR without sacrificing the FAR criteria. Nonetheless, the non-revocable biometric issue still remains unsolved. A more practical approach is to combine two-factor or more authenticators. This paper proposes a dual-factor authenticator based on the iterated inner product between tokenised pseudo-random numbers and user-specific palmprint features. This process generates a set of user-specific compact code called PalmHash. PalmHash is highly tolerant of data offset, thus, resulting in highly correlated bitstrings for palmprints from the same user. Moreover, there is no deterministic way to get the user-specific code without having both the pseudo-random number and the user palmprint feature. This offers strong protection against biometric fabrication. Furthermore, the proposed PalmHashing technique has significant advantages over a sole biometric factor. For example, it is able to produce a zero EER and yield clean separation of the genuine and imposter populations. These accomplishments offer the benefit of elimination of FAR without suffering from the increased occurrence of FRR.

Biographies of the authors

Tee Connie obtained her B.IT (Hons) Information Systems Engineering in 2002 from Multimedia University (MMU), Malaysia. Upon graduation, she joined the Faculty of Information Science and Technology, MMU as a tutor and researcher. Currently, she is a member of the Center of Excellent in Biometrics and Bioinformatics at the same university. Her research interests include biometrics, image processing and Web 3D.

Andrew Teoh Beng Jin obtained his B.Eng (Electronics) in 1999 and his Ph.D degree in 2003 from the National University of Malaysia. He is currently a lecturer and an associate Dean of the Faculty of Information Science and Technology, Multimedia University. He held the post of co-chair (Biometrics Division) in the Center of Excellent in Biometrics and Bioinformatics at the same university. His research interest is in multimodal biometrics, pattern recognition, multimedia signal processing and Internet security.

Goh Kah Ong Michael received his Bachelor of Information Technology (Software Engineering) from Multimedia University, Malaysia in 2002. Upon graduation, he joined MMU as an assistant lecturer for the Center of Affiliate and Diploma Programme (CADP). A few months later, he transferred to the Faculty of Information Science & Technology (FIST) as a tutor and researcher. Currently, he is a member of Center of Biometrics and Bioinformatics (CBB). His research interests include biometrics, Web 3D and artificial intelligent agent technology.

David Chek Ling Ngo is an associate Professor and the Dean of the Faculty of Information Science and Technology at Multimedia University, Malaysia. He has worked there since 1999. Ngo was awarded a B.AI in Microelectronics and Electrical Engineering and a Ph.D in Computer Science in 1990 and 1995 respectively, both from Trinity College, Dublin. Ngo’s research interests lie in the area of automatic screen design, aesthetic systems, biometric encryption and knowledge management. He is an author and co-author of over 20 invited and refereed papers. He is a member of the Review Committee of Displays and Multimedia Cyberscape.