A Critical Comparison of Fingerprint Fuzzy Vault Techniques Hachemi Nabil Dellys1, Noussaiba Benadjimi1, Meriem Romaissa Boubakeur1, Layth Sliman2, Karima Benatchba1, Saliha Artabaz1, Mouloud Koudil1. 1 Laboratoire de Méthodes de Conception de Systèmes (LMCS) Ecole nationale Supérieure en Informatique (ESI), BP 270 Oued-Smar, 160290 Algiers, Algeria. 1{h_dellys, an_benadjimi, am_boubakeur, k_benatchba, s_artabaz, m_koudil}@esi.dz, 2Ecole d'Ingénieur Informatique et technologies du numérique (EFREI), 32 Rue de la république Villejuif, 94800, Paris, France.
[email protected]
Abstract. Fuzzy Vault is an interesting error tolerant method to encrypt data. This method has been widely used in the field of biometrics because of the unstable nature of captured biometric modalities. In this paper, we present main works on Fuzzy Vault when used to secure fingerprint templates. We describe the contributions proposed in different stages of the two Fuzzy Vault phases. The purpose of this work is to show the implementation to be chosen at each stage of a specific Fuzzy Vault application. To this end, in this paper, we conduct a comparative study of these works from a theoretical point of view, and according to some practical criteria. Keywords: Fuzzy Vault, fingerprint, interpolation, feature extraction, feature representation.
1
Introduction
Fuzzy vault is a data securing method using public information and tolerating, to some extent, the error level. Juels and Sudan [1] proposed this method for the first time in 2002 to resolve the fuzzy cryptographic problem. Then, the Fuzzy Vault method has been applied in biometrics to secure templates. In this paper, we focus on the implementation of this method on the fingerprint [2, 3, 4, and 5]. The unstable nature of the different scanned fingerprint images make difficult to obtain a single biometric template. A certain error threshold is tolerated during recognition, but this error threshold does not allow the use of conventional encryption techniques, hence the use of new error-tolerant techniques such as Fuzzy Vault. Fuzzy vault is composed of two phases: data encoding and data decoding. The data encoding phase consists of five stages and the data decoding phase consists of three stages. Several works have been proposed for each of those specific stages. Most of those works focuses on three stages in the encoding phase and two in the decoding one).
However, due to the lack of test standards, each work was evaluated using different criteria. In this paper, we propose a comparative study of those works. We will discuss the performances of the different techniques used in three encoding phases: characteristic polynomial generation [6, 7, and 8], feature extraction [12, 13, and 14] and generation of chaffs points [15, 16, 17, 18, 19, and 20] and two decoding phases: points alignment [6, 7, 25, and 26] and polynomial reconstruction [7, 15, 23, and 29]. The various stages of each phase as well as the main work carried out on each of them will be presented in section 2. In section 3, we propose a synthetic study of these works, as well as a comparison from a theoretical point of view. 1.1
Purpose and related research
Data encryption using the fuzzy vault method involves several stages and many research works are proposed for each one. If one wants to make new proposals for a specific stage, it is important to choose the techniques to be used in other stages, in order to obtain optimal results. The purpose of this comparison is to provide a good idea about how algorithms or strategies to be chosen to ensure an optimal course of Fuzzy Vault processes against a new proposal in a given stage.
2
Fuzzy Vault Applied on Fingerprint
The principle of the fuzzy vault on fingerprint consist of two phases: 1. Encoding the Vault. The encoding consists to encrypt a secret key, generated randomly or imposed by the user, with fingerprint characteristics and chaff points. 2. Decoding the Vault. Decoding consists to regenerate the key from the vault. Each phase consists in several stages. In the following, we describe these stages and we give details of the main proposals in the literature that worked on each one. 2.1
Fuzzy Vault Encode Phase
There are five stages in the encoding phase of fuzzy vault, which are detailed below:
Stage 1: Compute the Characteristic Polynomial. Characteristic polynomials are generated from a secret key (S) [6, 7, 11, and 12] or its hash [9, 10]. The latter is divided into k parts of the same size, Si, i=1...k, and integrated into the polynomial coefficients. Multiple polynomial generation can also be used when the number of features extracted from fingerprint is small and does not allow the interpolation of a k-degree characteristic polynomial. This method divides the secret key into m sub-secret keys, from which m k-degree polynomials are generated. Stage 2: Fingerprint Feature Representation. There is a plethora of features that can be extracted from a fingerprint. Only two of these features verify biometrics constraints: minutiae and descriptor representations. Heaafter, we summarize the main proposals of these two types of representation. a. Singular Points Minutiae Representation. Minutiae are represented by a set of coordinates, several representations exist like 2D representation (Cartesian coordinates (x, y)) [6], 3D representation (Cartesian coordinates (x, y) and orientation θ) [12, 13, and 14] and 4D representation (Cartesian coordinates (x, y), orientation θ and the minutia type (Endpoint / Fork)) [15]. b. Structure Part Minutiae Representation. Minutiae can be represented according to its local or global structure based on its geometry. i. Representation by minutiae local structure. This representation is used to describe any detail compared to its neighbours, based on polar coordinates. The main proposals made for this representation are: The five nearest neighbours structure [16]. Voronoï neighbours. This representation determines the neighbours of the minutia according to the Voronoi diagram [16]. Composite representation [17]. The relative representation of mi regarding mj is described by a 3-tuple (𝑑𝑖−𝑗 ,𝜑𝑖−𝑗 ,𝜃𝑖−𝑗 ) where 𝑑𝑖−𝑗 : is the distance between mi and mj ; 𝜑𝑖−𝑗 : is the difference between the directions of mi and mj and 𝜃𝑖−𝑗 : is the difference in a counterclockwise direction, between the orientation of mi and the direction of mi to mj. ii. Representation according to the overall structure. This representation is based on fingerprint overall geometry. The main proposals concerning representation in triangle based, where the fingerprint template is described as a set of triples of distinct minutiae. c. Descriptors Based Representation. This part describes the fingerprint characteristics by non-minutiae descriptors [18 and 19].
Stage 3: Chaff Points Modelling. The characteristics extracted from fingerprint are represented by a vector of coordinates. However, fuzzy vault requires their representations in scalar form [20]. Consequently, the modeling by concatenation is used. In this modelling, fingerprint characteristics attribute are concatenated to form the encoding units [8, 10, 18, and 21]. Stage 4: Chaff Points Generation. The Chaff points are represented in two coordinates: abscissa ‘c’ and ordinate‘d’. All Chaff points are represented as CHAFF={(𝒄𝒊, 𝒅𝒊); 𝒅𝒊 ≠ 𝑷(𝒖𝒄𝒊)}𝑹𝒊=𝟏 ,where uci are the encoding units obtained from ci. 1. Chaff Points Abscissa Generation. The abscissa of the Chaff points, {𝑐𝑖}𝑅𝑖=1 , are generated following the characteristics of fingerprint points (or vectors) structure. a. Generation based on the spacing between points. This method generates distinct points randomly. The random generation of points is based on two strategies: i. A strategy that makes so that the point generated has one distance Euclidean, than a certain threshold which separates it from Chaff points set already generated and authentic points set [8, 15]. ii. The second strategy takes into account the distribution of the authentic points. Authentic points can be fairly close together and are points mass. The fact that chaff points are evenly scattered helps to distinguish this mass among the union of chaff and authentic point. To resolve this issue, two thresholds are used, the first distance separate between the chaff points. The second, which is bigger, separate chaff points from authentic points. b. Use of geometric forms. The methods in this class are based on geometric constraints like Algorithm based on squares [14] and Algorithm based on cell image segmentation [13]. 2. Chaff Points Ordinate Generation. One of the following strategies ensures chaff point ordinate generation: a. Ordinates are generated randomly about checking the constraint that (ci, di) chaff point is not in the secret polynomial. [6, 11, 15, 23]. b. Ordinates are generated by taking, every time, di = P (ui) + α, such that α is generated randomly, and ui is encoding unit [22]. c. The ordinates chaff points are first determined using one of the methods listed above. Then, misleading k-degree polynomials are integrated into the Vault, some abscissa of chaff points are re-evaluating by these misleading polynomials[23]. Stage 5: Vault Construction and Storage. In this stage, chaff and authentic points are combined to form a vault. The purpose is to hide all the encoding units by adding chaff points [24]. 2.2
Fuzzy Vault Decoding
This phase includes three main stages which are: the points’ alignment, correspondence set determination and polynomial reconstruction.
Stage 1: Points Alignment. There are two techniques to align the fingerprints: 1. Fingerprint Pre-alignment. Pre-alignment methods are based on fingerprint information extraction. a. Reference minutiae/point. This technique denotes a reference minutia against which other minutiae are represented using polar coordinates [19]. b. Helper data. Helper data are a public information, it carries enough information to perform the alignment without revealing any information about the original fingerprint [6, 25, and 26]. Extraction of helper data is based on the principle of Orientation Field Flow Curves (OFFC) [27]. The OFFC representation is robust against noise generated by fingerprint acquisitions, including the Islands and ridges cuts [6]. 2. Fingerprint Auto-alignment. Automatic alignment uses invariant representations to translation and rotation of fingerprint [24]. Thus, no pre-alignment process is used [28]. Amongst these techniques are found: a. Geometric hashing. Alignment by the geometric hash table is considered to be one of the most accurate. But requires a large storage space, and importantly computing time [1, 7, 18, and 21]. b. Minutia structure. These representations which described in the second stage of encoding phase are invariant to translations and rotations [24]. 3. Fingerprint Free-Alignment. This method has the advantage that doesn’t use alignment [21]. It uses the local texture around the minutia which is invariant to transformations of fingerprints that occurred during their acquisitions. Stage 2: Determination of Correspondence Set. The determination of correspondence set consist to identify the authentic points in the vault stored with those extracted from the aligned template in the query. This process creates a set of correspondence points that are authentic in their majority with a legitimate user [9, 16, 17, 23 and 27]. Stage 3: Secret Polynomial Reconstruction. The secret polynomial reconstruction is generated from correspondence set obtained during the first stage. If the polynomial is properly constructed, the secret key can be recovered, and the user is successfully authenticated [7, 11, 15, 23 and 29].
3
Comparison of Fingerprint Vault Techniques
Different contributions have been achieved for different stages of fuzzy vault applied to fingerprints.The question which arises when we want to implement this method for a specific application is what algorithm to be use in each stage? While for certain stages, such as vault storage stage, the same treatments are always used, for polynomial characteristics computation or chaff points generation, several methods can be used. The choice of what method to use depends mainly on the desired performance. Thus, in the next section, we will try to conduct a comparative study of the major contributions made on these particular stages, based on performance criteria.
3.1
Computing the Characteristic Polynomial
The main contributions can be classified according to three aspects: 1. Secret key type. The choice of the key type dependent on the type of the biometric system application.The table below summarizes and compares these cases [31 and 32]. Table 1.Comparison of the different types of keys. Key imposed
Random key
Used to protect the secret key. Used to protect the biometric template. Used only for to protect template.
Without hash With hash
Used only for to protect template. -
2. Number of characteristics. If the number of extracted characteristics is very small, the multiple generation is recommended.Otherwise, the singular generation is sufficient [22]. 3. Polynomial degree. The polynomial degree dependent on the number of extracted features [22], as this are summarized in the following table: Table 2. Comparison between single and multiple polynomial generation minutiae Number Polynomial degree
Performance
Multiple polynomial
A single polynomial
Small
Great
The degree d of all polynomials is subject to the m > d always constraint: number of polynomial * d= constant Degrees are greatest. (often 12 *) Degrees are small. Failed TO Capture Rate (FTCR) decreases The FTCR is relatively considerably, and the biometric system in this case greater. is less restrictive regarding the minimum number of When d increases, the minutia. In addition, the GAR (Grate acceptance FRR (False Rejection Rate) is improved without any degradation of the Rate) increases, the FAR FAR (False acceptance Rate). decreases.
*Most papers fix the value of the constant at 12 for this value gives the best results in the tests .
3.2
Features Extraction
The fingerprint characteristics can be classified according to the following criteria: 1. Need of alignment. extracted characteristics that requires an alignment between the Vault points and the template in query during decoding phase. Thus: Characteristics representation by minutiae in singular points and descriptive vector, requires an alignment point [6, 12 and 15]. Characteristics representation in a structure (local or global) and of points around the nucleus, are invariant to translation, rotation and distortion of fingerprints. The alignment in this case is Automatic [16 and 17].
2. Treatment required for representation. Fingerprint features extraction require different computing power according to their digital representation, thus: Representation by the minutiae point requires only the minutiae extraction [13]. Representation by descriptive vectors doesn’t require treatments because the statistical characteristics of images are computed during its preprocessing [18]. The representation by the local or global structure requires computing of distances and angles of extracted minutiae [16]. Voronoi representation requires the construction of the Voronoi diagram [16], in addition of computing distances. Points around the nucleus descriptor require nucleus detection [33]. 3. Number of extracted features. number of characteristics extracted from fingerprint differ according to their digital representation, change: m features are extracted in the case of minutia representations in singular points or by their local structure [13 and 16] In triangles representation, m minutiaes are first extracted, then, using the extracted m minutiaes, 𝐴3𝑚 features are generated [34]. In the representation by descriptors around the nucleus, the number of features is an entry of the biometric system, it is defined according to its requirements (performance of verification and security) [17]. In the representation by statistical descriptors, number of features, depends on the size of the image, and considered block size [33]. 4. Representations reproducibility. a representation is said to be reproducible if it remains stable despite of the presence of difference between the characteristics extracted from two fingerprints captures associated with the same individual [16, 17, 18 and 33]. Thus: Descriptive vectors are less reproducible because they depend on fingerprints’ acquisition conditions (brightness, grayscale etc.). Minutiae representations in a local structure, are less reproducible than minutiae representation by singular points; since this representation is relative between minutiae, change of a single detail affects all. Orientation descriptors of the points around the nucleus, offers a more reliable and reproducible representation compared to minutiae representation, particularly in the case of low quality fingerprint captures. 5. Matching techniques. the matching can be done in different ways [6, 23, 30 and 31]: The matching by computing of distance can be used in all representations. In the representation by minutiae structure and descriptors around the nucleus, it is possible to use a matching based on number of features correspondent between the Vault and template in query. Hierarchized matching concerns only the local structure representation. It verifies the correspondence between the structures associated with the attributes selected. 6. Response time. the representation of minutiae characteristics by singular points requires a low response time; while response time is relatively high for representation by the overall structure and medium for the other representations. Table 3 summarizes the different variations of features extracted representation from a fingerprint.
Table 3. Comparison between diffrent contribution of feature representation. Minutia structure Local Structure
Minutia alone
Response Time FRR/GAR FAR Number of extracted features
2D
3D
4D
5 nearest neighbours
+++
+++
+++
++ +
++ +++
++ +++
++ ++ +++
Composite Représentation ++ ++ +++
M
M
M
M
m
The Minutiae extraction
Required treatments Alignment need Reproducibility Matching
+: Bad
Yes +++
Yes +++
Yes +++
Distance between two points.
++: Medium
-Minutiae extraction -Distances and angles Computing
-Minutiae extraction -Construction of the Voronoi diagram -Distances and angles computing No No ++ ++ -Distance between two characteristics. -Matching attributes. -Hierarchical Matching
+++: Good
Global Structure Voronoï
Triangles
++ ++ +++
+ +++ +++
m
𝐴3𝑚
-Minutiae extraction -Distances and two types of angles commutation. No ++
Statistic descriptor
Descriptors around the core
+ + Depends on the size of the image, and considered blocks.
++ +++ +++ An entry for the system
-Minutiae extraction -Calculation of distances and angles. No +++ -Distance between two characteristics. -Matching attributes.
-Kernel detection -Tracing of circles and angles
Yes ++ -Distance between two vectors.
No +++ -Distance between two characteristics. -Matching attributes.
3.3
Chaff Points Generation
The generation of the chaff points remains one of the most critical steps in fuzzy vault, we compared separately the generation techniques of the abscissa and ordinates. A. Abscissa Generation. The abscissa generation methods of the Chaff points can be compared according to the following criteria [8, 13, 14 and 15]: 1. Response time. In the generation based on points spacing, the number of the computed Euclidean distances increases massively for each new chaff point generation. The computation time becomes too long. In the chaff generation method based on squares, the points are generated using non-greedy mathematical operations in computations, this reduces the overall response time of the system. In the generation by cells method, the number of the calculated Euclidean distances in each new generation of a chaff points is eight in maximum. Consequently, computing is much faster. 2. Verification performances. Single threshold generation has the lowest value of FRR and FAR rates. Chaff point generation by squares is unable to detect some overlap in few cases; this entails increasing chaff points by mistake, which, in turns increases FAR and FRR. Table 4. Comparison between chaff point's abscissa generation methods. Points spacing
Geometric forme
response Time
One threshold Very high
Two threshold Very high
Square Low
Cells Low
FRR/GAR FAR
++ ++
+++ +++
+++ +++
+++ +++
B. Ordinates Generation. Methods of ordinates generation of chaff points are compared based on the following criteria [6, 11, 15 and 23]: 1. Response time. The pseudo-random method seems to be the faster. Generation by misleading polynomials requires more time because many interpolations are made to construct polynomials. 2. Verification performances. The three methods of ordinates generation do not affect the FAR and FRR, because the matching algorithms use only abscissa.
3.4
Point Alignment
Several point alignment methods have been proposed. Herafter, we compare them according to the following criteria [6, 7, 18, 19, 21, 24, 25 and 26]: 1. Response time. The computation time is very high with regard to alignment method by the hash table due to the generation of verification table, as well as the establishment of correspondence between the two hash tables. Characteristics representation by their structures is ensured during registration. Thus, during the authentication, auto-alignment are used and no extra time is required. 2. Storage space. The space required for the storage of the hash table is very large due to the large size of the stored registration table. 3. Verification performances. The verification performances are affected by the alignment method used. Performance recognition in pre-registration-based solutions relies mainly on the detection accuracy of point reference or using helper data. Using large numbers of chaff points degrades verification performance, regardless of the type of the used alignment. Table 5. Comparative between points-alignment methods. Pre-alignment minutiae
Helper data
Geometric hashing
Invariant representation
Without alignment
Time
Medium
Medium
Very high
-
medium
Storage space
Low
Medium
Very high
Middle / High
Low
FRR/GAR
+ ++
++ +++
+++ +++
++ +++
+ ++
FAR
4
Self-aligning
Discussions and Conclusions
In this paper, we presented a comparison of the main works in fingerprint securisation with Fuzzy Vault. As shown in Table 2, we noted that the number of features extracted from the fingerprint influences the degree of the secret polynomial. Moreover, we found that polynomial multiple generation is recommended for a small number of features. As shown in Table3, the data representation in a structure does not require an alignment of the points when decoding the vault. However, these representations require more processing and thus more time. They offer fewer features and are less reproducible than minutiae representation. As shown in Table 4, chaff abscissa generation is faster and more efficient when it is in techniques based on squares and cells, than when it is used in those based on the points spacing. For ordinates generation, the pseudo-random generation technique is faster than the generation of misleading polynomial. As shown in Table 5, the points alignment in the decoding phase, techniques using a hash table require a large memory space and a higher computation time than other techniques.
Finally, the solutions based on a pre-alignment depends on the characteristic’s detection precision.
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