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A survey on biometric cryptosystems and cancelable biometrics
EURASIP Journal on Information Security volume 2011, Article number: 3 (2011)
Abstract
Form a privacy perspective most concerns against the common use of biometrics arise from the storage and misuse of biometric data. Biometric cryptosystems and cancelable biometrics represent emerging technologies of biometric template protection addressing these concerns and improving public confidence and acceptance of biometrics. In addition, biometric cryptosystems provide mechanisms for biometricdependent keyrelease. In the last years a significant amount of approaches to both technologies have been published. A comprehensive survey of biometric cryptosystems and cancelable biometrics is presented. Stateoftheart approaches are reviewed based on which an indepth discussion and an outlook to future prospects are given.
1. Introduction
The term biometrics is defined as "automated recognition of individuals based on their behavioral and biological characteristics" (ISO/IEC JTC1 SC37). Physiological as well as behavioral biometric characteristics are acquired applying adequate sensors and distinctive features are extracted to form a biometric template in an enrollment process. At the time of verification or identification (identification can be handled as a sequence of verifications and screenings) the system processes another biometric input which is compared against the stored template, yielding acceptance or rejection [1]. It is generally conceded that a substitute to biometrics for positive identification in integrated security applications is nonexistent. While the industry has long claimed that one of the primary benefits of biometric templates is that original biometric signals acquired to enroll a data subject cannot be reconstructed from stored templates, several approaches [2, 3] have proven this claim wrong. Since biometric characteristics are largely immutable, a compromise of biometric templates results in permanent loss of a subject's biometrics. Standard encryption algorithms do not support a comparison of biometric templates in encrypted domain and, thus, leave biometric templates exposed during every authentication attempt [4] (homomorphic and asymmetric encryption, e.g., in [5–7], which enable a biometric comparison in encrypted domain represent exceptions). Conventional cryptosystems provide numerous algorithms to secure any kind of crucial information. While user authentication is based on possession of secret keys, key management is performed introducing a second layer of authentication (e.g., passwords) [8]. As a consequence, encrypted data inherit the security of according passwords applied to release correct decrypting keys. Biometric template protection schemes which are commonly categorized as biometric cryptosystems (also referred to as helper databased schemes) and cancelable biometrics (also referred to as feature transformation) are designed to meet two major requirements of biometric information protection (ISO/IEC FCD 24745):

Irreversibility: It should be computationally hard to reconstruct the original biometric template from the stored reference data, i.e., the protected template, while it should be easy to generate the protected biometric template.

Unlinkability: Different versions of protected biometric templates can be generated based on the same biometric data (renewability), while protected templates should not allow crossmatching (diversity).
"Biometric cryptosystems (BCSs) are designed to securely bind a digital key to a biometric or generate a digital key from a biometric" [9] offering solutions to biometricdependent keyrelease and biometric template protection [10, 11]. Replacing passwordbased keyrelease, BCSs brings about substantial security benefits. It is significantly more difficult to forge, copy, share, and distribute biometrics compared to passwords [1]. Most biometric characteristics provide an equal level of security across a usergroup (physiological biometric characteristics are not user selected). Due to biometric variance (see Figure 1), conventional biometric systems perform "fuzzy comparisons" by applying decision thresholds which are set up based on score distributions between genuine and nongenuine subjects. In contrast, BCSs are designed to output stable keys which are required to match a 100% at authentication. Original biometric templates are replaced through biometricdependent public information which assists the keyrelease process.
"Cancelable biometrics (CB) consist of intentional, repeatable distortions of biometric signals based on transforms which provide a comparison of biometric templates in the transformed domain" [12]. The inversion of such transformed biometric templates must not be feasible for potential imposters. In contrast to templates protected by standard encryption algorithms, transformed templates are never decrypted since the comparison of biometric templates is performed in transformed space which is the very essence of CB. The application of transforms provides irreversibility and unlinkability of biometric templates [9]. Obviously, CB are closely related to BCSs.
As both technologies have emerged rather recently and corresponding literature is dispersed across different publication media, a systematic classification and indepth discussion of approaches to BCS and CB is given. As opposed to existing literature [4, 8], which intends to review BCSs and CB at coarse level, this article provides the reader with detailed descriptions of all existing key concepts and followup developments. Emphasis is not only placed on biometric template protection but on cryptographic aspects. Covering the vast majority of published approaches up to and including the year 2010 this survey comprises a valuable collection of references based on which a detailed discussion (including performance rates, applied data sets, etc.) of the stateoftheart technologies is presented and a critical analysis of open issues and challenges is given.
This survey is organized as follows: BCSs (Section 2) and CB (Section 3) are categorized and concerning literature is reviewed in detail. A comprehensive discussion including the current stateoftheart approaches to both technologies, security risks, privacy aspects, and open issues and challenges is presented and concluding remarks are given (Section 4).
2. Biometric Cryptosystems
The majority of BCSs require the storage of biometricdependent public information, applied to retrieve or generate keys, which is referred to as helper data [4]. Due to biometric variance it is not feasible for most biometric characteristics to extract keys directly. Helper data, which must not reveal significant information about original biometric templates, assists in reconstructing keys. Biometric comparisons are performed indirectly by verifying key validities, where the output of an authentication process is either a key or a failure message. Since the verification of keys represents a biometric comparison in encrypted domain [11], BCSs are applied as a means of biometric template protection [4], in addition to providing biometricdependent keyrelease. Based on how helper data are derived, BCSs are classified as keybinding or keygeneration systems (see Figure 2):

(1)
Keybinding schemes: Helper data are obtained by binding a chosen key to a biometric template. As a result of the binding process a fusion of the secret key and the biometric template is stored as helper data. Applying an appropriate key retrieval algorithm, keys are obtained from the helper data at authentication [8]. Since cryptographic keys are independent of biometric features these are revocable while an update of the key usually requires reenrollment in order to generate new helper data.

(2)
Keygeneration schemes: Helper data are derived only from the biometric template. Keys are directly generated from the helper data and a given biometric sample [4]. While the storage of helper data are not obligatory the majority of proposed keygeneration schemes does store helper data (if keygeneration schemes extract keys without the use of any helper data these are not updatable in case of compromise). Helper databased keygeneration schemes are also referred to as "fuzzy extractors" or "secure sketches", for both primitives formalisms (and further extensions) are defined in [13, 14]. A fuzzy extractor reliably extracts a uniformly random string from a biometric input while stored helper data assist the reconstruction. In contrast, in a secure sketch, helper data are applied to recover the original biometric template.
Several concepts of BCSs can be applied as both, keygeneration and keybinding scheme [15, 16]. Hybrid approaches which make use of more basic concepts [17] have been proposed, too. Furthermore, schemes which declare different goals such as enhancing the security of an existing secret [18, 19] have been introduced. In contrast to BCSs based on keybinding or keygeneration, keyrelease schemes represent a loose coupling of biometric authentication and keyrelease [8]. In case of successful biometric authentication a keyrelease mechanism is initiated, i.e., a cryptographic key is released. The loose coupling of biometric and cryptographic systems allows to exchange both components easily. However, a great drawback emerges, since the separate plain storage of biometric templates and keys offers more vulnerabilities to conduct attacks. Keyrelease schemes do not meet requirements of biometric template protection and, thus, are hardly appropriate for high security applications and not usually considered a BCS. Another way to classify BCSs is to focus on how these systems deal with biometric variance. While some schemes apply error correction codes [15, 16], others introduce adjustable filter functions and correlation [20] or quantization [21, 22].
Even though definitions for "biometric keys" have been proposed (e.g., in [23, 24]), these terms have established as synonyms for any kind of key dependent upon biometrics, i.e., biometric features take influence on the constitution of keys (as opposed to keybinding schemes). Like conventional cryptographic keys, biometric keys have to fulfill several requirements, such as keyrandomness, stability, or uniqueness [25, 26].
A. Performance measurement
When measuring the performance of biometric systems widely used factors include False Rejection Rate (FRR), False Acceptance Rate (FAR), and Equal Error Rate (EER) [1, 27] (defined in ISO/IEC FDIS 197951). As score distributions overlap, FRR and FAR intersect at a certain point, defining the EER of the system (in general, decreasing the FRR increases the FAR and vice versa).
These performance metrics are directly transferred to keyrelease schemes. In the context of BCSs the meaning of these metrics change since thresholdbased "fuzzy comparison" is eliminated. Within BCSs acceptance requires the generation or retrieval of hundred percent correct keys, while conventional biometric systems response with "Yes" or "No". The fundamental difference between performance measurement in biometric systems and BCSs is illustrated in Figure 3. The FRR of a BCS defines the rate of incorrect keys untruly generated by the system, that is, the percentage of incorrect keys returned to genuine users (correct keys are userspecific and associated with according helper data). By analogy, the FAR defines the rate of correct keys untruly generated by the system, that is, the percentage of correct keys returned to nongenuine users. A false accept corresponds to the an untrue generation or retrieval of keys associated with distinct helper data at enrollment.
Compared to biometric systems, BCSs generally reveal a noticeable decrease in recognition performance [8]. This is because within BCS in most cases the enrolled template is not seen and, therefore, cannot be aligned properly at comparison. In addition, the majority of BCSs introduce a higher degree of quantization at feature extraction, compared to conventional biometric systems, which are capable of setting more precise thresholds to adjust recognition rates.
B. Approaches to biometric keybinding
1) Mytec1 and Mytec2 (Biometric Encryption™)
The first sophisticated approach to biometric keybinding based on fingerprints was proposed by Soutar et al. [28–30]. The presented system was called Mytec2, a successor of Mytec1 [20], which was the first BCS but turned out to be impractical in terms of accuracy and security. Mytec1 and Mytec2 were originally called Biometric Encryption™, the trademark was abandoned in 2005. The basis of the Mytec2 (and Mytec1) algorithm is the mechanism of correlation.
Operation mode (see Figure 4): at enrollment a filter function, H(u), is derived from f_{0}(x), which is a twodimensional image array (0 indicates the first measurement). Subsequently, a correlation function c(x) between f_{0}(x) and any other biometric input f_{1}(x) obtained during verification is defined by c\left(x\right)=F{T}^{1}\left\{{F}_{1}\left(u\right){F}_{0}^{*}\left(u\right)\right\}, which is the inverse Fourier transform of the product of the Fourier transform of a biometric input, denoted by F_{1}(u), and {F}_{0}^{*}\left(u\right), where {F}_{0}^{*}\left(u\right) is represented by H(u). The output c(x) is an array of scalar values describing the degree of similarity. To provide distortion tolerance, the filter function is calculated using a set of T training images \left\{{f}_{0}^{1}\left(x\right),{f}_{0}^{2}\left(x\right),\dots ,{f}_{0}^{T}\left(x\right)\right\}. The output pattern of {f}_{0}^{t}\left(x\right) is denoted by {c}_{0}^{t}\left(x\right) with its Fourier transform {F}_{0}^{t}\left(u\right)H\left(u\right). The complex conjugate of the phase component of H(u), e^{iϕ} (H(u)), is multiplied with a random phaseonly array of the same size to create a secure filter, H_{ stored } (u), which is stored as part of the template while the magnitude of H(u) is discarded. The output pattern c_{0}(x) is then linked with an Nbit cryptographic key k_{0} using a linking algorithm: if the nth bit of k_{0} is 0 then L locations of the selected part of c_{0}(x) which are 0 are chosen and the indices of the locations are written into the nth column of a lookup table which is stored as part of the template, termed BioScrypt. During linking, redundancy is added by applying a repetitive code. Standard hashing algorithms are used to compute a hash of k_{0}, termed id_{0} which is stored as part of the template, too. During authentication a set of biometric images is combined with H_{ stored } (u) to produce an output pattern c_{1}(x). With the use of the lookup table an appropriate retrieval algorithm calculates an Nbit key k_{1} extracting the constituent bits of the binarized output pattern. Finally, a hash id_{1} is calculated and tested against id_{0} to check the validity of k_{1}.
The algorithm was summarized in a patent [31], which includes explanations of how to apply the algorithm to other biometric characteristics such as iris. In all the publications, performance measurements are omitted.
2) Fuzzy commitment scheme
In 1999 Juels and Wattenberg [15] combined techniques from the area of error correcting codes and cryptography to achieve a type of cryptographic primitive referred to as fuzzy commitment scheme.
Operation mode (see Figure 5): A fuzzy commitment scheme consists of a function F, used to commit a codeword c ∈ C and a witness x ∈ {0, 1} ^{n} . The set C is a set of error correcting codewords c of length n and x represents a bitstream of length n, termed witness (biometric data). The difference vector of c and x, δ ∈ {0, 1} ^{n} , where x = c + δ, and a hash value h(c) are stored as the commitment termed F(c, x) (helper data). Each x', which is sufficiently "close" to x, according to an appropriate metric, should be able to reconstruct c using the difference vector δ to translate x' in the direction of x. A hash of the result is tested against h(c). With respect to biometric keybinding the system acquires a witness x at enrollment, selects a codeword c ∈ C, calculates and stores the commitment F(c, x) (δ and h(c)). At the time of authentication, a witness x' is acquired and the system checks whether x' yields a successful decommitment.
Proposed schemes (see Table 1): The fuzzy commitment scheme was applied to iriscodes by Hao et al. [32]. In their scheme, 2048bit iriscodes are applied to bind and retrieve 140bit cryptographic keys prepared with Hadamard and ReedSolomon error correction codes. Hadamard codes are applied to eliminate bit errors originating from the natural biometric variance and ReedSolomon codes are applied to correct burst errors resulting from distortions. The system was tested with 700 iris images of 70 probands obtaining rather impressive results which were not achieved until then. In order to provide an error correction decoding in an irisbased fuzzy commitment scheme, which gets close to a theoretical bound, twodimensional iterative minsum decoding is introduced by Bringer et al. [33, 34]. Within this approach a matrix is created where lines as well as columns are formed by two different binary ReedMuller codes. Thereby a more efficient decoding is available. The proposed scheme was adapted to the standard iris recognition algorithm of Daugman to bind and retrieve 40bit keys. Due to the fact that this scheme was tested on nonideal iris images a more significant performance evaluation is provided. Rathgeb and Uhl [35] provide a systematic approach to the construction of irisbased fuzzy commitment schemes. After analyzing error distributions between iriscodes of different iris recognition algorithms, ReedSolomon and Hardamard codes are applied (similar to [32]). In other further work [36] the authors apply contextbased reliable component selection in order to extract keys from iriscodes which are then bound to Hadamard codewords. Different techniques to improve the performance of irisbased fuzzy commitment schemes have been proposed [37–39]. Binary iriscodes are suitable to be applied in a fuzzy commitment scheme, in addition, template alignment is still feasible since it only involves a onedimensional circular shift of a given iriscode. Besides iris, the fuzzy commitment scheme has been applied to other biometrics as well, which always requires a binarization of extracted feature vectors.
Teoh and Kim [40] applied a randomized dynamic quantization transformation to binarize fingerprint features extracted from a multichannel Gabor filter. Feature vectors of 375 bits are extracted and ReedSolomon codes are applied to construct the fuzzy commitment scheme. The transformation comprises a noninvertible projection based on a random matrix derived from a userspecific token. It is required that this token is stored on a secure device. Similar schemes based on the feature extraction of BioHashing [41] (discussed later) have been presented in [42, 43]. Tong et al. [44] proposed a fuzzy extractor scheme based on a stable and order invariant representation of biometric data called Fingercode reporting inapplicable performance rates. Nandakumar [45] applies a binary fixedlength minutiae representation obtained by quantizing the Fourier phase spectrum of a minutia set in a fuzzy commitment scheme, where alignment is achieved through focal point of high curvature regions. In [46] a fuzzy commitment scheme based on face biometrics is presented in which realvalued face features are binarized by simple thresholding followed by a reliable bit selection to detect most discriminative features. Lu et al. [47] binarized principal component analysis (PCA) based face features which they apply in a fuzzy commitment scheme.
A method based on user adaptive error correction codes was proposed by Maiorana et al. [48] where the error correction information is adaptively selected based on the intravariability of a user's biometric data. Applying online signatures this seems to be the first approach of using behavioral biometrics in a fuzzy commitment scheme. In [49] another fuzzy commitment scheme based on online signatures is presented.
While in classic fuzzy commitment schemes [15, 32] biometric variance is eliminated applying error correction codes, Zheng et al. [50] employ error tolerant lattice functions. In experiments a FRR of ~ 3.3% and a FAR of ~ 0.6% are reported. Besides the formalism of fuzzy extractors and secure sketches, Dodis et al. [13] introduce the socalled syndrome construction. Here an error correction code syndrome is stored as part of the template and applied during authentication in order to reconstruct the original biometric input.
3) Shielding functions
Tuyls et al. [51] introduced a concept which is referred to as shielding functions.
Operation mode (see Figure 6): It is assumed that at enrollment a noisefree realvalued biometric feature vector X of fixed length is available. This feature vector is used together with a secret S (the key) to generate the helper data W applying an inverse δcontracting function G^{}^{1}, such that G(W, X) = S. Like in the fuzzy commitment scheme [15], additionally, a hash F(S) = V of the secret S is stored. The core of the scheme is the δcontracting function G which calculates a residual for each feature, which is the distance to the center of the nearest evenodd or oddeven interval, depending on whether the corresponding bit of S is 0 or 1. W can be seen as correction vector which comprises all residuals. At authentication another biometric feature vector Y is obtained and G(W, Y) is calculated. In case X  Y ≤ δ, G(W, Y) = S' = S = G(W, X). In other words, noisy features are added to the stored residuals and the resulting vector is decoded. An additional application of error correction is optional. Finally, the hash value F(S') of the reconstructed secret S' is tested against the previously stored one (V) yielding successful authentication or rejection. In further work [52] the authors extract reliable components from fingerprints reporting a FRR of 0.054% and a FAR of 0.032%.
Buhan et al. [53] extend the ideas of the shielding functions approach by introducing a feature mapping based on hexagonal zones instead of square zones. No results in terms of FRR and FAR are given. Li et al. [54] suggest to apply fingerprint in a keybinding scheme based on shielding functions.
4) Fuzzy vault
One of the most popular BCSs called fuzzy vault was introduced by Juels and Sudan [16] in 2002.
Operation mode (see Figure 7): The key idea of the fuzzy vault scheme is to use an unordered set A to lock a secret key k, yielding a vault, denoted by V_{ A } . If another set B overlaps largely with A, k is reconstructed, i.e., the vault V_{ A } is unlocked. The vault is created applying polynomial encoding and error correction. During the enrollment phase a polynom p is selected which encodes the key k in some way (e.g., the coefficients of p are formed by k), denoted by p ← k. Subsequently, the elements of A are projected onto the polynom p, i.e., p(A) is calculated. Additionally, chaff points are added in order to obscure genuine points of the polynom. The set of all points, R, forms the template. To achieve successful authentication another set B needs to overlap with A to a certain extent in order to locate a sufficient amount of points in R that lie on p. Applying error correction codes, p can be reconstructed and, thus, k. The security of the whole scheme lies within the infeasibility of the polynomial reconstruction and the number of applied chaff points. The main advantage of this concept is the feature of order invariance, i.e., fuzzy vaults are able to cope with unordered feature set which is the case for several biometric characteristics (e.g., fingerprints [27]).
Proposed schemes (see Table 2): Clancy et al. [55] proposed the first practical and most apparent implementation of the fuzzy vault scheme by locking minutiae points in a "fingerprint vault". A set of minutiae points, A, are mapped onto a polynom p and chaff points are randomly added to construct the vault. During authentication, ReedSolomon codes are applied to reconstruct the polynom p out of which a 128bit key is recreated. An prealignment of fingerprints is assumed which is rarely the case in practice (feature alignment represents a fundamental step in conventional fingerprint recognition systems). To overcome the assumption of prealignment, Nandakumar et al. [56] suggest to utilize high curvature points derived from the orientation field of a fingerprint as helper data to assist the process of alignment. In their fingerprint fuzzy vault, 128bit keys are bound and retrieved. Uludag et al. [8, 57, 58] propose a linebased minutiae representation which the authors evaluate on a test set of 450 fingerprint pairs. Several other approaches have been proposed to improve the alignment within fingerprintbased fuzzy vaults [59–61]. Rotation and translation invariant minutiae representations have been suggested in [62].
Numerous enhancements to the original concept of the fuzzy vault have been introduced. Moon et al. [63] suggest to use an adaptive degree of the polynomial. Nagar and Chaudhury [64] arrange encoded keys and biometric data of fingerprints in the same order into separate grids, which form the vault. Chaff values are inserted into these grids in appropriate range to hide information.
In other work, Nagar et al. [17, 65] introduce the idea of enhancing the security and accuracy of a fingerprintbased fuzzy vault by exploiting orientation information of minutiae points. Dodis et al. [13] suggest to use a highdegree polynomial instead of chaff points in order to create an improved fuzzy vault. Additionally, the authors propose another syndromebased keygenerating scheme which they refer to as PinSketch. This scheme is based on polynomial interpolation like the fuzzy vault but requires less storage space. Arakala [66] provides an implementation of the PinSketch scheme based on fingerprints.
Apart from fingerprints, other biometric characteristics have been applied in fuzzy vault schemes. Lee et al. [67] proposed a fuzzy vault for iris biometrics. Since iris features are usually aligned, an unordered set of features is obtained through independent component analysis. Wu et al. [68, 69] proposed a fuzzy vault based on iris as well. After image acquisition and preprocessing, iris texture is divided into 64 blocks where for each block the mean gray scale value is calculated resulting in 256 features which are normalized to integers to reduce noise. At the same time, a ReedSolomon code is generated and, subsequently, the feature vector is translated to a cipher key using a hash function. In further work, Wu et al. [70] propose a system based on palmprints in which 362 bit cryptographic keys are bound and retrieved. A similar approach based on face biometrics is presented in [71]. PCA features are quantized to obtain a 128bit feature vector from which 64 distinguishable bits are indexed in a lookup table while variance is overcome by ReedSolomon codes. Reddy and Babu [72] enhance the security of a classic fuzzy vault scheme based on iris by adding a password with which the vault as well as the secret key is hardened. In case passwords are compromised the systems security decreases to that of a standard one, thus, according results were achieved under unrealistic preconditions. Kumar and Kumar [73, 74] present a fuzzy vault based on palmprints by employing realvalued DCT coefficients of palmprint images binding and retrieving 307 bit keys. Kholmatov and Yanikoglu [75] propose a fuzzy vault for online signatures.
C. Approaches to biometric keygeneration
The prior idea of generating keys directly out of biometric templates was presented in a patent by Bodo [76]. An implementation of this scheme does not exist and it is expected that most biometric characteristics do not provide enough information to reliably extract a sufficiently long and updatable key without the use of any helper data.
1) Private template scheme
The private template scheme, based on iris, was proposed by Davida et al. [77, 78] in which the biometric template itself (or a hash value of it) serves as a secret key. The storage of helper data which are error correction check bits are required to correct faulty bits of given iriscodes.
Operation mode (see Figure 8): In the enrollment process M, 2048bit iriscodes are generated which are put through a majority decoder to reduce the Hamming distance between them. The majority decoder computes the vector V ec(V) = (V_{1}, V_{2}, ..., V_{ n } ) for a nbit code vector, denoted by V ec(v_{ i } ) = (v_{ i }_{,1,}v_{ i }_{,2}, ..., v_{ i } ,_{n}), where V_{ j } = majority(v_{1, j}, v_{2, j}, ..., v_{ M } ,_{j}) is the majority of 0's and 1's at each bit position j of M vectors. A majority decoded iriscode T, denoted by V ec(T), is concatenated with check digits V ec(C), to generate V ec(T)V ec(C). The check digits V ec(C) are part of an error correction code. Subsequently, a hash value Hash (Name, Attr, V ec(T)V ec(C)) is generated, where Name is the user's name, Attr are public attributes of the user and Hash(·) is a hash function. Finally, an authorization officer signs this hash resulting in Sig(Hash(Name, Attr, V ec(T)V ec(C))). During authentication, several iriscodes are captured and majority decoded resulting in V ec(T'). With the according helper data, V ec(C), the corrected template V ec(T") is reconstructed. Hash(Name, Attr, V ec(T")V ec(C)) is calculated and compared against Sig(Hash(Name, Attr, V ec(T")V ec(C))). Experimental results are omitted and it is commonly expected that the proposed system reveals poor performance due to the fact that the authors restrict to the assumption that only 10% of bits of an iriscode change among different iris images of a single subject. In general, average intraclass distances of iriscodes lie within 2030%. Implementations of the proposed majority decoding technique (e.g., in [79]) were not found to decrease intraclass distances to that extent.
2) Quantization schemes
Within this group of schemes, helper data are constructed in a way that is assists in a quantization of biometric features in order to obtain stable keys.
Operation mode (see Figure 9): In general quantization schemes, which have been applied to physiological as well as behavioral biometric characteristics, process feature vectors out of several enrollment samples and derive appropriate intervals for each feature element (realvalued feature vectors are required). These intervals are encoded and stored as helper data. At the time of authentication, again, biometric characteristics of a subject are measured and mapped into the previously defined intervals, generating a hash or key. In order to provide updateable keys or hashes, most schemes provide a parameterized encoding of intervals. Quantization schemes are highly related to shielding functions [51] since both techniques perform quantization of biometric features by constructing appropriate feature intervals. In contrast to the shielding functions, generic quantization schemes define intervals for each single biometric feature based on its variance. This yields an improved adjustment of the stored helper data to the nature of the applied biometrics.
Proposed schemes (see Table 3): Feng and Wah [21] proposed a quantization scheme applied to online signatures in order to generate 40bit hashes. To match signatures, dynamic time warping is applied to x and ycoordinates and shapes of x, y waveforms of a test sample are aligned with the enrollment sample to extract correlation coefficients where low ones indicate a rejection. Subsequently, feature boundaries are defined and encoded with integers. If a biometric sample passed the shapematching stage, extracted features are fitted into boundaries and a hash is returned out of which a public and a private key are generated. Vielhauer et al. [22, 24] process online signatures to generate signature hashes, too. In their approach an interval matrix is generated for each subject such that hashes are generated by mapping every single feature against the interval matrix. In [80] the authors adopt the proposed feature extraction to an online signature hash generation based on a secure sketch. Authors report a decrease of the FRR but not of the EER. An evaluation of quantizationbased keygeneration schemes is given in [81]. Sutcu et al. [82] proposed a quantization scheme in which hash values are created out of face biometrics. Li et al. [83] study how to build secure sketches for asymmetric representations based on fingerprint biometrics. Furthermore, the authors propose a theoretical approach to a secure sketch applying twolevel quantization to overcome potential preimage attacks [84]. In [85] the proposed technique is applied to face biometrics. Rathgeb and Uhl [86] extended the scheme of [82] to iris biometrics generating 128bit keys. In [87] the authors apply a contextbased reliable component selection and construct intervals for the most reliable features of each subject.
D. Further investigations on BCSs
Besides the so far described key concepts of BCSs, other approaches have been proposed. While some represent combinations of basic concepts, others serve different purposes. In addition, multiBCSs have been suggested.
1) Password hardening
Monrose et al. [19] proposed a technique to improve the security of passwordbased applications by incorporating biometric information into the password (an existing password is "salted" with biometric data).
Operation mode (see Figure 10): The keystroke dynamics of a user a are combined with a password pwd_{ a } resulting in a hardened password hpwd_{ a } which can be tested for login purposes or used as cryptographic key. ϕ(a, l) denotes a single biometric feature ϕ acquired during the lth login attempt of user a. To initialize an account, hpwd_{ a } is chosen at random and 2m shares of hpwd_{ a } , denoted by \left\{{S}_{t}^{0},{S}_{t}^{1}\right\}, 1 ≤ t ≤ m, are created by applying Shamir's secretsharing scheme. For each b\in {\left\{0,\mathsf{\text{1}}\right\}}^{\frac{a}{m}} the shares \left\{{S}_{t}^{b\left(t\right)}\right\}, 1 ≤ t ≤ m, can be used to reconstruct hpwd_{ a } , where b(i) is the ith bit of b. These shares are arranged in an instruction table of dimension 2 × m where each element is encrypted with pwd_{ a } . During the lth login, pwd'_{a}, a given password to access account a, is used to decrypt these elements (the correctness of pwd' _{ a } is necessary but not sufficient). For each feature ϕ_{ i } , comparing the value of ϕ_{ i } (a, l) to a threshold t_{ i } ∈ ℝ indicates which of the two values should be chosen to reconstruct hpwd_{ a } . Central to this scheme is the notion of distinguishable features: let μ_{ ai } be the mean deviation and σ_{ ai } be the standard deviation of the measurement ϕ_{ i } (a, j_{1}) . . . ϕ_{ i } (a, j_{ h } ) where j_{1}, ..., j_{ h } are the last h successful logins of user a. Then, ϕ_{ i } is a distinguishable feature if μ_{ ai }  t_{ i } > kσ_{ ai } where k ∈ ℝ^{+}. Furthermore, the feature descriptor b_{ a } is defined as b_{ a } (i) = 0 if t_{ i } > μ_{ ai } + kσ_{ ai } , and 1 if t_{ i } < μ_{ ai }  kσ_{ ai } . For other features, b_{ a } is undefined. As distinguishing features ϕ_{ i } develop over time, the login program perturbs the value in the second column of row i if μ_{ ai } < t_{ i } , and vice versa. The reconstruction of hpwd_{ a } succeeds only if distinguishable features remain consistent. Additionally, if a subject's typing patterns change slightly over time, the system will adapt by conducting a constantsize history file, encrypted with hpwd_{ a } , as part of the biometric template. In contrast to most BCSs the initial feature descriptor is created without the use of any helper data.
Proposed schemes: In several publications, Monrose et al. [18, 23, 88] apply their passwordhardening scheme to voice biometrics where the representation of the utterance of a data subject is utilized to identify suitable features. A FRR of approximately 6% and a FAR below 20% was reported. In further work [25, 26] the authors analyze and mathematically formalize major requirements of biometric key generators, and a method to generate randomized biometric templates is proposed [89]. Stable features are located during a single registration procedure in which several biometric inputs are measured. Chen and Chandran [90] proposed a keygeneration scheme for face biometrics (for 128bit keys), which operates like a passwordhardening scheme [19], using Radon transform and an interactive chaotic bispectral oneway transform. Here, ReedSolomon codes are used instead of shares. A FRR of 28% and a FAR of 1.22% are reported.
2) BioHashing
A technique applied to face biometrics called "BioHashing" was introduced by Teoh et al. [41, 91–93]. Basically, the BioHashing approach operates as keybinding scheme, however, to generate biometric hashes secret userspecific tokens (unlike public helper data) have to be presented at authentication. Prior to the keybinding step, secret tokens are blended with biometric data to derive a distorted biometric template, thus, BioHashing can be seen as an instance of "Biometric Salting" (see Section 3).
Operation mode (see Figure 11): The original concept of BioHashing is summarized in two stages while the first stage is subdivided in two substages: first the raw image is transformed to an image representation in logpolar frequency domain Γ ∈ ℜ ^{M} , where M specifies the logpolar spatial frequency dimension by applying a wavelet transform, which makes the output immune to changing facial expressions and small occlusions. Subsequently, a FourierMellin transform is applied to achieve translation, rotation and scale invariance. The generated face feature Γ ∈ ℜ ^{M} is reduced to a set of single bits b\in {\left\{0,\mathsf{\text{1}}\right\}}^{{l}_{b}} of length l_{ b } via a set of uniform distributed secret random numbers r_{ i } ∈ { 1, 1} which are uniquely associated with a token. These tokenized random numbers, which are created out of a subject's seed, take on a central role in the BioHashing algorithm. First the user's seed is used for generating a set of random vectors {r_{ i } ∈ ℜ ^{M}i = 1, ..., l_{ b } }. Then, the GramSchmidt process is applied to the set of random vectors resulting in a set of orthonormal vectors \left\{{r}_{{\perp}_{i}}\in {\Re}^{M}i=1,\phantom{\rule{2.77695pt}{0ex}}.\phantom{\rule{2.77695pt}{0ex}}.\phantom{\rule{2.77695pt}{0ex}}.\phantom{\rule{2.77695pt}{0ex}},{l}_{b}\right\}. The dot product of the feature vector and all orthonormal vectors \left\{\u27e8\Gamma {r}_{{\perp}_{i}}\u27e9\in {\Re}^{M}i=1,\phantom{\rule{2.77695pt}{0ex}}.\phantom{\rule{2.77695pt}{0ex}}.\phantom{\rule{2.77695pt}{0ex}}.\phantom{\rule{2.77695pt}{0ex}},{l}_{b}\right\} is calculated. Finally a l_{ b } bit FaceHash b\in {\left\{0,\mathsf{\text{1}}\right\}}^{{l}_{b}} is calculated, where b_{ i } , the ith bit of b is 0 if \u27e8\Gamma {r}_{{\perp}_{i}}\u27e9\le \tau and 1 otherwise, where τ is a predefined threshold. In the second stage of BioHashing a key k_{ c } is generated out of the BioHash b. This is done by applying Shamir's secretsharing scheme.
Proposed schemes: Generating FaceHashes, a FRR of 0.93% and a zero FAR are reported. In other approaches the same group adopts BioHashing to several biometric characteristics including fingerprints [94, 95], iris biometrics [96, 97] as well as palmprints [98] and show how to apply generated hashes in generic keybinding schemes [99, 100]. The authors reported zero EERs for several schemes.
Kong et al. [101] presented an implementation of FaceHashing and gave an explanation for the zero EER, reported in the first works on BioHashing. Zero EER were achieved due to the tokenized random numbers, which were assumed to be unique across subjects. In a more recent publication, Teoh et al. [102] address the socalled "stolentoken" issue evaluating a variant of BioHashing, known as multistage random projection (MRP). By applying a multistate discretization the feature element space is divided into 2 ^{N} segments by adjusting the userdependent standard deviation. By using this method, elements of the extracted feature vector can render multiple bits instead of 1 bit in the original BioHash. As a result, the extracted bitstreams exhibit higher entropy and recognition performance is increased even if impostors are in possession of valid tokens. However, zero EERs were not achieved under the stolentoken scenario. Different improvements to the BioHashing algorithm have been suggested [103, 104].
3) MultiBCSs and hybridBCSs
While multibiometric systems [105] have been firmly established (e.g., combining iris and face in a single sensor scenario) a limited amount of approaches to BCSs utilize several different biometric traits to generate cryptographic keys. Nandakumar and Jain [106] proposed the best performing multibiometric cryptosystem in a fuzzy vault based on fingerprint and iris. The authors demonstrate that a combination of biometric modalities leads to increased accuracy and, thus, higher security. A FRR of 1.8% at a FAR of ~ 0.01% is obtained, while the corresponding FRR values of the iris and fingerprint fuzzy vaults are 12 and 21.2%, respectively. Several other ideas of using a set of multiple biometric characteristics within BCSs have been proposed [107–114].
Nagar et al. [17, 65] proposed a hybrid fingerprintbased BCS. Local minutiae descriptors, which comprise ridge orientations and frequency information, are bound to ordinate values of a fuzzy vault applying a fuzzy commitment scheme. In experiments FRR of 5% and a FAR of 0.01% is obtained, without minutiae descriptors the FAR increased to 0.7%. A similar scheme has been suggested in [115].
4) Other approaches
Chen et al. [116] extract keys from fingerprints and bind these to coefficients of nvariant linear equations. Any n (n < m) elements of a mdimensional feature vector can retrieve a hidden key where the template consists of true data, the solution space of the equation, and chaff data (false solutions of the equation). A FRR of 7.2% and zero FAR are reported. Bui et al. [117] propose a keybinding scheme based on face applying quantization index modulation which is originally targeted for watermarking applications. In [118, 119], approaches of combining biometric templates with syndrome codes based on the SlepianWolf theorem are introduced. Boyen et al. [120] presented a technique for authenticated key exchange with the use of biometric data. In order to extract consistent bits from fingerprints a locality preserving hash is suggested in [121]. Thereby minutiae are mapped to a vector space of real coefficients which are decorrelated using PCA. Kholmatov et al. [122] proposed a method for biometricbased secret sharing. A secret is shared upon several users and released if a sufficiently large number of the user's biometric traits is presented at authentication. Similar approaches have been proposed in [123, 124].
E. Security of biometric cryptosystems
Most BCSs aim at binding or generating keys, long enough to be applied in a generic cryptographic system (e.g., 128bit keys for AES). To prevent biometric keys from being guessed, these need to exhibit sufficient size and entropy. System performance of BCSs is mostly reported in terms of FRR and FAR, since both metrics and key entropy depend on the tolerance levels allowed at comparison, these three quantities are highly interrelated.
Buhan et al. [53, 125] have shown that there is a direct relation between the maximum length k of cryptographic keys and the error rates of the biometric system. The authors define this relation as k ≤  log_{2}(FAR), which has established as one of the most common matrices used to estimate the entropy of biometric keys. This means that an ideal BCS would have to maintain an FAR ≤ 2 ^{k} which appears to be a quite rigorous upper bound that may not be achievable in practice. Nevertheless, the authors pointed out the important fact that the recognition rates of a biometric system correlate with the amount of information which can be extracted, retaining maximum entropy. Based on their proposed quantization scheme, [22]. Vielhauer et al. [126] describe the issue of choosing significant features of online signatures and introduce three measures for feature evaluation: intrapersonal feature deviation, interpersonal entropy of hash value components and the correlation between both. By analyzing the discriminativity of chosen features the authors show that the applied feature vector can be reduced by 45% maintaining error rates [127]. This example underlines the fact that BCSs may generate arbitrary long keys while interclass distances (= Hamming distance between keys) remain low. Ballard et al. [25, 26] propose a new measure to analyze the security of a BCS, termed guessing distance. The guessing distance defines the number of guesses a potential imposter has to perform in order to retrieve either the biometric data or the cryptographic key. Thus, the guessing distance directly relates to intraclass distances of biometric systems and, therefore, provides a more realistic measure of the entropy of biometric keys. Kelkboom et al. [128] analytically obtained a relationship between the maximum key size and a target system performance. A increase of maximum key size is achieved in various scenarios, e.g., when applying several biometric templates at enrollment and authentication or when increasing the desired false rejection rates. In theoryoriented work, Tuyls et al. [129, 130] estimate the capacity and entropy loss for fuzzy commitment schemes and shielding functions, respectively. Similar investigations have been done by Li et al. [131, 132] who provide a systematic approach of how to examine the relative entropy loss of any given scheme, which bounds the number of additional bits that could be extracted if optimal parameters were used. A method for arranging secret points and chaff points in fuzzy vaults such that entropy loss is minimized is presented in [133].
Obviously, key lengths have to be maximized in order to minimize the probability that secret keys are guessed [128]. A second factor which affects the security of biometric cryptosystems is privacy leakage, i.e., the information that the helper data contain (leak) about biometric data [134]. Ideally, privacy leakage should be minimized (for a given key length), to avoid identity fraud. The requirements on key size and privacy leakage define a fundamental tradeoff within approaches to BCSs, which is rarely estimated. In [135] this tradeoff is studied from in an informationtheoretical prospective and achievable key length versus privacy leakage regions are determined. Additionally, stored helper data have to provide unlinkability.
3. Cancelable biometrics
Cancelable biometric transforms are designed in a way that it should be computationally hard to recover the original biometric data (see Figure 12). The intrinsic strength (individuality) of biometric characteristics should not be reduced applying transforms (constraint on FAR) while on the other hand transforms should be tolerant to intraclass variation (constraint on FRR) [12]. In addition, correlation of several transformed templates must not reveal any information about the original biometrics (unlinkability). In case transformed biometric data are compromised, transform parameters are changed, i.e., the biometric template is updated. To prevent impostors from tracking subjects by crossmatching databases it is suggested to apply different transforms for different applications. Two main categories of CB are distinguished [4]:

(1)
Noninvertible transforms: In these approaches, biometric data are transformed applying a noninvertible function (e.g., Figure 12b,c). In order to provide updatable templates, parameters of the applied transforms are modified. The advantage of applying noninvertible transforms is that potential impostors are not able to reconstruct the entire biometric data even if transforms are compromised. However, applying noninvertible transforms mostly implies a loss of accuracy. Performance decrease is caused by the fact that transformed biometric templates are difficult to align (like in BCSs) in order to perform a proper comparison and, in addition, information is reduced. For several approaches these effects have been observed [12, 136].

(2)
Biometric salting: Biometric salting usually denotes transforms of biometric templates which are selected to be invertible. Any invertible transform of biometric feature vector elements represents an approach to biometric salting even if biometric templates have been extracted in a way that it is not feasible to reconstruct the original biometric signal [137]. As a consequence, the parameters of the transform have to be kept secret. In case userspecific transforms are applied, the parameters of the transform (which can be seen as a secret seed [102] have to be presented at each authentication. Impostors may be able to recover the original biometric template in case transform parameters are compromised, causing a potential performance decrease of the system in case underlying biometric algorithms do not provide high accuracy without secret transforms. While approaches to biometric salting may maintain the recognition performance of biometric systems noninvertible transforms provide higher security [4].
Approaches to CB can be classified further with respect parts of biometric systems in which transforms are applied. In the signal domain, transformations are either applied to raw biometric measurements (e.g., face image [12]) or to preprocessed biometric signals (e.g., iris texture [138]). In case transforms are applied in signal domain comparators do not need to be adapted. In feature domain extracted biometric features (e.g., face features in [102]) are transformed, thus, a compromise of transforms requires further effort in reconstructing the original biometric from the template. Experimental results of key concepts of CB are summarized in Table 4.
A. The issue of performance evaluation
While in the majority of proposed approaches to CB template alignment is nontrivial and applied transforms are selected to be noninvertible, still some schemes (e.g., in [72, 102]), especially to biometric salting, report an increase in performance. In case userspecific transforms are applied at enrollment and authentication, by definition, twofactor authentication is yielded which may increase the security but does not effect the accuracy of biometric authentication.
A significant increase of recognition rates can be caused by unpractical assumptions during performance evaluations. If userspecific transforms are applied to achieve CB these transforms have to be considered compromised during interclass comparisons. Otherwise, biometrics becomes meaningless as the system could rely on secret tokens parameters without any risk [101]. Secret tokens, be it transform parameters, random numbers or any kind of passwords are easily compromised and must not be considered secure [1]. Thus, performance evaluations of approaches to CB have to be performed under the socalled "stolentoken scenario" where each impostor is in possession of valid secret tokens (the same applies to BCSs in case secret tokens are applied). Figure 13 illustrates how interclass distances may change with or without considering the stolentoken scenario. If different tokens are applied for each subject a clear separation of intraclass and interclass distributions is achieved by adopting a new threshold. In contrast, if secret tokens are considered compromised accuracy decreases. Performance is untruly gained if this scenario is ignored during experiments causing even more vulnerable systems in case of compromise [139].
B. Approaches to noninvertible transforms
1) IBM approaches
Ratha et al. [12] were the first to introduce the concept of CB applying noninvertible transforms.
Operation mode (see Figure 14): Generally, at enrollment, noninvertible transforms are applied to biometric inputs choosing applicationdependent parameters. During authentication, biometric inputs are transformed and a comparison of transformed templates is performed.
Several types of transforms for constructing multiple CB from prealigned fingerprints and face biometrics have been introduced in [12, 140, 141] including cartesian transform and functional transform. In further work [136], different techniques to create cancelable iris biometrics have been proposed. The authors suggest four different transforms applied in image and feature domain where only small performance drops are reported. HammerleUhl et al. [138] applied classic transformations suggested in [12] to iris biometrics. Furthermore, in [142] it is shown that applying both transforms to rectangular iris images, prior to preprocessing, does not work. Similar to [136] Rathgeb and Uhl [143] suggest to apply row permutations to iriscodes. Maiorana et al. [144–146] apply noninvertible transforms to obtain cancelable templates from online signatures. In their approach, biometric templates, which represent a set of temporal sequences, are split into nonoverlapping sequences of signature features according to a random vector which provides revocability. Subsequently, the transformed template is generated through linear convolution of sequences. The complexity of reconstructing the original data from the transformed template is computationally as hard as random guessing.
2) Revocable biotokens
Boult et al. [147, 148] proposed cryptographically secure biotokens which they applied to face and fingerprints. In order to enhance security in biometric systems, biotokens, which they refer to as Biotope™, are adopted to existing recognition schemes (e.g., PCA for face).
Operation mode (see Figure 15): Each measured biometric feature v is transformed via scaling and translation resulting in v' = (v  t) · s. The key idea is to split v' into a stable part g termed integer and an unstable part r. For face biometrics the authors suggest to simply split real feature values into an integer part and a fractional part (e.g., 15.4 is splitted into 15 and 0.4). Since g is considered stable, and a "perfect matching" is claimed to be feasible at authentication, comparisons can be performed in the encrypted domain. A oneway transform of g, denoted by w is stored as first part of the secure biometric template. As second part of the template the unencoded r which has been obscured via the transform, as well as s and t are stored. At authentication, features are transformed applying s and t onto a residual region defined by r. Then, the unencrypted r is used to compute the local distance within a "window", which is referred to as robust distance measure, to provide a perfect match of w. However, since a perfect match is required only for a number of features defined by the system threshold, biotokens are not matched exactly. Additionally, userspecific passcodes can be incorporated to create verificationonly systems. Although the authors ideas seem promising, several questions with respect to the presented approaches are left open, for instance, the design of the helper function which separates biometric features into stable and unstable parts and the adoption of this scheme to other biometric characteristics (which is claimed to be feasible). In further work, bipartite biotokens [149, 150] are introduced and applied to fingerprints in order to provide secure communication via an untrusted channel, where cryptographic keys are released based on successful comparisons of biotokens.
C. Approaches to biometric salting
Savvides et al. [137] generate cancelable face biometrics by applying socalled minimum average correlation filters which provide noninvertibility. Userspecific secret personal identification numbers (PINs) serve as seed for a random basis for the filters similar to [31]. As previously mentioned, BioHashing [41] without keybinding provides cancelable biometric templates, too. Early proposals of the BioHashing algorithm did not consider the stolentoken scenario. In more recent work [151] it is demonstrated that the EER for the extraction of cancelable 180bit fingercodes increases from 0% to 5.31% in the stolentoken scenario. The authors address this issue by proposing a new method which they refer to as MRP [152, 153]. It is claimed that MRP (which is applied to face and speech) retains recognition performance in the stolentoken scenario. Furthermore, the authors proposed a method to generate cancelable keys out of dynamic hand signatures [154, 155] based on the random mixing step of BioPhasor and userspecific 2 ^{N} discretization. To provide CB, extracted features are randomly mixed with a token T using a BioPhasor mixing method. Kim et al. [156] apply userspecific random projections to PCAbased face features followed by an error minimizing template transform. However, the authors do not consider a stolentoken scenario. Another approach to biometric salting was presented by Wang et al. [157] in which face features are transformed based on a secret key. Noninvertibility is achieved by means of quantization. Ouda et al. [158, 159] propose a technique to obtain cancelable iriscodes. Out of several enrollment templates a vector of consistent bits (BioCode) and their positions are extracted. Revocability is provided by encoding the BioCode according to a selected random seed. Pillai et al. [160] achieve cancelable iris templates by applying sector random projection to iris images. Recognition performance is only maintained if userspecific random matrices are applied.
D. Further investigations on cancelable biometrics
Jeong et al. [161] combine two different feature extraction methods to achieve cancelable face biometrics. PCA and ICA (independent component analysis) coefficients are extracted and both feature vectors are randomly scrambled and added in order to create a transformed template. Tulyakov et al. [162, 163] propose a method for generating cancelable fingerprint hashes. Instead of aligning fingerprint minutiae, the authors apply order invariant hash functions, i.e., symmetric complex hash functions. Ang et al. [164] suggest to apply a keydependent geometric transform to fingerprints. In the first step a core point is selected in the fingerprint image and a line is drawn through it where the secret key defines the angle of the line (0 ≤ key ≤ π). Secondly, all minutiae below the line are reflected above the line to achieve a transformed template. Yang et al. [165] apply random projections to minutiae quadruples to obtain cancelable fingerprint templates. In further work [166] the authors address the stolentoken scenario by selecting random projection matrices based on biometric features. Lee et al. [167] presented a method for generating alignmentfree cancelable fingerprint templates. Similar to [59, 162, 163], orientation information is used for each minutiae point. Cancelability is provided by a user's PIN and the userspecific random vector is used to extract translation and rotation invariant values of minutiae points. Hirata and Takahashi [168] propose CB for fingervain patterns where images are transformed applying a Fourierlike transform. The result is then multiplied with a random filter where the client stores the inverse filter on some token. At authentication the inverse filter is applied to regenerate the transformed enrollment data and correlationbased comparison is performed. A similar scheme is applied to fingerprints in [169]. Bringer et al. [170] presented an idea of generating timedependent CB to achieve untraceability among different identities across time.
E. Security of cancelable biometrics
While in the vast majority of approaches, security is put on a level with obtained recognition accuracy according to a reference system, analysis with respect to irreversibility and unlinkability is rarely done. According to irreversibility, i.e., the possibility of inverting applied transforms to obtain the original biometric template, applied feature transformations have to be analyzed in detail. For instance, if (invertible) block permutation of biometric data (e.g., fingerprints in [140] or iris in [138]) is utilized to generate cancelable templates the computational effort of reconstructing (parts of) the original biometric data has to be estimated. While for some approaches, analysis of irreversibility appear straight forward for others more sophisticated studies are required (e.g., in [145] irreversibility relies on the difficulty in solving a blind deconvolution problem).
In order to provide renewability of protected biometric templates, applied feature transformations are performed based on distinct parameters, i.e., employed parameters define a finite key space (which is rarely reported). In general, protected templates differ more as more distant the respective transformation parameters are [146]. To satisfy the property of unlinkability, different transformed templates, generated from a single biometric template applying different parameters, have to appear random to themselves (like templates of different subjects), i.e., the amount of applicable parameters (key space) is limited by the requirement of unlinkability.
F. Cancelable biometrics versus biometric cryptosystems
The demand for cancelable biometric keys results in a strong interrelation between the technologies of BCSs and CB [8]. Within common keybinding schemes in which chosen keys are bound to biometric templates, keys are updatable by definition. In most cases, revoking keys require reenrollment (original biometric templates are discarded after enrollment). In case a keybinding system can be run in secure sketch mode (e.g., [15, 16]), original biometric templates can be reconstructed from another biometric input. With respect to keygeneration schemes, revoking extracted keys require more effort. If keys are extracted directly from biometric features without the application of any helper data (e.g., as suggested in [76]), an update of the key is not feasible. Within helper databased keygeneration schemes stored helper data has to be modified in a way that extracted keys are different from previous ones (e.g., changing the encoding of intervals in quantization schemes). Alternatively, the keygeneration process could comprise an additional stage in which biometric salting performed prior to the keygeneration process [171, 172]. In [173] it is suggested to combine a secure sketch with cancelable fingerprint templates. While CB protect the representation of the biometric data, the biometric template is reconstructed from the stored helper data. Several other approaches to generating cancelable biometric keys have been proposed in [174–177].
4. Discussion and outlook
Based on the presented key concepts of BCSs and CB a concluding discussion is done, including advantages and applications, potential attacks to both technologies, the current stateoftheart, commercial vendors, and open issues and challenges.
A. Advantages and applications
BCSs and CB offer several advantages over generic biometric systems. Most important advantages are summarized in Table 5. In order to underline the potential of both technologies, two essential use cases are discussed.
1) Encryption/decryption with biometric keys
The most apparent application of BCSs is biometricdependent keyrelease within conventional cryptosystems, replacing insecure password or PINbased keyrelease [8]. Eliminating this weak link within cryptosystems, biometricdependent keyrelease results in substantial security benefits making cryptographic systems more suitable for high security applications.
Operation mode (see Figure 16): Any subject registered with the BCS is able to release cryptographic keys upon presenting biometric characteristics. Biometricdependent keys are then transferred to the applied cryptographic algorithm to encrypt plain data. While several approaches to BCSs fulfill the requirement of generating sufficiently long cryptographic keys to be used in symmetric cryptosystems, most schemes fail in extracting an adequate amount of information to construct public key infrastructures (with few exceptions, e.g., [178]). Subsequently, encrypted data are transmitted via any untrusted channel. To decrypt the cipher text again, biometrics are presented to release decrypting keys. It is important to point out that by using biometric keys in generic cryptosystems the generated cipher text is not harder to decipher (in fact it will be even easier to decipher since biometric keys often suffer from low entropy).
2) Pseudonymous biometric databases
BCSs and CB meet the requirements of launching pseudonymous biometric databases [9] since both technologies provide biometric comparisons in encrypted domain while stored helper data or transformed templates do not reveal significant information about original biometric templates.
Operation mode (see Figure 17): At enrollment, biometric characteristics of a subject are employed as input for a BCS or CB (as suggested in [12] diverse obscured templates are generated for different databases). Depending on the type of application further encrypted records are linked to the template where decryption could be applied based on biometricdependent keys. Since biometric templates are not exposed during comparisons [4], the authentication process is fully pseudonymous and, furthermore, the activities of any subject are untraceable.
Several other applications for the use of BCSs and CB have been suggested. In [10], biometric ticketing, consumer biometric payment systems and biometric boarding cards are suggested. VoIP packages are encrypted applying biometric keys in [179]. A remote biometric authentication scheme on mobile devices based on biometric keys is proposed in [180] and a framework for an alternative PIN service based on CB is presented in [181]. In [182], helper datafree keygeneration is utilized for biometric database hashing. Privacy preserving video surveillance has been proposed in [183].
B. Potential attacks
Several attacks have been encountered to infiltrate conventional biometric systems [4, 184]. The technologies of BCS and CB prevent from different traditional attacks while they appear still vulnerable to some. The most common points of attacks to a biometric system are shown in Figure 18. In addition, numerous techniques have been especially designed to attack key approaches to BCSs and CB.
BCSs and CB do not prevent from classic spoofing attacks [184] (presenting fake physical biometrics). However, there are other possibilities to detect fake biometric inputs (e.g., liveness detection [185]) which can be integrated in both technologies, the same holds for replay attacks. Performing substitution attacks to BCSs is more difficult compared to conventional biometric systems since biometric templates are either bound to cryptographic keys or used to extract helper data (the original biometric template is discarded). Substitution attacks against BCSs require additional knowledge (e.g., of bound keys in case of keybinding schemes). In case of CB substitution, attacks are feasible if impostors are in possession of secret transform parameters or secret keys within approaches to biometric salting. Both technologies are more resilient to masquerade attacks [10, 186]. Since reconstruction of original biometric templates should not be feasible the synthetization of original biometric inputs is highly complicated (e.g., [187]). Performance rates of both technologies decrease compared to conventional biometric systems which makes BCSs and CB even more vulnerable to false acceptance attacks. In contrast to CB, overriding final yes/no responses in a tampering scenario is hardly feasible within BCSs as these return a key instead of binary decisions (intermediate scorebased attacks could still be applied [188]).
In Table 6 an overview of specific attacks proposed against BCSs and CB technologies is given.
1) Attacks against BCSs
Boyen [189] was the first to point out the vulnerability of secure sketches and fuzzy extractors in case an impostor is in possession of multiple invocations of the same secret which are combined to reconstruct secrets and, furthermore, retrieve biometric templates. This (rather realistic) scenario is considered as basis for several attacks against BCSs and CB. Similar observations have been made by Sceirer and Boult [190] which refer to this attack as "attack via record multiplicity". Moreover, the authors point out that if the attacker has knowledge of the secret, the template can be recovered. In addition, a blended substitution attack is introduced in which a subjects and the attackers template are merged into one single template used to authenticate with the system. The Biometric Encryption™algorithm [20] is highly impacted or even compromised by these attacks. Adler [187] proposed a "hillclimbing" attack against the Biometric Encryption™algorithm in which a sample biometric input is iteratively modified while the internal comparison score is observed. Nearest impostor attacks [188] in which distinct parts of a large set of biometric templates is combined to obtain high match scores could be applied even more effectively.
Keys bound in fuzzy commitment schemes [15] have been found to suffer from low entropy (e.g., 44 bits in [32]) reducing the complexity for brute force attacks [40]. Attacks which utilize the fact that error correction codes underlie distinct structures have been suggested [10, 188]. Attacks based on error correction code histograms have been successfully conducted against irisbased fuzzy commitment schemes in [191]. In [134], privacy and security leakages of fuzzy commitment schemes are investigated for several biometric data statistics. It is found that fuzzy commitment schemes leak information in bound keys and nonuniform templates. Suggestions to prevent from information leakage in fuzzy commitment schemes have been proposed in [192]. In addition, attacks via record multiplicity could be applied to decode stored commitments [193, 194]. Kelkboom et al. [195] introduce a bitpermutation process to prevent from this attack in a fingerprintbased fuzzy commitment scheme. In addition, it has been found that a permutation of binary biometric feature vectors improves the performance of fuzzy commitment scheme [34], i.e., not only the entropy of the entire biometric template (which is commonly estimated in "degreesoffreedom" [196]) but the distribution of entropy across feature vectors contributes to the security of the system. As a successive encoding of chunks of biometric templates is essential to bind sufficiently long keys distinct parts of the commitment may suffer from low entropy and, thus, are easily decoded [188], i.e., an adaption of biometric templates (e.g., [195]) or an improved use of error correction (e.g., [48]) is necessary.
Applying shielding functions to fingerprints, Buhan et al. [197] estimate the probability of identifying protected templates across databases. It is demonstrated that any kind of quantization approaches do not meet the requirement of unlinkability in general.
Against fuzzy vaults [16], several attacks have been discovered. Chang et al. [198] present an observation to distinguish minutiae from chaff points attacking fuzzy vaults based on fingerprints. Since chaff points are created onebyone, those created later tend reveal smaller empty surrounding areas which is verified experimentally, i.e., the security of a fuzzy vault highly relies on the methodology of generating chaff points. Scheirer and Boult [190] introduce an attack via record multiplicity. If more instances of a fuzzy vault (generated using different keys) are obtained minutiae are likely recoverable, i.e., unlinkability represents a major issue constructing fuzzy vaults. A method for inserting chaff points with a minimal entropy loss has been proposed in [133]. A brute force attack against fuzzy vaults was proposed in [199]. A collusion attack where the attacker is assumed to be in possession of multiple vaults locked by the same key is presented in [200]. It is demonstrated how to effectively identify chaff points which are subsequently remove to unlock the vault. In [201], vulnerabilities within the concept of a hardened fuzzy vaults are pointed out. In contrast to other concepts (e.g., the fuzzy commitment scheme) the fuzzy vault scheme does not obscure the original biometric template but hides it by adding chaff points, i.e., helper data comprise original biometric features (e.g., minutiae) in plain form. Even if practical key retrieval rates are provided by proposed systems, impostors may still be able to unlock vaults in case the helper data does not hide the original biometric template properly, especially if attackers are in possession of several instances of a single vault.
Helper databased keygeneration schemes [77, 126] appear to be vulnerable to attack via record multiplicity. If an attacker is in possession of several different types of helper data and valid secret keys of the same user, a correlation of these can be utilized to reconstruct an approximation of biometric templates acquired at enrollment. In addition, keygeneration schemes tend to extract short keys which makes them easier to be guessed in brute force attacks within a realistic feature space. Methods to reconstruct raw biometric data from biometric hashes have been proposed in [202]. Since keygeneration schemes tend to reveal worse accuracy compared to keybinding approaches (unless a large number of enrollment samples are applied) these are expected to be highly vulnerable to false acceptance attacks.
The passwordhardening scheme [19] has been exposed to be vulnerable to power consumption observations. Side channel attacks to a key generator for voice [18, 23] were performed in [203]. Demonstrating another way of attacking biometric key generators, tolerance functions were identified, which either decide to authorize or reject a user. Another side channel attack to a BCS based on keystroke dynamics was presented in [204]. It is suggested to add noise and random bitmasks to stored parts of the template in order to reduce the correlation between the original biometric template and the applied key. A similar attack to initial steps of error correction decoding in BCSs is proposed in [205].
2) Attacks against CB
The aim of attacking CB systems is to expose the secret transform (and parameters) applied to biometric templates. Thereby potential attackers are able to apply substitution attacks. If transforms are considered invertible, original biometric templates may be reconstructed. In case of noninvertible transforms, attackers may reconstruct an approximation of the original biometric template. Comparison scores, calculated in encrypted domain, could be overwritten [184] and hillclimbing attacks [186] could be performed. In [206, 207], attacks against the block remapping and surfacefolding algorithm of [12] based on fingerprints are proposed.
Since most approaches to biometric salting become highly vulnerable in case secret tokens are stolen [101], false accept attacks could be effectively applied. If the salting process is invertible, templates may be reconstructed and applied in masquerade attacks. Approaches to biometric salting which do not comprise a keybinding step are vulnerable to overwriting final decisions. Several vulnerabilities in the original concept of the BioHashing algorithm [41] have been encountered in [103]. The main drawback of BioHashing (and other instances of biometric salting) resides in exhibiting low performance in case attackers are in possession of secret tokens.
C. Privacy aspects
Subjects can no longer be trusted based on credentials; however, credentials can be revoked and reissued. In order to abolish credentialbased authentication, biometrics are increasingly applied for authentication purposes in a broad variety of commercial (e.g., fingerprint door locks) and institutional applications (e.g., border control). Therefore, biometric authentication requires more stringent techniques to identify registered subjects [208]. Besides the fact that subjects share biometric traits rather reluctantly, the common use of biometrics is often considered as a threat to privacy [209]. Most common concerns include abuse of biometric data (e.g., intrusion by creating physical spoofs) as well as permanent tracking and observation of activities (e.g., function creep by crossmatching).
BCSs and CB are expected to increase the confidence in biometric authentication systems (trusted identification). Both technologies permanently protect biometric templates against unauthorized access or disclosure by providing biometric comparisons in the encrypted domain, preserving the privacy of biometric characteristics [8, 27]. BCSs and CB keep biometric templates confidential meeting security requirements of irreversibility, and unlinkability.
D. The stateoftheart
The stateoftheart of BCSs and CB is estimated according to several magnitudes, i.e., reported performance rates, biometric modalities, applied test sets, etc., and the best performing and evaluated approaches are compared and summarized.
In early approaches to BCSs [31, 77], performance rates were omitted. Moreover, most of these schemes have been found to suffer from serious security vulnerabilities [8, 190]. Representing one of the simplest keybinding approaches the fuzzy commitment scheme [15] has been successfully applied to iris [32] (and other biometrics). Iriscodes appear to exhibit sufficient information to bind and retrieve long cryptographic keys. Shielding functions [51] and quantization scheme [22, 82] have been applied to several physiological and behavioral biometrics, while focusing on reported performance rates, these schemes require further studies. The fuzzy vault scheme [16] which represents one of the most popular BCS has frequently been applied to fingerprints. Early approaches [55], which required a prealignment of biometric templates, have demonstrated the potential of this concept. Recently, several techniques [56, 57] to overcome the shortcoming of prealignment have been proposed. In addition, the feature of orderinvariance offers solutions to implement applications such as biometricbased secret sharing in a secure manner [122]. Within the BioHashing approach [41], biometric features are projected onto secret domains applying userspecific tokens prior to a keybinding process. Variants of the BioHashing approach have been exposed to reveal unpractical performance rates under the nonstolentoken scenario [101]. While generic BCSs are designed to extract or bind keys from or to a biometric the passwordhardening scheme [19] aims at "salting" an existing password with biometric features.
An overview of key approaches of BCSs, with respect biometric characteristics, applied data sets etc., is given in Table 7. Best results are achieved for fingerprints and iris (e.g., in [32, 56]). Both characteristics seem to provide enough information to release sufficiently long keys at practical performance rates while an alignment of templates is feasible. In [32] a FRR of 0.42% at zero FAR is achieved for the first irisbased fuzzy commitment scheme. Performance rates decrease applying scheme to larger datasets captured under unfavorable conditions [34]. Focusing on fingerprints the first implementations of fuzzy vaults [55] have been significantly improved. In [56] a FRR of 4.0% is achieved at a negligible FAR without prealignment. Multibiometric schemes [106] were found improve accuracy even for binding rather long keys. Quantization schemes, which are mostly applied to behavioral biometric characteristics, are limited to generating rather short keys or hashes (e.g., 24 bits in [22]) while performance rates are found unpractical (e.g., FRR of 28.0% in [21]). With respect to recognition rates, the vast majority of BCSs are by no means comparable to conventional biometric systems. While numerous approaches to BCSs generate too short keys at unacceptable performance rates, several enrollment samples may be required as well, (e.g., four samples in [55]). Approaches which report practical rates are tested on rather small datasets (e.g., 70 persons in [32]) which must not be interpreted as significant. The introduction of additional tokens, be it random numbers or secret PINs, often clouds the picture of reported results (e.g., zero EER in [92]).
Cancelable biometrics schemes are summarized in Table 8. First approaches to noninvertible transforms [12], which have been applied to face and fingerprints, include block permutation and surface folding. Diverse proposals [136, 138] have shown that recognition performance decreases noticeably compared to original biometric systems while sample images of transformed biometric images render noninvertibility doubtable. Within the biotoken approach [147] a performance increase is claimed to be achieved due to the application of the robust distance measure. An EER of ~ 0.08% showed an improvement of ~ 36% compared to the original system (this is likely the only approach to CB that claims to perform better in transformed domain).
BioHashing [41] (without keybinding) represents the most popular instance of biometric salting which represents a twofactor authentication scheme [139]. Since additional tokens have to be kept secret [137, 157] result reporting turns out to be problematic. Perfect recognition rates have been reported (e.g., in [91]) while the opposite is true [101].
E. Deployments of BCSs and CB
Though BCSs and CB are still in statu nascendi, first deployments are already available.
privID^{a}, an independent company that was once part of Philips specializes in biometric encryption. By applying a oneway function, which is referred to as BioHASH^{®}, to biometric data pseudonymous codes are obtained. PerSay^{b}, a company that provides voice biometric speaker verification collaborates with privID to integrate privID engine to voice biometrics. Genkey^{c}, a Norway company (which has a large deployment in New Delhi), offers solutions to fingerprintbased keygeneration. The company utilized a concept, which is referred to as FlexKey, where several enrollment samples are applied to select only the most discriminating features in order to extract longer keys. Precise Biometrics^{TMd} is a Swedish company which offers solutions to secure matchoncard fingerprint verification. Securics: The science of security^{TMe}, founded by T. Boult, provide revocable biometric tokens based on the BioToken approach [147].
The EU project TURBINE [210] which aims to transform a description of fingerprints through cryptobiometrics techniques received a EU funding of over $9 million.
F. Open issues and challenges
With respect to the design goals, BCSs and CB offer significant advantages to enhance the privacy and security of biometric systems, providing reliable biometric authentication at an high security level. Techniques which provide provable security/privacy, while achieving practical recognition rates, have remained elusive (even on small datasets). Additionally, several new issues and challenges arise deploying these technologies [10]. One fundamental challenge, regarding both technologies, represents the issue of alignment, which significantly effects recognition performance. Biometric templates are obscured within both technologies, i.e., alignment of obscured templates without leakage is highly nontrivial. While for some biometric characteristics (e.g., iris) alignment is still feasible, for others (e.g., fingerprints) additional information, which must not lead to template reconstruction, has to be stored. Within conventional biometric systems, aligninvariant approaches have been proposed for several biometric characteristics. So far, hardly any suggestions have been made to construct aligninvariant BCSs or CB. Feature adaptation schemes that preserve accuracy have to be utilized in order to obtain common representations of arbitrary biometric characteristics (several approaches to extract binary fingerprint templates have been proposed, e.g., [211, 212]) allowing biometric fusion in a form suitable for distinct template protection schemes. In addition, several suggestions for protocols providing provable secure biometric authentication based on template protection schemes have been made [150, 192, 213, 214].
Focusing on BCSs it is not actually clear which biometric characteristics to apply in which type of application. In fact it has been shown that iris or fingerprints exhibit enough reliable information to bind or extract sufficiently long keys providing acceptable tradeoffs between accuracy and security, where the best performing schemes are based on fuzzy commitment and fuzzy vault. However, practical error correction codes are designed for communication and data storage purposes such that a perfect error correction code for a desired code length has remained evasive (optimal codes exist only theoretically under certain assumptions [215]). In addition, a technique to generate chaff points that are indistinguishable from genuine points has not yet been proposed. The fact that false rejection rates are lower bounded by error correction capacities [216] emerges a great challenge since unbounded use of error correction (if applicable) makes the system even more vulnerable [188]. Other characteristics such as voice or keystroke dynamics (especially behavioral characteristics) were found to reveal only a small amount of stable information [18, 19], but can still be applied to improve the security of an existing secret. In addition, several characteristics can be combined to construct multiBCSs [107], which have received only little consideration so far. Thereby security is enhanced and feature vectors can be merged to extract enough reliable data. While for some characteristics, extracting of a sufficient amount of reliable features seems to be feasible it still remains questionable if these features exhibit enough entropy. In case extracted features do not meet requirements of discriminativity, systems become vulnerable to several attacks (e.g., false acceptance attacks). In addition, stability of biometric features is required to limit information leakage of stored helper data. Besides, several specific attacks to BCSs have been proposed. While key approaches have already been exposed to fail high security demands, more sophisticated security studies for all approaches are required since claimed security of these technologies remains unclear due to a lack formal security proofs and rigorous security formulations [135]. Due to the sensitivity of BCSs, more usercooperation (compared to conventional biometric systems) or multiple enrollment samples [216] are demanded in order to decrease intraclass variation, while sensoring and preprocessing require improvement as well.
Cancelable biometrics require further investigations as well. Transformations and alignment of transformed templates have to be optimized in order to maintain the recognition performance of biometric systems. Additionally, result reporting remains an issue since unrealistic preconditions distort performance rates.
As plenty different approaches to BCSs and CB have been proposed a large number of pseudonyms and acronyms have been dispersed across literature such that attempts to represented biometric template protection schemes in unified architectures have been made [217]. In addition, a standardization on biometric template protection is currently under work in ISO/IEC FCD 24745.
Endnotes
^{a}privID B.V., The Netherlands, http://www.privid.com/.
^{b}PerSay Ltd., Israel, http://www.persay.com/.
^{c}Genkey AS, Norway (BioCryptics), http://genkeycorp.com/.
^{d}Precise Biometrics AB, Sweden, http://www.precisebiometrics.com/.
^{e}Securics Inc., Colorado Springs, CO, http://www.securics.com/.
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This work has been funded by the Austrian Science Fund, project no. L554N15. We thank all the reviewers who significantly helped to improve this work.
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Rathgeb, C., Uhl, A. A survey on biometric cryptosystems and cancelable biometrics. EURASIP J. on Info. Security 2011, 3 (2011). https://doi.org/10.1186/1687417X20113
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DOI: https://doi.org/10.1186/1687417X20113
Keywords
 biometrics
 cryptography
 biometric cryptosystems
 cancelable biometrics
 biometric template protection