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automation of financial and legal processes requires enforcement of confidentiality and integrity of transactions . for practical integration with the existing manual systems , such enforcement should be transparent to users . for instance , a person continually signs paper - based documents ( e.g. , bank checks ) by hand , while his embedded handwritten signature images are used to secure the digitized version of the signed documents . such scenario can be realizable using biometric cryptosystems ( also known as bio - cryptographic systems @xcite ) by means of the offline handwritten signature images . in bio - cryptography , biometric signals like fingerprints , iris , face or signature images , etc . , secure private keys within cryptography schemes like digital signatures and encryption . biometric samples provide a more trusted identification tool when compared to simple passwords . for instance , a fingerprint is attached to a person and it is harder to impersonate than traditional passwords .    despite its identification power , biometrics forms a challenging design problem due to its fuzzy nature . for instance , while it is easy for a person to replicate his password during authentication , it rarely happens that a person applies exact fingerprint each time . the main source of variability in physiological biometrics like fingerprint , face , iris , retina , etc . is the imperfect acquisition of the traits . on the other hand , behavioral biometrics like handwritten signatures , gait , and even voice , have intrinsic variability that is harder to cancel . fuzzy vault ( fv ) is a reliable scheme presented mainly to enable usage of fuzzy keys for cryptography @xcite . a fv decoder permits limited variations in the decryption key so that secrets can be decrypted even with variable keys . accordingly , this scheme fits the bio - cryptography implementations , where biometrics are considered as fuzzy keys by which private cryptographic keys are secured . since the fv scheme has been proposed , it has being extensively employed for bio - cryptography , where most implementations focused on physiological biometrics , e.g. , fingerprints @xcite , face @xcite and iris @xcite . fv implementations based on the behavioral handwritten signatures are few and mostly employed online signature traits , where dynamic features like pressure and speed are acquired in real time by means of special devices as electronic pens and tablets @xcite . static offline signature images , that are scanned after the signing process ends , however , integrate too much variability to cancel by a fv decoder @xcite . recently , the authors have proposed the first offline signature - based fuzzy vault ( osfv ) implementation @xcite-@xcite . this implementation is employed to design a practical digital signature system by means of handwritten signatures @xcite . in this paper , this implementation is reviewed and extended . in particular , we propose an extension to enhance the security and accuracy of the basic osfv system by adapting cryptographic key size for individual users . finally , system performance on the gpds public signature database @xcite , besides the private pucpr brazilian database @xcite , are presented and interpreted . the rest of the paper is organized as follows . in the next section , the osfv implementation and its application to produce digital signatures by means of the handwritten signature images are reviewed . section iii describes the signature representation and lists some aspects for enhanced representations . section iv introduces some osfv variants for enhanced accuracy . section v lists some variants for enhanced security . the new variant that adapts key sizes for enhanced security and accuracy is described in section vi . the simulation results are presented in section vii . finally , some research directions and conclusions are discussed in section viii . the system proposed for osfv consists of two main sub - systems : enrollment and authentication ( see figure [ fig : figure6 ] ) . in the enrollment phase , some signature templates @xmath0 are collected from the enrolling user . these templates are used for the user representation selection , as described in section iii . the user representation selection process results in a user representations matrix @xmath1 , where @xmath2 is the vector of indexes of the selected features , @xmath3 is a vector of indexes mapping represented in @xmath4-bits , and @xmath5 is the vector of expected variabilities associated with the selected features . this matrix is user specific and contains important information needed for the authentication phase . accordingly , @xmath6 is encrypted by means of a user password @xmath7 . both fv and password are then stored as a part of user bio - cryptography template ( @xmath8 ) . then , the user parameters @xmath9 and @xmath10 are used to lock the user cryptography key @xmath11 by means of a single signature template @xmath12 in a fuzzy vault @xmath13 .    in the authentication phase , user password @xmath7 is used to decrypt the matrix @xmath6 . then , the vectors @xmath14 and @xmath15 are used to decode the fv by means of user query signature sample @xmath16 . finally , user cryptographic key @xmath11 is released to the user so he can use it to decrypt some confidential information or digitally signs some documents . the enrollment sub - system uses the user templates @xmath0 , the password @xmath7 , and the cryptography key @xmath11 to generate a bio - cryptography template ( bct ) that consists of the fuzzy vault @xmath13 and the encrypted user representation matrix @xmath17 . the user representation selection module generates the @xmath6 matrix as described in section iii . the osfv encoding module ( illustrated in figure [ fig : figure7 ] ) describes the following processing steps :    1 . the virtual indexes @xmath3 are quantized in @xmath4-bits and produces a vector @xmath18 . 2 .   the user feature indexes @xmath19 are used to extract feature representation @xmath20 from the signature template @xmath12 . this representation is then quantized in @xmath4-bits and produces a vector @xmath21 . the features are encoded to produce the locking set @xmath22 , where @xmath23 consists of @xmath24-bits fv points 4 . the cryptography key @xmath11 of size @xmath25 where : + @xmath26 + is split into @xmath27 parts of @xmath24-bits each , that constitutes a coefficient vector @xmath28 . a polynomial @xmath29 of degree @xmath30 is encoded using @xmath31 , where @xmath32 . the polynomial is evaluated for all points in @xmath22 and constitutes the set @xmath33 where @xmath34 . chaff ( noise ) points @xmath35 are generated , where @xmath36 , i \in [ 1,t ] $ ] , and @xmath37 $ ] . a chaff point @xmath38 is composed of two parts : the index part @xmath39 and the value part @xmath40 . two groups of chaff points are generated . chaffs of @xmath41 have their indexes equal to the indexes of the genuine points . the chaff points and the genuine point that have the same index part are all equally spaced by a distance @xmath42 , eliminating the possibility to differentiate between the chaffs and the genuine point . chaffs of @xmath43 have their index part differs than that of the genuine points as the number of chaffs in @xmath41 is limited by the parameters @xmath44 and @xmath42 , so to inject higher quantity of chaffs we define @xmath45 as a chaff groups ratio , where : + @xmath46 + where @xmath47 and @xmath48 are the amount of chaff features belong to @xmath41 and @xmath43 , respectively . @xmath43 chaffs are generated with @xmath49 indexes different than the @xmath44 genuine indexes . hence , the fv size @xmath50 is given by : + @xmath51 + so , the total number of chaffs @xmath52 is given by : + @xmath53 7 . the genuine set @xmath54 , and the chaff set @xmath55 are merged to constitute the fuzzy vault @xmath56 , where @xmath57 , @xmath22 , @xmath58 and @xmath59 , @xmath60 . the authentication sub - system uses the user query sample @xmath16 and the password @xmath7 , to decode the fuzzy vault @xmath13 and restore the user cryptography key @xmath11 . first the password @xmath7 is used to decrypt the @xmath6 matrix . then the vectors @xmath14 , and @xmath15 are used to decode the fv by means of the query @xmath16 . the osfv decoding module ( illustrated in figure [ fig : figure9 ] ) describes the following processing steps :    1 . the virtual indexes @xmath3 are quantized in @xmath4-bits and produces a vector @xmath61 . 2 .   the user feature indexes @xmath19 are used to extract feature representation @xmath62 from @xmath16 . this representation is then quantized in @xmath4-bits and produces a vector @xmath63 . the features are encoded to produce the unlocking set @xmath64 , where @xmath65 . hence , the unlocking elements are represented in a field @xmath66 . the unlocking set @xmath67 is used to filter the chaff points from the fv . an adaptive matching method is applied to match unlocking and locking points . items of @xmath67 are matched against all items in @xmath68 . this process results in a matching set @xmath69 , where @xmath70 represents the projection of the matching features on the polynomial space . chaff filtering is done as follows . if the feature indexes are correct , then all elements of @xmath71 will have corresponding elements in @xmath72 . so , all of chaffs of @xmath43 will be filtered out . then , each of the remaining fv points will be compared to corresponding points extracted from the query sample . an adaptive matching method is applied : for every feature @xmath73 , a matching window @xmath74 is adapted to the feature modeled variability @xmath75 , where @xmath76 . a fv point @xmath77 is considered matching with an unlocking point @xmath78 , if they reside in the same matching window . i.e. , @xmath79 . the matching set @xmath80 is used to reconstruct a polynomial @xmath81 of degree @xmath30 by applying the rs decoding algorithm @xcite . the coefficients of @xmath81 are assembled to constitute the secret cryptography key @xmath82 .      in @xcite , the osfv implementation is employed to produce digital signatures using offline handwritten signatures . this methodology facilitates the automation of business processes , where users continually employ their handwritten signatures for authentication . users are isolated from the details related to the generation of digital signatures , yet benefit from enhanced security . figure [ signature ] illustrates the osfv - based digital signature framework . the user fv that is constructed during enrollment is used to sign user documents offline as follows . when a user signs a document by hand , his handwritten signature image is employed to unlock his private key @xmath83 . the unlocked key produces a digital signature by encrypting some message @xmath84 extracted from the document ( e.g. , check amount ) . the encrypted message is considered as a digital signature and it is attached to the digitized document . any party who possesses the user public key can verify the digital signature , where verification of the digital signature implies authenticity of the manuscript signature and integrity of the signed document ( e.g. , check amount did not change ) . according to aforementioned osfv implementation , the fv points encode some features extracted from the signature images . it is obvious that accuracy of a fv system relies on the feature representation . representations of intra - personal signatures should sufficiently overlap so that matching errors lie within the error correction capacity of the fv decoder . on contrary , representations of inter - personal signatures should sufficiently differ so that matching errors are higher than the error correction capacity of the fv decoder . accordingly , the authors proposed to design signature representations adapted for the fv scheme by applying a feature selection process in a feature - dissimilarity space . in this space , features are extracted from each pair of template and query samples and the pair - wise feature distances are used as space dimensions .        to illustrate this approach , see figure [ fig : figure12 ] . in this example , three signature images are represented : @xmath85 is the template signature , @xmath86 is a genuine query sample and @xmath87 is a forgery query sample . in the left side , signatures are represented in the fv feature encoding space , where a fv point encodes a feature index @xmath73 and its value @xmath88 . for simplicity , only two features ( @xmath89 and @xmath90 ) are shown , while the full representation consists of @xmath44 dimensions . on the right side , signatures are represented in the feature dissimilarity space . in this space , a feature is replaced by its distance from a reference value . for instance , @xmath89 and @xmath90 are replaced by their dissimilarity representations @xmath91 , where @xmath92 , and @xmath93 . accordingly , while a point in the feature encoding space represents a signature image , a point in the feature dissimilarity space represents the dissimilarity between two different signature images . the point @xmath94 represents the dissimilarity between the genuine signature @xmath86 and the template @xmath85 , and a point @xmath95 represents the dissimilarity between the forgery signature @xmath87 and the template @xmath85 , where @xmath94= ( @xmath96 ) , and @xmath95= ( @xmath97 ) .    in this example , @xmath98 and @xmath99 are discriminant features . for instance , for all genuine query samples like @xmath86 , @xmath100 and for all forgery query samples like @xmath87 , @xmath101 . unfolding these discriminant dissimilarity features to the original feature encoding space produces discriminant features in the encoding feature space , where the distance between two feature instances is used to determine their similarity . for instance , a genuine feature ( like @xmath102 ) lies close to the template feature @xmath103 , so they are similar , where closeness here implies that both features reside in a matching window @xmath76 . features extracted from a forgery image ( like @xmath104 ) do not resemble the template feature @xmath103 , as they reside outside the matching window @xmath74 . aforementioned description of the process to design representations is generic . some extensions are reviewed and compared below . shortage of user samples for training is addressed by designing a global writer - independent ( wi ) representation @xcite . a large number of signature images from a development database are represented in the feature - dissimilarity space of high dimensionality , and feature selection process runs to produce a global space of reduced dimensionality . such global approach permits designing fv systems for any user even who provides a single signature sample during enrollment .    for performance improvement , the global representation is specified for individual users once enough number of enrolling samples becomes available . to this end , training samples are firstly represented in the global representation space , then an additional training step runs to produce a local writer - dependent ( wd ) representation that discriminates the specific user from others . simulation results have shown that local representations enhanced fv decoding accuracy by about 30% , where the average error rate ( aer ) is decreased from 25% in case of global representations to 17.75% for the local ones .      in @xcite , the extended shadow code ( esc ) feature extraction method is adapted for the fv implementation @xcite . these features consist in the superposition of a bar mask array over a binary image of handwritten signatures . each bar is assumed to be a light detector related to a spatially constrained area of the 2d signal . this method is powerful in detecting various levels of details in the signature images by varying the extraction scale . for instance , an image could be split to @xmath105 of horizontal and vertical cells , respectively , and shadow codes are extracted within individual cells . the higher the number of cells , the higher the resolution of detectors . the authors observed that designing fvs based on a single extraction scale results in varying performance for the different users . for instance , while high resolution scales are fine with users whose signatures are easy to forge or those who have high similarities with others , the low resolutions are better for users whose signatures integrate high variabilities . accordingly , a multi - scale feature fusion method is proposed , where different feature vectors are extracted based on different extraction scales and they are combined to produce a high - dimensional representation . this representation is then processed through the wi and wd design phased and produces the final local representation that encodes in the fv .          besides fusing feature vectors that are extracted based on different scales , it is possible to fuse different types of features . in @xcite , the directional probability density function ( dpdf ) features @xcite are fused with esc features to constitute a huge dimensional representation ( of 30,201 dimensionality ) . this representation is reduced through the wi and wd training steps and produced a concise representation of only 20 features . it is shown that injecting the additional feature type increased the fv decoding accuracy by about 22% ( aer is reduced from 17.75% to 13.75% ) . the aforementioned approach provides a practical scenario to produce representations with low intra - personal and high inter - personal variabilities which is mandatory feature for fv systems . however , the authors observed that the margin between the intra and the inter classes differs when using different signature prototypes ( templates ) for fv encoding . accordingly , a prototype selection method is proposed @xcite . the wd representation is projected to a dissimilarity space where distances to different user prototypes are the space constituents . then , a feature selection process runs in the dissimilarity space and locates the best prototype . this method has enlarged the separation between the intra and inter clusters significantly ( area under roc curve ( auc ) is increased from 0.93 to 0.97 ) . although accuracy of an osfv system relies mainly on quality of the feature representation , the proposed implementation provides additional opportunities for enhanced accuracy by applying some other design variants as described in this section . the results mentioned so far report accuracy of fv decoders that apply strict matching approach . two fv points are matching only if they have identical values . accuracy of a fv decoder is enhanced by applying the adaptive matching method , where the feature variability matrix @xmath15 is used for matching so that corresponding fv points are considered matching if their difference lies within the expected variability of their encoding feature ( see figure [ fig : figure3 ] ) . this method increased accuracy by about 27% ( aer is reduced from 13.75% to 10.08% ) @xcite .      instead of decoding a single fv token , it is possible to decode several fvs for enhanced performance . in case that some fvs are correctly decoded , the decrypted key is released to the user based on the majority vote rule . this method has increased detection accuracy by about 18% ( aer is reduced from 10.08% to 8.21% ) @xcite . the limited discriminative power of fvs is alleviated by using an additional password @xmath7 , so that the false accept rate ( far ) is reduced without significantly affecting the false reject rate ( frr ) . for the results reported so far , it was assumed that the user password @xmath7 is compromised . however , to report the actual performance of the system we have to consider the case when an attacker neither possesses a correct password nor a genuine signature sample . in this case , he can not decrypt the ur model and hence he randomly guesses the feature indexes . it is shown that the additional password has increased detection accuracy by about 65% ( aer is reduced from 8.21% to 2.88% ) @xcite .      using additional passwords for enhanced system accuracy comes with the expense of the user inconvenience . in @xcite , a novel user - convenient approach is proposed for enhancing the accuracy of signature - based biometric cryptosystems . since signature verification ( sv ) systems designed in the original feature space have demonstrated higher discriminative power to detect impostors @xcite , they can be used to improve the fv systems . instead of using an additional password , the same signature sample is processed by a sv classifier before triggers the fv decoders ( see figure [ sv - fv ] ) . using this cascaded approach , the high far of fv decoders is alleviated by the higher capacity of sv classifiers to detect impostors . this method has increased detection accuracy by about 35% ( aer is reduced from 10.08% to 6.55% ) . when multiple fvs are fused , the aer is decreased by 31.30% ( from 8.21% to 5.64% ) . security of the osfv implementation is analyzed in terms of the brute - force attack @xcite . assume an attacker could compromise the fv without possessing neither valid password nor genuine signature sample . in this case , the attacker tries to separate enough number of genuine points ( @xmath27 ) from the chaff points . security of a fv is given by :    @xmath106    where @xmath45 is the chaff group ratio , @xmath44 is the number of genuine points in the fv , @xmath30 is the degree of the encoding polynomial and @xmath42 is the chaff separation distance . high value of @xmath45 implies a high number of g2 features which are compromised in case that the password is compromised . the parameter @xmath44 should be concise as it impacts the accuracy and complexity of the fv . accordingly , entropy of the system can be increased through using different values of the parameters : @xmath42 and @xmath30 . however , there is a trade - off between system security and its recognition accuracy that could be alleviated by applying the following approaches .      in the traditional chaff generation method , equal - spaced chaff points are generated with a separation factor @xmath42 @xcite . in such case , there is a trade - off between security and robustness . for instance , with small separation , e.g. , @xmath107 , there are 40 fv points generated with the same index ( 1 genuine + 39 chaff points ) . in this case , a high number of chaffs is generated and results in high system entropy of about 68-bits and low accuracy of about @xmath108 aer . the adaptive chaff generation method enables the injection of high number of chaff with minimal impact on the fv decoding robustness . to this end , the feature variability vector @xmath15 is used during the fv locking phase so that chaff points are generated adaptively according to feature variability . for each feature @xmath88 , @xmath109 ( see figure [ fig : figure3 ] ) . by this method , it is less likely that an unlocking element equates a chaff element . for or instance , the same entropy ( 68-bits ) could be achieved with a minimal impact on system robustness ( aer = 10.52% ) @xcite .      according to eq.[s ] , the longer the cryptographic key size the higher entropy of the fv . however , this comes with expense of the accuracy @xcite . in @xcite , different key sizes ( ks ) are tried ( 128 , 256 , 512 , 1024-bits ) and it is shown that different key sizes result in different performance for the different users . this observation motivates adapting the key length for each user as proposed in the following section , in @xcite , functionality of a fv decoder is formulated as a simple dissimilarity threshold as follows :    = -1 pt    @xmath110    where a fv encoded by a template @xmath85 can be correctly decoded by a query @xmath16 only if the total dissimilarity between @xmath16 and @xmath85 is less than the error correction capacity @xmath111 of the fv decoder . here , @xmath112 is the dissimilarity part that results from the variability between the two samples , and @xmath113 is the dissimilarity part that results from wrong matches with chaff points . the methods discussed so far aimed to optimize the dissimilarity parts of eq.[fvd ] . for instance , the multi - scale and multi - type feature extraction approach results in separating intra - personal and inter - personal dissimilarity ranges . selection of robust templates ( prototypes ) and applying adaptive matching enlarged this separation . also , impact of the chaff error is minimized by presenting the adaptive chaff method . with applying all these methods , however , accuracy of a signature - based fv is still below the level required for practical applications . accordingly , performance is increased by applying some complex and user inconvenient solutions like ensemble of fvs and using additional passwords or cascading sv and fv systems .    here we investigate a new room for enhancing fvs by optimizing the error correction capacity @xmath114 which is given by :    = -1 pt    @xmath115    it is obvious that this parameter relies on the fv encoding size @xmath44 and the encoding polynomial degree @xmath30 . also , from eq.[ks ] , we see that @xmath30 determines the key size @xmath25 . accordingly , we select user specific key sizes through changing the parameter @xmath30 so that @xmath114 for a specific user covers the range of his expected signature variability . to this end , we set @xmath114 for a user to his maximum intra - personal variability @xmath116 . based on the resulting user - specific error correction capacity , the parameter @xmath30 is determined using eq.[fv ] and user key size @xmath25 is computed using eq.[ks ] . once appropriate key size is computed for a user , his key is enlarged through injecting some padding bits in the original key during fv encoding . during authentication , the enlarged key is reconstructed and the padding bits are removed to produce the original cryptographic key . all aforementioned performance results are reported for the pucpr brazilian signature database @xcite . here we test the system for the public gpds-300 database @xcite as well . this database contains signatures of @xmath117 users , that were digitized as 8-bit greyscale at resolution of 300 dpi and contains images of different sizes ( that vary from @xmath118 pixels to @xmath119 pixels ) . all users have 24 genuine signatures and 30 simulated forgeries . it is split into two parts . the first part contains signatures of the first 160 users . a subset of this part is used to design the local representation and the remaining of this part is used for performance evaluation . the second part contains signatures of the last 140 users and it is used to design the global representation . see @xcite for a similar experimental protocol for both databases . table [ table : impact of using a user password ] shows results for the two databases for fixed and adaptive key sizes . it is obvious that employing the adaptive key size approach decreased the far significantly with low impact on the frr . for instance , the aer for the pucpr database in decreased by about 21% ( from 10.08 to 7.94 ) . also , performance of the system for the gpds database is comparable to state - of - the - art traditional sv systems ( aer is about 15% ) that employ more complex classifiers @xcite . moreover , the proposed method also enhances system security as it is possible to increase the key size , and hence the polynomial degree @xmath30 , without much impact on the accuracy . for instance , figure [ fig : adaptive ] shows the adapted polynomial degrees for different users in the pucpr database and the corresponding user variability @xmath116 . it is obvious that users with more stable signatures have their cryptographic keys more enlarged than users with less stable signatures . according to eq.[s ] , system entropy of the standard osfv implementation ( with fixed keys of size 128-bits and polynomial degree @xmath120 ) is about 45-bits . with applying the adaptive key size method , the average @xmath30 is about 9.6-bits ( see figure [ fig : adaptive ] ) which provides an average entropy of about 51-bits . .impact of using a user password as a second authentication measure [ cols="^,^,^,^,^ " , ] in this paper , a recently published offline signature - based fv implementation is reviewed . several variants of the system are listed and compared for enhanced accuracy and security . a novel method to adapt cryptography key sizes for different users is proposed and have shown accuracy and security enhancement . the performance is also validated on a public signature database where comparable results of complex sv in the literature is reported . although the proposed key adaptation method sounds , there is need to propose more intelligent tuning technique taking in consideration the similarities with simulated forgeries for higher forgery detection . this study listed many new approaches that are applied successfully to the signature based bio - cryptography . we believe that these methods shall be investigated for other biometrics which might enhance state - of - the - art of the area of bio - cryptosystems . , r.  sabourin , and e.  granger , on the dissimilarity representation and prototype selection for signature - based bio - cryptographic systems . , york , uk , 3 - 5 july 2013 , lncs , vol.7953 , pp.265 - 280 . eskander . , r.  sabourin , and e.  granger , improving signature - based biometric cryptosystems using cascaded signature verification fuzzy vault ( sv - fv ) approach . , crete island , greece , 1 - 4 september 2014 . g.  eskander , r.  sabourin , and e.  granger . `` hybrid writer - independent  writer - dependent offline signature verification system '' . _ iet - biometrics journal , special issue on handwriting biometrics _ , vol.2 , no.4 , pp .
an offline signature - based fuzzy vault ( osfv ) is a bio - cryptographic implementation that uses handwritten signature images as biometrics instead of traditional passwords to secure private cryptographic keys . having a reliable osfv implementation is the first step towards automating financial and legal authentication processes , as it provides greater security of confidential documents by means of the embedded handwritten signatures . 
 the authors have recently proposed the first osfv implementation which is reviewed in this paper . in this system , 
 a machine learning approach based on the dissimilarity representation concept is employed to select a reliable feature representation adapted for the fuzzy vault scheme . 
 some variants of this system are proposed for enhanced accuracy and security . in particular , a new method that adapts user key size is presented . 
 performance of proposed methods are compared using the brazilian pucpr and gpds signature databases and results indicate that the key - size adaptation method achieves a good compromise between security and accuracy . while average system entropy is increased from 45-bits to about 51-bits , the aer ( average error rate ) is decreased by about 21% .