Integrated Approach to User Authentication Based on Handwritten Signature Evgeny Kostyuchenko, Egor Krivonosov, Alexander Shelupanov Department of Complex Information Security and Electronic Computing Systems Tomsk State University of Control Systems and Radioelectronics Tomsk, Russia key@keva.tusur.ru; egor-yrga@mail.ru; saa@tusur.ru Abstract—A new approach to the integration of the results of The problem can be solved by using a majority system, but several tools aimed at solving a single problem is considered. The in this case it is necessary to bring the number of decisive approach is illustrated by the example of solving the classifiers (or authentication factors) at least to three, which authentication task for signature dynamics based on the naive significantly increases the complexity of the system being Bayesian classifier and the neural network. The approach developed. There arises the problem of developing an approach guarantees results not worse than any of the classifiers separately to integration that guarantees accuracy not worse than the best from the point of view of a monotonous combination of the of the combined classifiers from the point of view of any probabilities of errors of the first and second kind. The obtained possible monotonic combination of the probabilities for first results can be applied in the construction of a multifactor and second kind errors. authentication system. Keywords—naive Bayesian classifier, neural network, II. THE INTEGRATION OF SEVERAL APPROACHES handwritten signature The basic idea used for integrating several approaches is as follows. Suppose that we have a set (vector) of parameters P I. INTRODUCTION describing the set for authentication. In this case, the task of There are many different methods of user authentication, authentication can be reduced to the classification task with an one of such methods is biometric authentication. They can be illegal user. In this case a system containing n users classifies separated into static methods and dynamic methods. Static they to n + 1 class. Authentication is considered passed when biometric authentication includes using of fingerprint [1-3], iris the received class matches with the identifier. The work of one [4-6], facial geometry [7-10], voice [11-13], hand geometry classifier can be represented as a mapping Ai of a parameters [14-16] and other physiological characteristics of a person. set P to a vector U with dimension n + 1. Vector U describes Examples of dynamic biometric authentication are using of belonging a given set of parameters Ai to each of the users or keystroke dynamics [17-19] and signature dynamics [20]. More none of them: part of these approaches are intended to be used even when Ui=Ai(P) (1) organizing user authentication for mobile devices. In this case, as a rule, the class (user) is selected as the However, such methods in most cases are either costly maximum component of the output vector U exceeding a (typically, for static methods), or do not provide the required certain threshold T. Note that the last class (none of the users) authentication accuracy for practical use (typically, fordynamic may not exist, but be defined as "none of the classes reached methods) [21]. There is a problem of increasing the accuracy of the minimum threshold". such systems. First way to solving this problem is the simultaneous use of several classifiers in the analysis of the To integrate classifiers, we apply the function F to combine characteristics of one biometric source. The second way is the outputs Ui of k classifiers into a single output U. The constructing a multifactor authentication system. However, resulting vector for decision can be defined as: simple "AND" scheme (the authentication is passed when all U=F(Ui … Ui )=F(A1(P)… A1(P)) (2) decision subsystems vote for the same user) can't be used for this purpose. The reason of this is a significant jump of the At the same time, it is obvious that there are some probabilities for the first kind error, payed for reduction of the restrictions to integration function F and not every function can probabilities for the second kind error, not allowing for be used for this task: practical using of such integration.  The function F must be monotonous function of any component of the vector Ui. In otherwise, we can have a This work was supported by the Ministry of Education and Science of the Russian Federation within 1.3 federal program «Research and development in priority areas of scientific-technological complex of Russia for 2014-2020» (grant agreement № 14.577.21.0172 on October 27, 2015; identifier RFMEFI57715X0172). 66 mistake in the user's rank detection. For example, the functions are given in Table 1. In this case, functions 1 and 2 user with the maximum rank in the output vector Ui essentially show a degenerate classifier. Also should be noted (identifier of user that is authentication system solution) that not all the above functions satisfy the above restrictions. may cease to be such not under the influence of other This is done to practically confirm necessity of this restrictions. classifiers, but only under the influence of one function N - output of the neural network, B - output of the Bayesian F, which contradicts common sense. classifier, α, β - weighting coefficients.  The integration function must contain weight values describing the influence of each of the classifiers I1 ... Ik. We can detect settings of our integration function using TABLE I. INTEGRATION FUNCTIONS changing of this coefficients for minimization of total classifier error. Function Function number  There should be a "neutral" value of each of the 1 f(x)= α0∙N+β∙B∙0 coefficients Ii, under which this classifier does not f(x)= α∙N∙0+ β0∙B affect the integration as a whole. The example of such 2 values is "1" for the multiplying integration functions or 3 f(x)=α∙B+β∙N "0" for the sum integration functions. This restriction f(x)=B∙α∙N∙β guarantees that there is a set of weights in which the 4 complex degenerates into a separate classifier. As a 5 f(x)=Bα*Nβ consequence, integration classifier shows the final f(x)=lg(Bα+Nβ ) 6 results no worse than this individual classifier from any of the possible points of view and any type of error 7 f(x)=sinh(B+α)*sinh(N+β) calculation, because integration and individual f(x)=sinh(B∙α)+sinh(N∙β) 8 classifiers are equal in case of using this "neutral" coefficient value. 9 f(x)=sinh(Bα )+sinh(Nβ)  The final function implicitly contains the vector of 10 f(x)=tanh(B+α)*tanh(N+β) thresholds T (possibly individually for each user), 11 f(x)=tanh(b∙α)+tanh(N∙β) which is necessary for the principal possibility of f(x)=tanh(Bα )+tanh(Nβ) making a decision in favor of each users. In case of 12 every outputs are lesser than this threshold we have no 13 f(x)=√(B∙α)+√(N∙β) legal class in our system and current user who is trying f(x)=√(Bα )+√(Nβ ) to pass authentication is an intruder. 14 15 f(x)=sinh(B∙α+N∙β) In view of the foregoing, the final function can be described as: 16 f(x)=Bα+N∙β U=F(I, T, Ui … Ui )=F(I, T, A1(P)… A1(P)) (3) 17 f(x)=lg(Bα+N∙β) Setting up the integration system for the chosen function F 18 f(x)=tanh(B+α)∙tanh(N∙β) is represented as the task of optimizing the final error in this f(x)=√(Bα )+tanh(N∙β) case. Final error can be any fixed monotonous combination of 19 the probabilities of errors of the first and second kind. 20 f(x)=tanh(B∙α)+sinh(N∙β) Optimization result depends from the values of the parameters f(x)=tanh(B∙α)∙sinh(N∙β) of the vectors I and T. This solution, based on the above 21 restrictions, includes the results of each of the individual 22 f(x)=tanh(B+α)+sinh(N∙β) classifiers. This, as a consequence, should guarantee the f(x)=tanh(B+α)∙sinh(N∙β) results no worse than any of the individual classifiers, include 23 the best. III. AUTHENTICATION BASED ON A HANDWRITTEN IV. EXPERIMENT SIGNATURE AS TWO CLASSIFICATION METHODS INTEGRATION At the time of the experiment, the database contains EXAMPLE signatures from 8 users in the number of more than 1500 The first 8 harmonics of the Fourier decomposition of the signatures. At the preliminary stage, 10 training cycles were pen's coordinates x, y, z, the pressure p and the slope angles α done for all functions, after that 100 cycles for the top 10 and and θ are used as the parameters. Also velocities and functions 1 and 2, for comparing. PFEK is an error of the first accelerations of their change was used. Total count of kind, PSEK is an error of the second kind, the PE is simply the parameters is 6 × 3 × 8 = 144 per signature. probability of error, the CE is a linear combination of errors, with a 10-fold importance of the second kind of error. The The combination of two classifiers was considered. As results of 100 training cycles are presented in Table 2. approaches for integration the naive Bayesian classifier [22, 23] and the perceptron [24] were used. The integration 67 From the presented results it is clear that some integration functions outperform the results of each of the integrated systems separately. An additional check showed the statistical It can be concluded that, on the one hand, the results are no significance [25] of these differences except the functions worse than those for similar systems. On the other hand, only number 5, 9, 10, 11, 12 (1 and 2 were not checked). On closer the work [22] can act as a direct analogue with comparing the examination, it can be seen that all the remaining functions volume of the database and the number of users in it. Works satisfy the above restrictions. This fact confirms the correctness with an open database of examples for confirmation are not of the assumption that these restrictions must be met for correct presented in open repositories such as [32]. The idea of integration functions. A statistically significant improvement of including to the repository our own set data for future the criterion of the total error (PE) due to the application of researchers is actual. It can be reliably asserted that the results integration is also shown. obtained using the integration of the Bayesian classifier and the neural network are no worse than using separate classifiers on identical sets of data and no worse than using a separate neural TABLE II. INTEGRATION FUNCTIONS network in comparison with the analogous work [31]. № Function PFEK PSEK PE CE 1 f(x)= α0∙N+β∙B∙0 0,0568 0,0148 0,0150 0,1413 V. CONCLUSIONS f(x)= α∙N∙0+ β ∙B 0 0,0658 0,0050 0,0123 0,1098 The approach to the integration of several decision-making 2 apparatuses is theoretically and experimentally proved in the 3 f(x)=α∙B+β∙N 0,0605 0,0046 0,0111 0,0999 course of the work done. This is shown on the example of f(x)=sinh(B∙α)+ 0,0621 0,0042 0,0111 0,0998 combining the neural network and the naive Bayesian classifier 4 sinh(N∙β) for solving the task of user authentication based on the f(x)=tanh(B+α)∙ 0,0598 0,0057 0,0118 0,1087 dynamics of the signature. A statistically significant 5 tanh(N+β) improvement of the criterion based on probability of error is f(x)=tanh(b∙α)+ 0,0588 0,0051 0,0111 0,0997 6 tanh(N∙β) shown. This makes it possible to speak about the applicability f(x)=√(B∙α)+√(N∙β) 0,0454 0,0066 0,0109 0,0944 of the proposed approach. This integration approach allows to 7 guarantee increasing the efficiency of the complex of several 8 f(x)=sinh(B∙α+N∙β) 0,0597 0,0048 0,0111 0,0991 decision-making methods in comparison with any of them f(x)=tanh(B+α) ∙tanh(N∙β) 0,0617 0,0054 0,0121 0,1085 separately. 9 f(x)=tanh(B∙α)+ 0,0579 0,0047 0,0115 0,1016 In the future, it is planned to test the efficiency of the 10 proposed approach when constructing a multifactor sinh(N∙β) f(x)=tanh(B+α)+ 0,0594 0,0048 0,0114 0,1005 authentication system in mobile devices and using examples 11 sinh(N∙β) from the UCI Machine Learning Repository [32]. f(x)=tanh(B+α)∙ 0,0624 0,0053 0,0119 0,1071 12 sinh(N∙β) ACKNOWLEDGMENT When we tried to compare this results with results of other This work was supported by the Ministry of Education and authors, a problem of open dynamic signature database was Science of the Russian Federation within 1.3 federal program detected. Other scientist work with image of the signature only «Research and development in priority areas of scientific- or not provide a signature sources for result comparing. In this technological complex of Russia for 2014-2020» (grant case we can only compare numerical results on different agreement № 14.577.21.0172 on October 27, 2015; identifier signature databases. This information is presented in Table 3. RFMEFI57715X0172). TABLE III. COMPARISON OF THE RESULTS WITH THE RESULTS OF SIMILAR SYSTEMS OF IDENTIfiCATION BY SIGNATURE REFERENCES Accur User count Article Method [1] Ram A. Athira and T.S. Jyothis, “Reducing Vulnerability of a acy Basic concepts of graph 94,25 27 Fingerprint Authentication System”, In: Abawajy J., Mukherjea S., [26] Thampi S., Ruiz-Martínez A. (eds) Security in Computing and theory % Multi-section vector 98% 330 Communications SSCC 2015. 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