Integrated Approach to User Authentication Based on Handwritten Signature

Abstract

-A new approach to the integration of the results of several tools aimed at solving a single problem is considered. The approach is illustrated by the example of solving the authentication task for signature dynamics based on the naive Bayesian classifier and the neural network. The approach guarantees results not worse than any of the classifiers separately from the point of view of a monotonous combination of the probabilities of errors of the first and second kind. The obtained results can be applied in the construction of a multifactor authentication system.

Keywords

• Keywords-naive handwritten signature
• network

-

INTRODUCTION

There are many different methods of user authentication, one of such methods is biometric authentication. They can be separated into static methods and dynamic methods. Static biometric authentication includes using of fingerprint [ 1-3 ], iris [4-6], facial geometry [ 7-10 ], voice [ 11-13 ], hand geometry [ 14-16 ] and other physiological characteristics of a person. Examples of dynamic biometric authentication are using of keystroke dynamics [ 17-19 ] and signature dynamics [ 20 ]. More part of these approaches are intended to be used even when organizing user authentication for mobile devices.

However, such methods in most cases are either costly (typically, for static methods), or do not provide the required authentication accuracy for practical use (typically, fordynamic methods) [ 21 ]. There is a problem of increasing the accuracy of such systems. First way to solving this problem is the simultaneous use of several classifiers in the analysis of the characteristics of one biometric source. The second way is constructing a multifactor authentication system. However, simple "AND" scheme (the authentication is passed when all decision subsystems vote for the same user) can't be used for this purpose. The reason of this is a significant jump of the probabilities for the first kind error, payed for reduction of the probabilities for the second kind error, not allowing for practical using of such integration.

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).

The problem can be solved by using a majority system, but in this case it is necessary to bring the number of decisive classifiers (or authentication factors) at least to three, which significantly increases the complexity of the system being developed. There arises the problem of developing an approach to integration that guarantees accuracy not worse than the best of the combined classifiers from the point of view of any possible monotonic combination of the probabilities for first and second kind errors.

II.

THE INTEGRATION OF SEVERAL APPROACHES

The basic idea used for integrating several approaches is as follows. Suppose that we have a set (vector) of parameters P describing the set for authentication. In this case, the task of authentication can be reduced to the classification task with an illegal user. In this case a system containing n users classifies they to n + 1 class. Authentication is considered passed when the received class matches with the identifier. The work of one classifier can be represented as a mapping Ai of a parameters set P to a vector U with dimension n + 1. Vector U describes belonging a given set of parameters Ai to each of the users or none of them:

Ui=Ai(P) (1)

In this case, as a rule, the class (user) is selected as the maximum component of the output vector U exceeding a certain threshold T. Note that the last class (none of the users) may not exist, but be defined as "none of the classes reached the minimum threshold".

To integrate classifiers, we apply the function F to combine the outputs Ui of k classifiers into a single output U. The resulting vector for decision can be defined as:

U=F(Ui … Ui )=F(A1(P)… A1(P)) (2)

At the same time, it is obvious that there are some restrictions to integration function F and not every function can be used for this task:

The function F must be monotonous function of any component of the vector Ui. In otherwise, we can have a    mistake in the user's rank detection. For example, the user with the maximum rank in the output vector Ui (identifier of user that is authentication system solution) may cease to be such not under the influence of other classifiers, but only under the influence of one function F, which contradicts common sense.

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 changing of this coefficients for minimization of total classifier error.

There should be a "neutral" value of each of the coefficients Ii, under which this classifier does not affect the integration as a whole. The example of such values is "1" for the multiplying integration functions or "0" for the sum integration functions. This restriction guarantees that there is a set of weights in which the complex degenerates into a separate classifier. As a consequence, integration classifier shows the final results no worse than this individual classifier from any of the possible points of view and any type of error calculation, because integration and individual classifiers are equal in case of using this "neutral" coefficient value.

The final function implicitly contains the vector of thresholds T (possibly individually for each user), which is necessary for the principal possibility of making a decision in favor of each users. In case of every outputs are lesser than this threshold we have no legal class in our system and current user who is trying to pass authentication is an intruder.

In view of the foregoing, the final function can be described as:

U=F(I, T, Ui … Ui )=F(I, T, A1(P)… A1(P)) (3)

Setting up the integration system for the chosen function F is represented as the task of optimizing the final error in this case. Final error can be any fixed monotonous combination of the probabilities of errors of the first and second kind. Optimization result depends from the values of the parameters of the vectors I and T. This solution, based on the above restrictions, includes the results of each of the individual classifiers. This, as a consequence, should guarantee the results no worse than any of the individual classifiers, include the best.

III. AUTHENTICATION BASED ON A HANDWRITTEN SIGNATURE AS TWO CLASSIFICATION METHODS INTEGRATION

EXAMPLE

The first 8 harmonics of the Fourier decomposition of the pen's coordinates x, y, z, the pressure p and the slope angles α and θ are used as the parameters. Also velocities and accelerations of their change was used. Total count of parameters is 6 × 3 × 8 = 144 per signature.

The combination of two classifiers was considered. As approaches for integration the naive Bayesian classifier [ 22, 23 ] and the perceptron [ 24 ] were used. The integration functions are given in Table 1. In this case, functions 1 and 2 essentially show a degenerate classifier. Also should be noted that not all the above functions satisfy the above restrictions. This is done to practically confirm necessity of this restrictions. N - output of the neural network, B - output of the Bayesian classifier, α, β - weighting coefficients. Function number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Function f(x)= α0∙N+β∙B∙0

EXPERIMENT

At the time of the experiment, the database contains signatures from 8 users in the number of more than 1500 signatures. At the preliminary stage, 10 training cycles were done for all functions, after that 100 cycles for the top 10 and functions 1 and 2, for comparing. PFEK is an error of the first kind, PSEK is an error of the second kind, the PE is simply the probability of error, the CE is a linear combination of errors, with a 10-fold importance of the second kind of error. The results of 100 training cycles are presented in Table 2.

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 significance [ 25 ] of these differences except the functions number 5, 9, 10, 11, 12 (1 and 2 were not checked). On closer examination, it can be seen that all the remaining functions satisfy the above restrictions. This fact confirms the correctness of the assumption that these restrictions must be met for correct integration functions. A statistically significant improvement of the criterion of the total error (PE) due to the application of integration is also shown. № 1 2 3 4 5 6 7 8 9 10 11 12

Function f(x)= α0∙N+β∙B∙0

When we tried to compare this results with results of other authors, a problem of open dynamic signature database was detected. Other scientist work with image of the signature only or not provide a signature sources for result comparing. In this case we can only compare numerical results on different signature databases. This information is presented in Table 3.

It can be concluded that, on the one hand, the results are no worse than those for similar systems. On the other hand, only the work [ 22 ] can act as a direct analogue with comparing the volume of the database and the number of users in it. Works with an open database of examples for confirmation are not presented in open repositories such as [ 32 ]. The idea of including to the repository our own set data for future researchers is actual. It can be reliably asserted that the results 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 network in comparison with the analogous work [ 31 ].

V.

CONCLUSIONS

The approach to the integration of several decision-making apparatuses is theoretically and experimentally proved in the course of the work done. This is shown on the example of combining the neural network and the naive Bayesian classifier for solving the task of user authentication based on the dynamics of the signature. A statistically significant improvement of the criterion based on probability of error is shown. This makes it possible to speak about the applicability of the proposed approach. This integration approach allows to guarantee increasing the efficiency of the complex of several decision-making methods in comparison with any of them separately.

In the future, it is planned to test the efficiency of the proposed approach when constructing a multifactor authentication system in mobile devices and using examples from the UCI Machine Learning Repository [ 32 ].

ACKNOWLEDGMENT

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 scientifictechnological complex of Russia for 2014-2020» (grant agreement № 14.577.21.0172 on October 27, 2015; identifier RFMEFI57715X0172).

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