Int. J. Communications, Network and System Sciences, 2010, 3, 722-729 doi:10.4236/ijcns.2010.39096 Published Online September 2010 (http://www.SciRP.org/journal/ijcns) Copyright © 2010 SciRes. IJCNS A New Method for Improving Robustness of Registered Fingerprint Data Using the Fractional Fourier Transform Reiko Iwai, Hiroyuki Yoshimura Graduate School of Engineering, Chiba University, Chiba, Japan E-mail: reiko@tu.chiba-u.ac.jp, yoshimura@faculty.chiba-u.jp Received June 21, 2010; revised July 29, 2010; accepted August 30, 2010 Abstract Inspired by related studies, a new data processing method in fingerprint authentication using the fractional Fourier transform (FRT) was proposed for registered fingerprint data. In this proposal, protection of personal information was also taken into account. We applied the FRT instead of the conventional Fourier transform (FT) which has been used as one of the representative fingerprint authentication algorithm. Our method solved the problem of current registration method and the robustness was verified. In this study, a modeled fingerprint image instead of the original raw fingerprint images was analyzed in detail to make the character- istic clear. As one dimensional (1D) modeled fingerprint image, we used the finite rectangular wave which is regarded as the simplification of the grayscale distribution in an arbitrary scanned line of the raw fingerprint images. As a result, it was clarified that the data processed by the FRT provide higher safety than those proc- essed by the FT, because it is difficult to specify the orders from the intensity distribution of FRTs (the in- tensity FRTs) when the combination of the various FRT’s order at every scanned line is used. Keywords: Fractional Fourier Transform, Fingerprint Authentication, Biometrics, Personal Information Protection 1. Introduction The fingerprint images are indispensable and easy to use the information to identify individuals. It is often-used for logging into a PC, access control, as well as diligence and indolence management in an office. Registration methods of the fingerprint images are classified into three major categories. One method is to register the whole fingerprints images as two dimensional (2D) data without modification. The others include to register a priori extracted features of the images, such as minutiae templates [1], and to register spatial frequency data transformed from 1D data extracted from the original 2D image in a specific direction [2]. In the former two methods, there exists the problem that un- fair use is possible when the information leaks out. For the security reasons, the third method might be more preferable. However, it also has following problems: 1) the registered data can easily be decoded to the original 1D data by the inverse FT (IFT), when the registered data are generated using the conventional FT; 2) additional processing time is necessary for any trials to solve the issue 1). We focused on the application of the FRT [3] by genera- lizing the FT to solve these problems, where the FRT’s order can be set arbitrarily. Because of this unique feature of the FRT, it has capability of the encryption if the FRT’s order is not revealed. The FRT of the 1D image out of a 2D fingerprint image includes such features as less computa- tional complexity to retrieve the original, if needed, and impossibility to be decoded to the corresponding raw data by unauthorized persons who have no knowledge on the FRT’s order used. Therefore, even if the registered finger- print information leaked out from an identification system, security would be guaranteed. Since the FRT will be processed by an optical system incorporating a lens and a laser light source to conduct the necessary process physi- cally from scanning the fingerprint images to generating the FRT image [4]. Therefore, it could drastically reduce the time needed for individual identification. In the present study, taking into account such future application, the intensity FRTs are considered in terms of any possibility of unlawful reveal of the hidden FRT’s or- ders used to register the information corresponding to the fingerprint images. Namely, we compare the intensity dis- tribution data obtained by the FT and FRT. In the com- parison, the actual data are simplified to be the finite-length rectangular waveforms because the analytical results could be explained easily. The purpose of this analysis is to demonstrate that unauthorized third persons cannot retrieve