A New Way of Generating Grid-Scroll Chaos and Its Application to Biometric Encryption

A new circuit design is proposed for generating grid-scroll chaos in the phase plane by using a second-order linear system with a control of double-hysteresis series. The double-hysteresis series is constructed in a systematic way by using the basic double-hysteresis building blocks. With the proposed scheme, the number of scrolls can be arbitrarily assigned, and the multi-scroll chaotic attractors can be placed anywhere and can cover any chosen area in the phase plane. The grid-scroll chaotic attractor is applied to biometric (fingerprint image) authentication. In this application, a two-dimensional (2D) discrete chaotic image is created from these grid-scroll chaotic attractors. Some of the parameters of the 2D chaotic image are extracted from the stable global structure of fingerprint image, and used to derive the encryption key at a terminal. Decryption, minutiae extraction and matching are fulfilled at the central server. Based on our previous research [13~15], the grid-scroll chaotic attractors were generated via linear second-order systems and hysteresis series. In this paper analytical analyse for the working principles of the double-hysteresis block is presented and a new circuit design is proposed for the chaos generation. By feeding-back the state variables of the secondorder system into two independent double-hysteresis series, n×m grid-scroll chaotic attractors can be placed anywhere and cover any chosen area in the phase plane. Experimental results verify the proposed design. Application of this result to biometric authentication will be explored in this paper. The rest parts of the paper are organized as follows: Section II introduces the double-hysteresis block and its series. Generation of grid-scroll attractors is presented in section III. Section IV demonstrates the application of the grid-scroll chaotic attractors in fingerprint image authentication. Conclusions are drawn in the last section.