Period distribution of generalized discrete Arnold cat map》.pdfVIP

Theoretical Computer Science 552 (2014) 13–25 Contents lists available at ScienceDirect Theoretical Computer Science /locate/tcs Period distribution of generalized discrete Arnold cat map Fei Chen a,b,∗, Kwok-wo Wong c , Xiaofeng Liao d,e , Tao Xiang e a Department of Computer Science and Technology, Shenzhen University, China b Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong c Department of Electronic Engineering, City University of Hong Kong, Hong Kong d School of Electronic and Information Engineering, Southwest University, China e College of Computer Science, Chongqing University, Chongqing 400044, China a r t i c l e i n f o a b s t r a c t Article history: The generalized discrete Arnold cat map is adopted in various cryptographic and stegano- Received 26 February 2014 graphic applications where chaos is employed. In this paper, we analyze the period Received in revised form 18 June 2014 distribution of this map. A systematic approach for addressing the general period Accepted 2 August 2014 distribution problem for any integer value of the modulus N is outlined, followed by a Available online 8 August 2014 Communicated by G. Ausiello complete analysis for the case of prime N . The analysis is based on similar techniques studying linear feedback shift register (LFSR) sequences. Together with our previous result