A chaotic encryption scheme for real-time embedded systems: design and implementation

Chaotic encryption schemes are believed to provide greater level of security than conventional ciphers. In this paper, a chaotic stream cipher is first constructed and then its hardware implementation details over Xilinx Virtex-6 FPGA are provided. Logistic map is the simplest chaotic system and has high potential to be used to design a stream cipher for real-time embedded systems. Its simple construct and non-linear dynamics makes it a common choice for such applications. In this paper, we present a Modified Logistic Map (MLM) which improves the performance of Logistic Map in terms of higher Lyapunov exponent and uniformity of bifurcation map. It also avoids the stable orbits of logistic map giving a more chaotic behavior to the system. A stream cipher is built using MLM and random feedback scheme. The proposed cipher gives 16 bits of encrypted data per clock cycle. The hardware implementation results over Xilinx Virtex-6 FPGA give a synthesis clock frequency of 93 MHz and a throughput of 1.5 Gbps while using 16 hardware multipliers. This makes the cipher suitable for embedded devices which have tight constraints on power consumption, hardware resources and real-time parameters.

[1]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[2]  Kwok-Wo Wong,et al.  Embedding Compression in Chaos-Based Cryptography , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  M. Baptista Cryptography with chaos , 1998 .

[4]  R. A. Rueppel Analysis and Design of Stream Ciphers , 2012 .

[5]  Donald W. Davies,et al.  Advances in Cryptology — EUROCRYPT ’91 , 2001, Lecture Notes in Computer Science.

[6]  Sadasivan Puthusserypady,et al.  Self-synchronizing chaotic stream ciphers , 2008, Signal Process..

[7]  Xiaohua Xia,et al.  Improving the Security of Chaotic Synchronization With a $\Delta$-Modulated Cryptographic Technique , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[8]  Guanrong Chen,et al.  A Novel Fast Image Encryption Scheme Based on 3D Chaotic Baker Maps , 2004, Int. J. Bifurc. Chaos.

[9]  Robert A. J. Matthews,et al.  On the Derivation of a "Chaotic" Encryption Algorithm , 1989, Cryptologia.

[10]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[11]  L. Kocarev Chaos-based cryptography: a brief overview , 2001 .

[12]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[13]  Z. Hong,et al.  Generating Chaotic Secure Sequences with Desired Statistical Properties and High Security , 1997 .

[14]  Zhengquan Xu,et al.  An Improved Chaos-Based Stream Cipher Algorithm and its VLSI Implementation , 2008, 2008 Fourth International Conference on Networked Computing and Advanced Information Management.

[15]  Franz Pichler,et al.  Finite Dimensional Generalized Baker Dynamical Systems for Cryptographic Applications , 1995, EUROCAST.

[16]  Ljupco Kocarev,et al.  From chaotic maps to encryption schemes , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[17]  Ranjan Bose,et al.  A novel compression and encryption scheme using variable model arithmetic coding and coupled chaotic system , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Ljupco Kocarev,et al.  Chaotic block ciphers: from theory to practical algorithms , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Ninan Sajeeth Philip,et al.  Chaos for Stream Cipher , 2001, ArXiv.

[20]  Mohamed Hamdi,et al.  Four dimensional chaotic ciphers for secure image transmission , 2008, 2008 IEEE International Conference on Multimedia and Expo.

[21]  G. Álvarez,et al.  Cryptanalysis of dynamic look-up table based chaotic cryptosystems , 2003, nlin/0311043.

[22]  C. Robilliard,et al.  Enhancing the Security of Delayed Differential Chaotic Systems With Programmable Feedback , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[23]  Daniel D. Wheeler,et al.  Supercomputer Investigations of a Chaotic Encryption Algorithm , 1991, Cryptologia.

[24]  Daniel D. Wheeler,et al.  Problems with Chaotic Cryptosystems , 1989, Cryptologia.

[25]  K. Aihara,et al.  Cryptosystems with discretized chaotic maps , 2002 .

[26]  C. Chui,et al.  A symmetric image encryption scheme based on 3D chaotic cat maps , 2004 .

[27]  D. R. Frey,et al.  Chaotic digital encoding: an approach to secure communication , 1993 .

[28]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[29]  A. Wolf,et al.  13. Quantifying chaos with Lyapunov exponents , 1986 .

[30]  Iwao Sasase,et al.  A Secret Key Cryptosystem by Iterating a Chaotic Map , 1991, EUROCRYPT.

[31]  Tao Yang,et al.  A SURVEY OF CHAOTIC SECURE COMMUNICATION SYSTEMS , 2004 .

[32]  Eli Biham,et al.  Cryptanalysis of the Chaotic-Map Cryptosystem Suggested at EUROCRYPT'91 , 1991, EUROCRYPT.