References 
 
 
[1] Rivest; Ronald L. (Belmont, MA), Shamir; Adi (Cambridge, MA), Adleman; 
Leonard M. (Arlington, MA), “RSA - Cryptographic communications system and 
method” U.S. Patent 4,405,829, December 14, 1977. 
 
[2] National Bureau of Standards, “Data Encryption Standard”, FIPS-Pub.46. National 
Bureau of Standards, U.S. Department of Commerce, Washington D.C., January 
1977. 
 
[3] Baptista M.S, “Cryptography with chaos”, Phys. Lett. A 240, pp.50, 1998. 
 
[4] Ivan B.R., Dhodapkar S.D. and Lawande Q.V., “Cryptography using Lorenz 
dynamics”, National Workshop on Cryptology-2004, pp.10-12, Sept. 2004. 
 
[5] Lorenz E.N., “Deterministic non periodic flow”, J. Atmos. Sci. 20, pp.130, 1963. 
 
[6] Shanon, C., “Communication theory of secrecy systems,” Bell Sys. Tech. J. 28, pp. 
656–715, 1949.  
 
[7] Devaney, R. L., “An Introduction to Chaotic Dynamical Systems”, Redwood City, 
California, USA: Addison-Wesley, 1989. 
 
[8] Hasler, M. “Synchronization of chaotic systems and transmission of information,” 
Int. J. Bifurc. Chaos 8,  pp.647–659, 1998. 
 
[9] Alvarez, G., Montoya, F., Romera, M. & Pastor, G. “Chaotic cryptosystems,” in L. 
D. Sanson, ed., Proc. 33rd Annual 1999 International Carnahan Conference on 
Security Technology, pp.332–338, 1999. 
 
 
91
[10] Silva, C. P. & Young, A. M. “Introduction to chaos-based communications and     
         signal processing,” in Proc. IEEE Aerospace Conference, pp.279–299, 2000. 
 
[11]  Kocarev, L. “Chaos-based cryptography: A brief overview,” IEEE Circuits and  
        Systems Magazine 1, pp.6–21, 2001. 
 
[12]  Li, C., Li, S., Zhang, D. & Chen, G. “Cryptanalysis of a chaotic neural network 
based multimedia encryption scheme,” in Advances in Multimedia Information 
Processing – PCM 2004 Proceedings, Part III, Lecture Notes in Computer 
Science, vol. 3333, pp. 418–425, 2004. 
 
[13] Yang, T. “A survey of chaotic secure communication systems,” Int. J. Comp. 
Cognition 2, pp.81–130, 2004. 
 
[14]  R.M. May, “Simple mathematical model with very complicated dynamics”,  
         Nature 261,  pp.459, 1976. 
 
[15] Boccaletti S., Kurths J., Osipov G., Valladares D., and Zhou C., “The 
synchronization of chaotic systems,” Phys. Rep., vol. 366, no. 1-2, pp.1–101, 
2002. 
 
[16] Li S., Gonzalo G., Li Z., and Wolfgang A. Halang “Analog Chaos-based Secure 
Communications and Cryptanalysis: A Brief Survey” 
 
[17] Wolfram, S. “Cryptography with cellular automata,” in Advances in Cryptology 
CRYPTO’85, Lecture Notes in Computer Science, vol. 218, pp.429–432, 1985. 
 
[18] Matthews, R. A. J. “On the derivation of a ‘chaotic’ encryption algorithm,” 
Cryptologia XIII, pp.29–42, 1989. 
 
[19] Berstein, G. M. & Lieberman, M. A. “Method and apparatus for generating 
secure random numbers using chaos,” US Patent No. 5007087, 1991. 
 
[20] Zhou, H. & Ling, X.  “Generating chaotic secure sequences with desired 
statistical properties and high security,” Int. J. Bifurc. Chaos 7,  pp.205–213, 
1997. 
 
 
92
[21] Lee, P.-H., Pei, S.-C. & Chen, Y.-Y. “Generating chaotic stream ciphers using 
chaotic systems,” Chinese J. Phys. 41, pp. 559–581, 2003. 
 
[22] Frey, D. R. “Chaotic digital encoding: An approach to secure communication,” 
IEEE Trans. Circuits Syst. II 40, pp. 660–666, 1993. 
 
[23] Zhou, H. & Ling, X. “Problems with the chaotic inverse system   encryption 
approach,” IEEE Trans. Circuits Syst. I 44,  pp.268–271, 1997. 
 
[24] Zhou, L.-H. & Feng, Z.-J. “A new idea of using one-dimensional PWL map in 
digital secure communications–dual-resolution approach,” IEEE Trans. Circuits 
Syst. II 47, pp.1107–1111, 2000. 
 
[25]  Kocarev, L., Jakimoski, G., Stojanovski, T. & Parlitz, U. “From chaotic maps to 
encryption schemes,” in Proc. IEEE Int. Symposium Circuits and Systems 
(ISCAS’98), vol. 4, pp.514–517, 1998. 
 
[26] Guo, D., Cheng, L. M. & Cheng, L. L. “A new symmetric probabilistic 
encryption scheme based on chaotic attractors of neural networks,” Applied 
Intelligence 10, pp.71–84, 1999. 
 
[27] Jakimoski, G. & Kocarev, L. “Chaos and cryptography: Block encryption ciphers 
based on chaotic maps,” IEEE Trans. Circuits Syst. I 48, pp.163–169, 2001. 
 
[28]  Papadimitriou, S., Bountis, T., Mavaroudi, S. & Bezerianos, A. “A probabilistic 
symmetric encryption scheme for very fast secure communications based on 
chaotic systems of difference equations,” Int. J. Bifurc. Chaos 11, pp.3107–
3115, 2001. 
 
[29]   Tang, G., Liao, X. & Chen, Y. “A novel method for designing S-boxes based on 
chaotic maps,” Chaos Solitons Fractals 23, pp.413–419, 2005. 
 
[30] Habutsu, T., Nishio, Y., Sasase, I. & Mori, S. “A secret key cryptosystem by 
iterating a chaotic map,” in Advances in Cryptology – EUROCRYPT’91, Lecture 
Notes in Computer Science, vol. 547, pp.127–140, 1991. 
 
 
93
[31] Fridrich, J. “Symmetric ciphers based on two-dimensional chaotic maps,” Int. J. 
Bifurc. Chaos 8, pp.1259–1284, 1998. 
 
[32] U´ıs, J., Ugalde, E. & Salazar, G.  “A cryptosystem based on cellular automata,” 
Chaos 8, pp.819–822, 1998. 
 
[33] Masuda, N. & Aihara, K. “Cryptosystems with discretized chaotic maps,” IEEE 
Trans. Circuits Syst.I  49, pp.28–40, 2002. 
 
[34] Wen J., Severa M., Zeng W., Maximilian H. Luttrell, and Jin W., “A format 
compliant configurable encryption framework for access control of multimedia.” 
In Proc. IEEE 4th Workshop on Multimedia Signal Processing (MMSP’2001), 
pp 435–440, 2001. 
 
[35] David S. Taubman and Michael W.M., “JPEG2000: Standard for interactive 
imaging.” Proceedings of the IEEE, 90(8), pp.1336–1357, 2002. 
 
[36] Benoıt M. Macq and Jean-Jacques Q., “Cryptology for digital TV broadcasting.” 
Proceedings of the IEEE, 83(6), pp.944–957, 1995. 
 
[37] Ali S.¸ Tosun A., and Wu-chi Feng. “Lightweight security mechanisms for 
wireless video transmission.” In Proc. IEEE Int. Conference on Information 
Technology: Coding and Computing, pp 157–161, 2001. 
 
[38]  Pareek N.K, Patidar V, Sud K.K. “Discrete chaotic cryptography using external 
key.” Phys Lett A 2003;309, pp.75-82, 2003. 
 
[39] Chen G, Mao YB, Chui CK. “A symmetric image encryption scheme based on 
3D chaotic cat maps.” Chaos, Solutions & Fractals 2004;12, pp.749-761, 2004. 
 
[40] Mao Y.B, Chen G, Lian S.G, “A novel fast image encryption scheme based on 
the 3D chaotic baker map.” Int. J. Bifurcat Chaos 2004;14(10), pp.3613-24, 
2004. 
 
[41] Guan ZH, Huang FJ, Guan WJ. “Chaos-based image encryption algorithm,” Phys 
Lett A 2005;346, pp.153-7, 2005. 
 
 
94
[42]  Lian SG, Sun J, Wang Z. “A block cipher based on a suitable use of chaotic 
standard map.” Chaos, Solitons and Fractals 2005;26(1), pp.117-29, 2005. 
 
[43] Li, S., Mou, X., Yang, B. L., Ji, Z. & Zhang, J. “Problems with a probabilistic 
encryption scheme based on chaotic systems,” Int. J. Bifurc. Chaos 13,  
pp.3063–3077, 2003. 
 
[44] Alvarez, G., Hern´andez, L., Montoya, F. & Mu˜noz, J. “Cryptanalysis of a novel 
cryptosystem based on chaotic oscillators and feedback inversion,” J. Sound 
Vibrat, pp.275, 423–430, 2004. 
 
[45] Cerm´ak, J.  “Digital generators of chaos,” Phys. Lett. A 214, pp.151–160, 1996. 
 
[46] Sang, T., Wang, R. & Yan, Y. “Perturbance-based algorithm to expand cycle 
length of chaotic key stream,” Electron. Lett. 34, pp.873–874, 1998. 
 
[47] Fog, A. “How to optimize for the Pentium family of microprocessors”, 2000 
[Online], Available: http://www.codingnow.com/2000/download/pentopt.htm. 
[Accessed: Sept. 13, 2008]. 
 
[48] Li, S. “Analyse and New Designs of Digital Chaotic Ciphers”, PhD thesis, 
School of Electronics and Information Engineering, Xi’an Jiaotong University, 
Xi’an, China, 2003, [online], available: http://www.hooklee.com/pub.html, 
[Accessed: June. 11, 2008]. 
 
[49] Menezes, A. J., van Oorschot, P. C. & Vanstone, S. A.  Handbook of Applied 
Cryptography, CRC Press, 1997. 
 
[50]  Wang, X., Zhan, M., Lai, C.-H. & Gang, H. “Error function attack of chaos 
synchronization based encryption schemes,” Chaos 14, pp.128–137, 2004. 
 
[51] ´Alvarez, G., Montoya, F., Romera, M. & Pastor, G. “Breaking parameter 
modulated chaotic secure communication system,” Chaos Solitons Fractals 21, 
pp.783–787, 2004. 
 
 
 
95
[52] Stinson, D. R. “Cryptography: Theory and Practice”, CRC Press, 1995. 
 
[53]  Beth, T., Lazic, D. E. & Mathias, A. “Cryptanalysis of cryptosystems based on 
remote chaos replication,” in Y. G. Desmedt, ed., Advances in Cryptology – 
CRYPTO’94, Lecture Notes in Computer Science, vol. 839, pp.318–331, 1994. 
 
[54] Sinha A., Singh K., “A technique for image encryption using digital signature”, 
Optics Communications, pp.1-6, 2003. 
 
[55] Maniccam S.S., Bourbakis N.G., “Lossless image compression and encryption 
using SCAN”, Pattern Recognition 34, pp.1229-1245, 2001. 
 
[56] Chin-Chen C., Min-Shian H., Tung-Shou C., “A new encryption algorithm for 
image cryptosystems”, The Journal of Systems and Software 58, pp.83-91, 2001. 
 
[57]  Jiun-In G., Jui-Cheng Y., “A new mirror-like image encryption algorithm and its 
VLSI architecture”, Department of Electronics Engineering National Lien-Ho 
College of Technology and Commerce. 
 
[58]  Zhang S. and Mohammed A.K., “Color image encryption using double random 
phase encoding”, MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / 
Vol. 21, No. 5, pp. 318-322, June 5 1999. 
 
[59] Young-Chang H., “Visual cryptography for colour images”, Pattern Recognition 
36, 2003, [online], Available: www.elsevier.com/locate/patcog, pp.1619-1629, 
[Accessed: Jan. 20, 2008]. 
 
[60] Kuo C.J. , “Novel image encryption technique and its application in progressive 
transmission.” J. Electron. Imaging 24, pp. 345–351, 1993. 
 
[61] Chang, H.K., Liou, J.L., “An image encryption scheme based on quad-tree 
compression scheme.” In: Proceedings of the International Computer 
Symposium, Taiwan, pp. 230–237, 1994. 
 
 
 
96
[62] Scharinger J., “Fast encryption of image data using chaotic Kolmogrov flow”, J. 
Electronic Eng 7 (2), pp. 318–325, 1998. 
 
[63] Hossam El-din H.A., Hamdy M. K., and Osama S. F.A, “Encryption Efficiency 
Analysis and Security Evaluation of RC6 Block Cipher for Digital Images” 
 
[64] Hossam El-din H. A, Hamdy M. K., and Osama S. F.A., “Encryption Quality 
Analysis of RC5 Block Cipher Algorithm for Digital Images.” Journal of 
Optical Engineering, vol. 45, 2006. 
 
[65] ElGamal T., "A Public-Key Cryptosystem and a Signature Scheme Based on 
Discrete Logarithms", IEEE Transactions on Information Theory, vol. IT-31, 
no.4, pp.469–472, 1985. 
 
[66] Schneier B., “Description of a New Variable-Length Key, 64-bit Block Cipher 
(Blowfish)”, Fast Software Encryption, pp. 191-204, 1993 
 
[67] Courtois N., Pieprzyk J., "Cryptanalysis of Block Ciphers with over defined 
Systems of Equations". pp267–287, ASIACRYPT 2002.  
 
[68] Rivest, R. L. "The RC5 Encryption Algorithm" Proceedings of the Second 
International Workshop on Fast Software Encryption (FSE) 1994e: 86–96.  
 
 
 
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