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Cryptography using multiple one-dimensional chaotic maps. (English) Zbl 1075.68027
Summary: Recently, the authors [Phys. Lett., A 309, 75--82 (2003; Zbl 1010.68063)] have developed a symmetric key block cipher algorithm using a one-dimensional chaotic map. In this paper, we propose a symmetric key block cipher algorithm in which multiple one-dimensional chaotic maps are used instead of a one-dimensional chaotic map. However, we also use an external secret key of variable length (maximum 128-bits) as used by Pareek et al. In the present cryptosystem, plaintext is divided into groups of variable length (i.e. number of blocks in each group is different) and these are encrypted sequentially by using randomly chosen chaotic map from a set of chaotic maps. For block-by-block encryption of variable length group, number of iterations and initial condition for the chaotic maps depend on the randomly chosen session key and encryption of previous block of plaintext, respectively. The whole process of encryption/decryption is governed by two dynamic tables, which are updated time to time during the encryption/decryption process. Simulation results show that the proposed cryptosystem requires less time to encrypt the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having flat distribution of same size as the plaintext.

68P25Data encryption
Full Text: DOI
[1] Schneier, B.: Applied cryptography: protocols, algorithms and source code in C. (1996) · Zbl 0853.94001
[2] Menezes, A. J.; Oorschot, P. C. V.; Vanstone, S. A.: Handbook of applied cryptography. (1997) · Zbl 0868.94001
[3] Matthews, R. A. J.: On the derivation of a chaotic encryption algorithm. Cryptologia 12, No. 1, 29-42 (1989)
[4] Habutsu, T.; Nishio, Y.; Sasase, I.; Mori, S.: A secret key cryptosystem by iterating a chaotic map. Advances in cryptology-EUROCRYPT’91, 127-140 (1991) · Zbl 0766.94011
[5] Kotulski, Z.; Szczepanski, J.: Discrete chaotic cryptography. Ann. phys. 6, No. 5, 381-394 (1997) · Zbl 0899.94007
[6] Baptista, M. S.: Cryptography with chaos. Phys. lett. A 240, No. 1--2, 50-54 (1998) · Zbl 0936.94013
[7] Kotulski, Z.; Szczepanski, J.; Górski, K.; Paszkiewicz, A.; Zugaj, A.: Application of discrete chaotic dynamical systems in cryptography----DCC method. Int. J. Bifurcat. chaos 9, 1121-1135 (1999) · Zbl 1089.94505
[8] Alvarez, E.; Fernández, A.; Garciá, P.; Jiménez, J.; Marcano, A.: New approach to chaotic encryption. Phys. lett. A 263, 373-375 (1999)
[9] Wong, W. K.; Lee, L. P.; Wong, K. W.: A modified chaotic cryptographic method. Comput. phys. Commun. 138, 234-236 (2000) · Zbl 0987.94033
[10] Wong, K. W.: A fast chaotic cryptography scheme with dynamic look-up table. Phys. lett. A 298, 238-242 (2002) · Zbl 0995.94029
[11] Wong, K. W.; Ho, S. W.; Yung, C. K.: A chaotic cryptography scheme for generating short ciphertext. Phys. lett. A 310, 67-73 (2003) · Zbl 1011.94013
[12] Pareek, N. K.; Patidar, V.; Sud, K. K.: Discrete chaotic cryptography using external key. Phys. lett. A 309, 75-82 (2003) · Zbl 1010.68063