A New Block Cipher Based on Chaotic Tent Maps

TIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 49, NO. 12, DECEMBER 2002
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Jakimoski et al. [5] and the application of a chaotic piecewise-linear one-dimensional (1-D) map as a random number generator was analyzed by Stojanovski et al. [6] and [7]. Virtually, most of chaos-based software encryption techniques employ chaotic maps to generate a sequence of pseudorandom numbers, which are viewed as a one-time pad for encrypting messages. However, Wheeler et al. [8] and [9] pointed out that computer implementations of chaotic maps may exhibit surprisingly different behavior, e.g., very short cycles, depending on the particular numerical representation. In this brief, we propose a new chaotic block cipher at a higher level of security. In the new cipher, a sequence of decimal numbers generated by a chaotic tent map is used to determine not only 4n-b noise vectors by choosing two disjoint interval ranges representing 0 and 1 but also n permutations of 1, 2, 3, and 4 by looking up a table. Noise vectors and permutations are then alternately applied on 4n-b plaintexts to produce 4n-b ciphertexts (where n 16). The rest of the paper is arranged as follows. Section II describes the new block cipher; Section III performs security and performance analysis; Section IV discusses software implementation; Conclusions are drawn in Section V. II. DESCRIPTION OF NEW BLOCK CIPHER A. Preliminaries A chaotic tent map is a 1-D and piecewise-linear map as follows:
F : xi =
A New Block Cipher Based on Chaotic Tent Maps
Xun Yi, Chik How Tan, and Chee Kheong Siew, Member, IEEE
Abstract—In this paper, we come up with a new block cipher based on chaos obtained by iterating the simplest one-dimensional chaotic tent map. In the new cipher, the chaotic tent map is employed to generate noise vectors and permutations which are then alternately applied on 4 -b plaintexts to produce 4 -b ciphertexts (where 16). Index Terms—Chaotic tent map, cryptography, permutation, secure communication.
x
1
This map transforms an interval [0; 1] onto itself as shown in Fig. 1, and contains only one parameter . A sequence computed by iterating F from an arbitrary initial point in (0; 1) acts chaotically because the function F is expansionary everywhere in the interval (0; 1). Such a sequence distributes in uniform U (0; 1). B. A New Block Cipher The new block cipher operates on 4n-b plaintexts to produce 4n-b ciphertexts with four secret keys (where n 16). The basic design criterion of the new cipher is combining noise vectors and permutations to achieve a higher level of security. 1) Secret Keys: The new cipher requires both the sender and the receiver to share four secret parameters ( ; ; ; K ) (secret keys) in advance, where 0 < ; ; < 1, 6= , F ( ) 6= and K is 4n-b long. With and , one map G( ; ) can be obtained from F as follows: