# IMAGE CRYPTOSYSTEM BASED ON CHAOTIC MAP AND CONTINUED FRACTIONS

Recently, a variety of chaos-based cryptosystems have been proposed. Some of these novel chaotic encryption schemes are not very suitable for image encryption due to their density function which is not uniformly distributed or due to their small key space. In this paper, we propose a new scheme for image encryption based on the use of a chaotic map with large key space and Engle Continued Fractions (ECF) map. The ECF-map is employed to generate a pseudo random sequence which satisﬁes uniform distribution, zero cocorrelation and ideal nonlinearity to achieve higher level of security. The proposed scheme is resistant to the known attacks. Theoretic and numerical simulation analyses indicate that our scheme is efﬁcient and satisﬁes high security.

Recently, cryptographic algorithms based on chaos systems [11, 24, 22, 23, 25] have been proposed with good cryptographic properties. Chaos systems have many important features such ergodicity, sensitivity to initial conditions, sensitivity to control parameters and randomness [9]. These features are very important in cryptography and they have suggested some new and efﬁcient ways to develop encryption algorithms for secure digital image transmission over the Internet and through public networks. In addition, a chaotic system would have a large key space, for resistance to bruteforce attacks, and generates sequence with an uniform invariant density function for resistance to statistic attacks. The problem is not all chaotic systems can satisfy these characteristics [10, 21]. For example, the logistic map is widely used to design chaotic system. The known 1-Dimensional logistic map is deﬁned as xn+1 = l xn(1 xn) where l 2 [0; 4] and proposed a new chaotic encryption scheme based on randomized arithmetic coding using the logistic map as the pseudo random bit generator. In proposed a new block cipher based on the use of logistic map in the diffusion process. In [7], Kanso et al. proposed a new cipher based on logistic maps for generating two pseudo random binary sequences. The logistic map is weak in security because it does not satisfy uniform distribution property and it has a small key space [1, 2]. Recently, a new chaos-based image cryptosystems using piecewise linear chaotic map (PWLCM) has been proposed. The PWLCM is a chaotic map which depends on the computing precision, and its phase space includes a linear structure. Although a PWLCM has a non uniform distribution in ﬁ- nite computing precision and has weak security. In , Li et al. demonstrated that the chaotic encryption scheme proposed by which is based on a kind of computerized PWLCM realized in ﬁnite computing precision is not secure enough from strict cryptographic viewpoint. Thus, ﬁnd a secure and efﬁcient cryptosystem motivates us to propose a new scheme which consists of using the standard map with large key space and the Engle Continued Fractions (ECF) map. The use of ECF-map increases the complexity of a cryptosystem based only on one chaotic system and thus makes difﬁculties in extraction of information about it . In addition, ECF-map conserves the cryptography properties of the chaotic system; like sensibility to initial conditions and control parameters non periodicity and randomness; and add interesting statistical properties such uniform distribution density function and zero co-correlation

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