A Probabilistic Symmetric Encryption Scheme for Very Fast Secure Communication Based on Chaotic Systems of Difference Equations

Abstract

We present a new probabilistic symmetric key encryption scheme based on the chaotic dynamics of properly designed chaotic systems. This technique exploits the concept of virtual attractors, which are not real attractors of the underlying chaotic dynamics but are created and maintained artificially. Each virtual attractor represents a symbol of the alphabet used to encode messages. The state space is partitioned over the virtual attractors creating clusters of states. The enciphering process randomizes over the set of states mapped to a virtual attractor in order to construct the ciphertext for the transmited symbol. The receiver can reconstruct perfectly this virtual state space, given the possession of the same chaotic system of difference equations with parameters tuned perfectly to those of the transmitter. Therefore, from the ciphertext chunk corresponding to a state, the virtual attractor can be derived from the details of the virtual state space. The knowledge of the virtual attractor leads to the recovery of the transmitted symbol.We demonstrate that the new algorithm is secure, reliable and very fast. It uses discrete time chaotic recurrent systems and is simple, flexible and modular. These systems can be constructed easily dynamically from an alphanumeric encryption key. The cryptographic security of the algorithm is evaluated with combinatorial arguments. † The implementation of the presented chaotic encryption algorithms in C++ as well as the paper document are available upon request to the

On the Dynamical Degradation of Digital Piecewise Linear Chaotic Maps

“…1D PWLCM have been widely used to construct digital chaotic ciphers [Alvarez et al, 1999;García & Jiménez, 2002;Habutsu et al, 1990Habutsu et al, , 1991Jessa, 2000Jessa, , 2002Li et al, 2001bLi et al, ,c, 2002Masuda & Aihara, 2001, 2002aPapadimitriou et al, 2001;Protopopescu et al, 1995;Sang et al, 1998a,b;Yi et al, 2002;Zhou, 1996;Zhou & Ling, 1997a,c;Zhou et al, ,b, 1998Zhou & Feng, 2000]. The theoretical results about the proposed dynamical indicators P 1 ∼ P n of digital 1D PWLCM will be very useful for the design and performance analyses of such chaotic ciphers.…”

Selection of chaotic states in cryptosystem based on chaos with differential analysis

“…The design of cryptographic algorithm may be simplified with the help of chaotic system since it becomes unnecessary to compose sophisticated structure such as S-box, Feistel and so on to achieve diffusion & confusion performances. As a result, a number of encrypting scheme [1][2][3][4][5][6][7][8][9] based on chaos have been proposed since 1989.…”

“…Recently, many novel ideas of chaotic encryption [1][2][3][4][5][6][7][8][9] have already appeared in the literature, but most of them were cracked soon after publication. Though ref.…”

Cryptanalyzing a nonlinear chaotic algorithm (NCA) for image encryption

“…There are two main approaches to the design of chaotic cryptosystems: analog and digital. This paper is concerned with the latter, digital chaotic ciphers, which are designed for digital computers: in general, one or more chaotic maps are implemented in finite computing precision to encrypt the plain-message in a number of ways [8,9,10,11,12,13,14,15,16,17,18,19,20]. Also, a number of chaotic ciphers were specially designed for the encryption of digital images and videos [21,Sec.…”