Generating Chaotic Secure Sequences with Desired Statistical Properties and High Security

Abstract

This work proposes a class of one-dimensional analogue chaotic signals which have perfect statistical properties. A non-invertible transformation is introduced to generate a class of binary (symbolic) chaotic sequences with desired distribution function and correlation function. These binary chaotic secure sequences are proven to have near-ideal linear complexity and infinite large discrete correlation dimension, thus they cannot be reconstructed by linear-feedback shift-register (LFSR) techniques or nonlinear dynamics (NLD) forecasting in finite order.

Pseudo-random Bit Generator Based on Couple Chaotic Systems and Its Applications in Stream-Cipher Cryptography

“…Digital chaotic stream ciphers: Many different chaotic systems have been employed to generate pseudo-random keystream, 2-D Hénon attractor in [3], logistic map in [10], generalized logistic map in [6], quasi-chaotic nonlinear filter in [7], piecewise linear chaotic map in [4,5,8,19], and first-order nonuniformly sampling digital phase-locked loop (DPLL) circuits in [11]. In [12] multiple different chaotic maps are suggested, Bernoulli shift and logistic map are used for demonstration.…”

“…The algorithms generating chaotic pseudo-random keystreams can be divided into three classes: A1) -extracting from some bits of the chaotic orbits [4][5][6]12]; A2) -determining by which interval the chaotic orbits reach [3,8,10,11]; A3) -just equaling the chaotic orbits themselves [7]. It should be noticed that some algorithms in A2) [8,10,11] can be considered as the corresponding ones in A1), and A3) can be deemed as a special case of A1). Several chaotic stream ciphers [3,6,7] have been known not secure enough [20][21][22][23].…”

“…So r must be selected near 4.0 in these ciphers, which makes the key space much smaller. Other good candidates for simple realization are piecewise linear chaotic maps, such as tent map [13,18] and the ones used in [4,5,8,9,19]. But we must be very careful to use them since there exist some weaknesses for their piecewise linearity [24,25,34].…”

“…Generally speaking, there are two chief ways to design digital chaotic ciphers: 1) using chaotic systems to generate pseudo-random keystream to encrypt plaintext [3,[5][6][7][8][10][11][12]; 2) using plaintext and/or secret key as the initial conditions and/or control parameters, iterating/counter-iterating chaotic systems n times to obtain ciphertext [2,9,[13][14][15][16]. The first way corresponds to the stream ciphers and the second does to the block ciphers.…”

Chaotic Cryptographic Scheme Based on Composition Maps

“…There exist two main approaches of designing chaos-based cryptosystems: analog mode and digital mode. From 1989, along with the use of analog chaotic systems in the design of secure communication systems [Alvarez, 1999;Zhou and Ling, 1997;Lai et al, 1999;Memon, 2003;Parlitz et al, 1992;Chen et al, 2003], applications of computerized (also called digital) chaotic systems in cryptography have attracted more and more attention [Baptista, 1998;Hong and Xieting, 1997;Jakimoski and Kocarev, 2001;Masuda and Aihara, 2002;Matthews, 1989;Papadimitriou, 2001;Guan et al, 2005;Xiao et al, 2005;Tang et al, 2005;Huang and Guan, 2005]. This paper chiefly focuses on the digital chaotic ciphers.…”