Cryptography with chaotic mixing

We propose a cryptosystem based on one-dimensional chaotic maps of the form H-p(x) = r(-1) o G o r(p)(x) defined in the interval [0, 10(P)) for a positive integer parameter p, where G(x) = 10x(mod 10) and r(p)(x) = p root x, which is a topological conjugacy between G and the shift map sigma on the space Sigma of the sequences with 10 symbols. There are three advantages in comparison with the recently proposed cryptosystern based on chaotic logistic maps F-mu (x) = mu x(1 - x) with 3 < mu <= 4: (a) H-p is always chaotic for all parameters p, (b) the knowledge of an ergodic measure allows assignments of the alphabetic symbols to equiprobable sites of H-p's domain and (c) for each p, the security of the cryptosystern is manageable against brute force attacks. (C) 2006 Elsevier Ltd. All rights reserved.