Cryptography with chaotic mixing

We propose a cryptosystem based on one-dimensional chaotic maps of the form Hp(x)=rp-1∘G∘rp(x) defined in the interval [0, 10p) for a positive integer parameter p, where G(x)=10x(mod10) and rp(x)=xp, which is a topological conjugacy between G and the shift map σ on the space Σ of the sequences with 10 symbols. There are three advantages in comparison with the recently proposed cryptosystem based on chaotic logistic maps Fμ(x)=μx(1-x) with 3 < μ ⩽ 4: (a) Hp is always chaotic for all parameters p, (b) the knowledge of an ergodic measure allows assignments of the alphabetic symbols to equiprobable sites of Hp's domain and (c) for each p, the security of the cryptosystem is manageable against brute force attacks.