  In this work, Pseudo-Random Bit Generation (PRBG) based on 2D chaotic
mappings of logistic type is considered. The sequences generated with two
Pseudorandom Bit Generators (PRBGs) of this type are statistically tested and
the computational effectiveness of the generators is estimated. The role played
by the symmetry and the geometrical properties of the underlying chaotic
attractors is also explored. Considering these PRBGs valid for cryptography,
the size of the available key spaces are calculated. Additionally, a novel
mechanism called 'symmetry-swap' is introduced in order to enhance the PRBG
algorithm. It is shown that it can increase the degrees of freedom of the key
space, while maintaining the speed and performance in the PRBG.
