This paper completes recent results obtained by extending the running-key cipher procedure from
natural language to applications over chaotic systems. We apply the new running-key approach on the
chaotic tent map and prove its utility in obtaining practically zero-redundant pseudo-random number
generators, alongside with the possibility to consider the initial condition and the tent map control
parameter as elements in the secret key – a desideratum in chaos-based cryptography. The results are
both theoretically and experimentally supported by combining concepts from information theory and
statistical methods in the context of the chaotic system. The statistical evaluation includes NIST test
suite for testing the randomness of the proposed binary generator. Based upon the results presented in
this paper, the provided generator can be used for designing new cryptosystems where the pseudo
random binary sequences can be a chief support.