1 Before this work, the second class of
2 chaos-based PRNG $\textit{CIPRNG}_f^2$ was robust against
3 batteries of statistical tests and was abusively said to be chaotic.
4 This work has formally established the proof that
5 the $\textit{CIPRNG}_f^2$ is chaotic according to the Devaney
6 definition for some well-chosen functions $f$.
7 The chaos condition is expressed as a necessary and sufficient condition
8 on a graph of iterations: this one has to be strongly connected.
10 It has thus bridged the gap between the need of true chaos for some
11 applications and the practical efficiency.
12 In a future work, we plan to study sufficient conditions on $f$ to
15 and to study computed functions in the perspective
16 of mixing time to improve their practical efficiency.
