The analysis consists in evaluating the randomness level of the sequences generated by the PRBG.
One can remark that, for the proposed PRBG, all the tested sequences pass successfully the NIST tests.
For more sensitivity, one must choose very different seed values, which reduces considerably the key space and then the security of the PRBG.
Another important aspect for any PRBG is the execution time of the algorithm.
Some points related to the security of the PRBG are discussed here, such as: the size of the seed space, the period length of the logistic map and some basic-known attacks (brute-force attack and differential attack).
A robust PRBG should have a large key space, to allow a large choice for the pseudo-random number generation.
The period length is a fundamental indicator of any PRBG.
Therefore, the binary32 format is not appropriate and must be avoided, when implementing a PRBG with such logistic map.
The best way to avoid the problem of short period and use efficiently this PRBG, is to generate pseudo-random bit sequences of only small sizes.
Thus, we consider that the proposed PRBG should resist to the differential cryptanalysis.
The assets of the PRBG are: the simplicity of implementation, a high randomness level for outputs, a high sensitivity related to the initial seeds and a fast execution time, allowing to use the algorithm even in real-time applications.