The entropy source of pseudo random number generators: from low entropy to high entropy

The pseudo random number generators (PRNG) is one type of deterministic functions. The information entropy of the output sequences depends on the entropy of the input seeds. The output sequences can be predicted if attackers could know or control the input seeds of PRNGs. Against that, it is necessary that the input seeds is unpredictable, that is to say, the information entropy of the seeds is high enough. However, if there is no high enough entropy sources in environment, how to generate the seeds of PRNG? In other words, how to increase the entropy of the input seeds? Many approaches for extracting entropy from physical environment have been proposed, which lack of theoretical analysis. The condition of entropy’s increasing is given. A model is built to verify the condition based on the functional programming language F*. An example of entropy’s increasing is proposed utilizing execution time randomness of arbitrary codes. Then an algorithm is described, which can generate the seed when the entropy value is given.