A pseudo-random number generator is a deterministic algorithm that produces numbers whose distribution is indistinguishable from uniform. A formal security model for pseudo-random number generator with input was proposed in 2005 by Barak and Halevi. This model involves an internal state that is refreshed with a (potentially biased) external random source, and a cryptographic function that outputs random numbers from the internal state. We briefly discuss the Barak-Halevi model and its extension proposed in 2013 by Dodis, Pointcheval, Ruhault, Wichs and Vergnaud to include a new security property capturing how a pseudo-random number generator should accumulate the entropy of the input data into the internal state. This property states that a pseudo-random number generator with input should be able to eventually recover from compromise even if the entropy is injected into the system at a very slow pace, and expresses the real-life expected behavior of existing designs. We also outline some variants of this model that were proposed recently.
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