Sustainable pseudo-random number generator

Abstract

Barak and Halevi (BH) have proposed an efficient architecture for robust pseudorandom generators that ensure resilience in the presence of attackers with partial knowledge or partial controls of the generators’ entropy resources. The BH scheme is constructed from the Barak, Shaltiel and Tromer’s randomness extractor and its security is formalized in the simulation-based framework. The BH model however, does not address the scenario where an attacker completely controls the generators’ entropy resources with no knowledge of the internal state. Namely, the BH security model does not consider the security of bad-refresh conditioned on compromised = false. The security of such a case is interesting since if the output of the protocol conditioned on compromised = false looks random to the attacker, then the proposed scheme is secure even if the attacker completely controls entropy resources (recall that attackers with partial knowledge or partial controls of the generators’ entropy resources in the BH model). The BH scheme is called sustainable if the above mentioned security requirement is guaranteed. This paper studies the sustainability of the BH pseudorandom generator and makes the following two contributions: in the first fold, a new notion which we call sustainable pseudorandom generator which extends the security definition of the BH’s robust scheme is introduced and formalized in the simulation paradigm; in the second fold, we show that the BH’s robust scheme achieves the sustainability under the joint assumptions that the underlying stateless function G is a cryptographic pseudorandom number generator and the output of the underlying randomness extractor extract() is statistically close to the uniform distribution.