Abstract
We revisit the impossibility of a variety of cryptographic tasks including privacy and differential privacy with imperfect randomness. For traditional notions of privacy, such as security of encryption, commitment or secret sharing schemes, dramatic impossibility results are known [MP90, DOPS04] for several concrete sources \(\mathcal {R}\), including a (seemingly) very “nice and friendly” Santha-Vazirani (SV) source. Somewhat surprisingly, Dodis et al. [DLMV12] showed that non-trivial differential privacy is possible with the SV sources. This suggested a qualitative gap between traditional and differential privacy, and left open the question of whether differential privacy is possible with more realistic (i.e., less structured) sources than the SV sources.
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