Paper 2012/435

Differential Privacy with Imperfect Randomness

Yevgeniy Dodis, Adriana Lopez-Alt, Ilya Mironov, and Salil Vadhan


In this work we revisit the question of basing cryptography on imperfect randomness. Bosley and Dodis (TCC'07) showed that if a source of randomness R is "good enough" to generate a secret key capable of encrypting k bits, then one can deterministically extract nearly k almost uniform bits from R, suggesting that traditional privacy notions (namely, indistinguishability of encryption) requires an "extractable" source of randomness. Other, even stronger impossibility results are known for achieving privacy under specific "non-extractable" sources of randomness, such as the gamma-Santha-Vazirani (SV) source, where each next bit has fresh entropy, but is allowed to have a small bias gamma< 1$ (possibly depending on prior bits). We ask whether similar negative results also hold for a more recent notion of privacy called differential privacy (Dwork et al., TCC'06), concentrating, in particular, on achieving differential privacy with the Santha-Vazirani source. We show that the answer is no. Specifically, we give a differentially private mechanism for approximating arbitrary "low sensitivity" functions that works even with randomness coming from a gamma-Santha-Vazirani source, for any gamma<1. This provides a somewhat surprising "separation" between traditional privacy and differential privacy with respect to imperfect randomness. Interestingly, the design of our mechanism is quite different from the traditional "additive-noise" mechanisms (e.g., Laplace mechanism) successfully utilized to achieve differential privacy with perfect randomness. Indeed, we show that any (accurate and private) "SV-robust" mechanism for our problem requires a demanding property called consistent sampling, which is strictly stronger than differential privacy, and cannot be satisfied by any additive-noise mechanism.

Available format(s)
Publication info
Published elsewhere. An extended abstract of this work appears in the proceedings of CRYPTO 2012. This is the full version.
Contact author(s)
lopez @ cs nyu edu
2012-08-05: received
Short URL
Creative Commons Attribution


      author = {Yevgeniy Dodis and Adriana Lopez-Alt and Ilya Mironov and Salil Vadhan},
      title = {Differential Privacy with Imperfect Randomness},
      howpublished = {Cryptology ePrint Archive, Paper 2012/435},
      year = {2012},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.