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Impossibility of Strong KDM Security with Auxiliary Input

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 12238)

Abstract

We show that a strong notion of KDM security cannot be obtained by any encryption scheme in the auxiliary input setting, assuming Learning With Errors (LWE) and one-way permutations. The notion of security we deal with guarantees that for any (possibly inefficient) function f, it is computationally hard to distinguish between an encryption of \(\mathbf {0}\) and an encryption of \(f(\mathsf {pk}, z)\), where \(\mathsf {pk} \) is the public key and z is the auxiliary input. Furthermore, we show that this holds even when restricted to bounded-length auxiliary input where z is much shorter than \(\mathsf {pk} \) under the additional assumption that (non-leveled) fully homomorphic encryption exists.

Notes

Acknowledgements

This work was supported in part by NSF Award SATC-1704788, NSF Award RI-1703846, AFOSR Award FA9550-18-1-0267, and by NSF Award DGE-1650441. This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2019-19-020700006. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Cornell TechNew York CityUSA
  2. 2.NTT ResearchPalo AltoUSA

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