On the (Im)Possibility of Key Dependent Encryption

  • Authors:
  • Iftach Haitner;Thomas Holenstein

  • Affiliations:
  • Microsoft Research,;Department of Computer Science, Princeton University,

  • Venue:
  • TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
  • Year:
  • 2009

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Abstract

We study the possibility of constructing encryption schemes secure under messages that are chosen depending on the key k of the encryption scheme itself. We give the following separation results that hold both in the private and in the public key settings: Let $\mathcal{H}$ be the family of poly(n )-wise independent hash-functions. There exists no fully-black-box reduction from an encryption scheme secure against key-dependent messages to one-way permutations (and also to families of trapdoor permutations) if the adversary can obtain encryptions of h (k ) for $h \in \mathcal{H}$. There exists no reduction from an encryption scheme secure against key-dependent messages to, essentially, any cryptographic assumption, if the adversary can obtain an encryption of g (k ) for an arbitrary g , as long as the reduction's proof of security treats both the adversary and the function g as black boxes.