Paper 2013/286

Salvaging Indifferentiability in a Multi-stage Setting

Arno Mittelbach


The indifferentiability framework by Maurer, Renner and Holenstein (MRH; TCC 2004) formalizes a sufficient condition to safely replace a random oracle by a construction based on a (hopefully) weaker assumption such as an ideal cipher. Indeed, many indifferentiable hash functions have been constructed and could since be used in place of random oracles. Unfortunately, Ristenpart, Shacham, and Shrimpton (RSS; Eurocrypt 2011) discovered that for a large class of security notions, the MRH composition theorem actually does not apply. To bridge the gap they suggested a stronger notion called reset indifferentiability and established a generalized version of the MRH composition theorem. However, as recent works by Demay et al.~(Eurocrypt 2013) and Baecher et al.~(Asiacrypt 2013) brought to light, reset indifferentiability is not achievable thereby re-opening the quest for a notion that is sufficient for multi-stage games and achievable at the same time. We present a condition on multi-stage games that we call \emph{unsplittability}. We show that if a game is unsplittable for a hash construction then the MRH composition theorem can be salvaged. Unsplittability captures a restricted yet broad class of games together with a set of practical hash constructions including HMAC, NMAC and several Merkle-Damgård variants. We show unsplittability for the chosen distribution attack (CDA) game of Bellare et al. (Asiacrypt 2009), a multi-stage game capturing the security of deterministic encryption schemes; for message-locked encryption (Bellare et al.; Eurocrypt 2013) a related primitive that allows for secure deduplication; for universal computational extractors (UCE) (Bellare et al., Crypto 2013), a recently introduced standard model assumption to replace random oracles; as well as for the proof-of-storage game given by Ristenpart et al.~as a counterexample to the general applicability of the indifferentiability framework.

Note: Clarification on keyed constructions. Added reference to proceedings version.

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Publication info
A minor revision of an IACR publication in EUROCRYPT 2014
10.1007/978-3-642-55220-5 33
Hash functionsRandom oracleIndifferentiabilityMulti-stage
Contact author(s)
arno mittelbach @ cased de
2014-05-08: last of 2 revisions
2013-05-23: received
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      author = {Arno Mittelbach},
      title = {Salvaging Indifferentiability in a Multi-stage Setting},
      howpublished = {Cryptology ePrint Archive, Paper 2013/286},
      year = {2013},
      doi = {10.1007/978-3-642-55220-5 33},
      note = {\url{}},
      url = {}
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