Abstrakt | 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 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-Damg˚ard 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 messagelocked 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. |
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