Salvaging Indifferentiability in a Multi-stage Setting

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8441)


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 called 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 (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.


Hash Function Random Oracle Compression Function Random Oracle Model Composition Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  1. 1.Darmstadt University of TechnologyGermany

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