Cryptology ePrint Archive: Report 2013/286
Salvaging Indifferentiability in a Multi-stage Setting
Arno Mittelbach
Abstract: 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.
Category / Keywords: foundations / Hash functions, Random oracle, Indifferentiability, Multi-stage
Original Publication (with minor differences): IACR-EUROCRYPT-2014
DOI: 10.1007/978-3-642-55220-5 33
Date: received 15 May 2013, last revised 8 May 2014
Contact author: arno mittelbach at cased de
Available format(s): PDF | BibTeX Citation
Note: Clarification on keyed constructions. Added reference to proceedings version.
Version: 20140508:122922 (All versions of this report)
Short URL: ia.cr/2013/286
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