International Association
for Cryptologic Research

Ristenpart, Shacham and Shrimpton (Eurocrypt 2011) recently presented schemes which are provably secure in the random-oracle model (ROM),

but easily broken if the random oracle is replaced by typical indifferentiable hash constructions such as chop-MD or prefix-free-MD.

They found that the indifferentiability framework, due to Maurer, Renner and Holenstein (TCC 2004), does not

necessarily allow composition in multi-stage settings, that is, settings consisting of multiple disjoint adversarial stages. On the positive

side, they prove that the non-adaptive chosen distribution attack (CDA) game of Bellare et al.~(Asiacrypt 2009), a multi-stage game capturing the security of deterministic encryption schemes,

remains secure if the random oracle is implemented by an NMAC-like hash function.

In this paper we introduce a framework to work with the indifferentiability notion in multi-stage scenarios. For this we provide

a model for iterative hash functions which is general enough to cover not only NMAC-like functions, but also functions such as chop-MD

or even hash trees. We go on to define a property on multi-stage games called \\emph{unsplittability} which intuitively captures that

adversaries cannot split the computation of a single hash value over several stages. We present a composition theorem for

unsplittable multi-stage games which generalizes the single-stage composition theorem for indifferentiable hash functions. We then show that

the CDA game (adaptive or non-adaptive) is unsplittable for \\emph{any} iterative hash function (thereby extending the preliminary results

by Ristenpart et al.). Finally, we prove that the \\emph{proof-of-storage} game presented by Ristenpart et al.~as a counterexample to

the general applicability of the indifferentiability framework is unsplittable for any multi-round iterative hash function, such as

Liskov\'s Zipper Hash (SAC~2006).