We exhibit a hash-based storage auditing scheme which is provably secure in the random-oracle model (ROM), but easily broken when one instead uses typical indifferentiable hash constructions. This contradicts the widely accepted belief that the indifferentiability composition theorem applies to any cryptosystem. We characterize the uncovered limitation of the indifferentiability framework by showing that the formalizations used thus far implicitly exclude security notions captured by experiments that have multiple, disjoint adversarial stages. Examples include deterministic public-key encryption (PKE), password-based cryptography, hash function nonmalleability, key-dependent message security, and more. We formalize a stronger notion, reset indifferentiability, that enables an indifferentiabilitystyle composition theorem covering such multi-stage security notions, but then show that practical hash constructions cannot be reset indifferentiable. We discuss how these limitations also affect the universal composability framework. We finish by showing the chosen-distribution attack security (which requires a multi-stage game) of some important public-key encryption schemes built using a hash construction paradigm introduced by Dodis, Ristenpart, and Shrimpton.
['Thomas Ristenpart', 'Hovav Shacham', 'Thomas Shrimpton']
Careful with Composition: Limitations of Indifferentiability and Universal Composability