## Cryptology ePrint Archive: Report 2012/644

Impossibility Results for Indifferentiability with Resets

Atul Luykx and Elena Andreeva and Bart Mennink and Bart Preneel

Abstract: The indifferentiability framework of Maurer, Renner, and Holenstein (MRH) has gained immense popularity in recent years and has proved to be a powerful way to argue security of cryptosystems that enjoy proofs in the random oracle model. Recently, however, Ristenpart, Shacham, and Shrimpton (RSS) showed that the composition theorem of MRH has a more limited scope than originally thought, and that extending its scope required the introduction of reset-indifferentiability, a notion which no practical domain extenders satisfy with respect to random oracles.

In light of the results of RSS, we set out to rigorously tackle the specifics of indifferentiability and reset-indifferentiability by viewing the notions as special cases of a more general definition. Our contributions are twofold. Firstly, we provide the necessary formalism to refine the notion of indifferentiability regarding composition. By formalizing the definition of stage minimal games we expose new notions lying in between regular indifferentiability (MRH) and reset-indifferentiability (RSS).

Secondly, we answer the open problem of RSS by showing that it is impossible to build any domain extender which is reset-indifferentiable from a random oracle. This result formally confirms the intuition that reset-indifferentiability is too strong of a notion to be satisfied by any hash function. As a consequence we look at the weaker notion of single-reset-indifferentiability, yet there as well we demonstrate that there are no meaningful'' domain extenders which satisfy this notion. Not all is lost though, as we also view indifferentiability in a more general setting and point out the possibility for different variants of indifferentiability.

Category / Keywords: foundations / indifferentiability, reset-indifferentiability, random oracle, hash functions