Black-box composition does not imply adaptive security

Abstract

In trying to provide formal evidence that composition has security increasing properties, we ask if the composition of non-adaptively secure permutation generators necessarily produces adaptively secure generators. We show the existence of oracles relative to which there are non-adaptively secure permutation generators, but where the composition of such generators fail to achieve security against adaptive adversaries. Thus, any proof of security for such a construction would need to be non-relativizing. This result can be used to partially justify the lack of formal evidence we have that composition increases security, even though it is a belief shared by many cryptographers. © International Association for Cryptologic Research 2004.