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In trying to provide formal evidence that composition has se- curity 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 composi- tion of such generators fail to achieve security against adaptive adver- saries. 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.

Black-Box Composition Does Not Imply Adaptive Security