New Impossibility Results for Concurrent Composition and a Non-interactive Completeness Theorem for Secure Computation

We consider the

client-server

setting for the concurrent composition of secure protocols: in this setting, a single server interacts with multiple clients concurrently, executing with each client a specified protocol where only the client should receive any nontrivial output. Such a setting is easily motivated from an application standpoint. There are important special cases for which positive results are known – such as concurrent zero knowledge protocols – and it has been an open question whether other natural functionalities such as Oblivious Transfer (OT) are possible in this setting.

In this work:

We resolve this open question by showing that unfortunately, even in this very limited concurrency setting,

broad new impossibility results

hold, ruling out not only OT, but in fact all nontrivial finite asymmetric functionalities. Our new negative results hold even if the inputs of all honest parties are fixed in advance, and the adversary receives no auxiliary information.

Along the way, we establish a new

unconditional completeness result

for asymmetric functionalities, where we characterize functionalities that are

non-interactively complete

secure against active adversaries. When we say that a functionality

$\mathcal{F}$

is non-interactively complete, we mean that every other asymmetric functionality can be realized by parallel invocations of several copies of

$\mathcal{F}$

, with no other communication in any direction. Our result subsumes a completeness result of Kilian [STOC’00] that uses protocols which require additional interaction in both directions.