Lower Bounds for Concurrent Self Composition

Yehuda Lindell

Dennis Hofheinz, Dominique Unruh

Andrew Y. Lindell

Yehuda Lindell

In the setting of concurrent self composition, a single protocol is executed many times concurrently by a single set of parties. In this paper, we prove lower bounds and impossibility results for secure protocols in this setting. First and foremost, we prove that there exist large classes of functionalities that cannot be securely computed under concurrent self composition, by any protocol. We also prove a communication complexity lower bound on protocols that securely compute a large class of functionalities in this setting. Specifically, we show that any protocol that computes a functionality from this class and remains secure for m concurrent executions, must have bandwidth of at least m bits. The above results are unconditional and hold for any type of simulation (i.e., even for non-black-box simulation). In addition, we prove a severe lower bound on protocols that are proven secure using black-box simulation. Specifically, we show that any protocol that computes the blind signature or oblivious transfer functionalities and remains secure for m concurrent executions, where security is proven via black-box simulation, must have at least m rounds of communication. Our results hold for the plain model, where no trusted setup phase is assumed. While proving our impossibility results, we also show that for many functionalities, security under concurrent self composition (where a single secure protocol is run many times) is actually equivalent to the seemingly more stringent requirement of security under concurrent general composition (where a secure protocol is run concurrently with other arbitrary protocols). This observation has significance beyond the impossibility results that are derived by it for concurrent self composition.

Jing Wang, Ming Li, Hongfang Li +2 more

Yehuda Lindell

Until recently, most research on the topic of secure computation focused on the stand-alone model, where a single protocol execution takes place. In this paper, we construct protocols for the setting of bounded-concurrent self composition, where a (single) secure protocol is run many times concurrently, and there is a predetermined bound on the number of concurrent executions. In short, we show that any two-party functionality can be securely computed under boundedconcurrent self composition, in the plain model (where the only setup assumption made is that the parties communicate via authenticated channels). Our protocol provides the first feasibility result for general two-party computation in the plain model, for any model of concurrency. All previous protocols assumed a trusted setup phase in order to obtain a common reference string. On the downside, the number of rounds of communication in our protocol is super-linear in the bound on the number of concurrent executions. However, we believe that our constructions will lead to more efficient protocols for this task.