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Journal of Cryptology

Concurrent Composition of Secure Protocols in the Timing Model

Yael Tauman Kalai, Yehuda Lindell, Manoj Prabhakaran

Published Oct 1, 2007• 25 citations
Publisher
DOI
10.1007/s00145-007-0567-1

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Concurrent Composition of Secure Protocols in the Timing Model.

Yael Tauman Kalai, Yehuda Lindell, Manoj Prabhakaran

In the setting of secure multiparty computation, a set of mutually distrustful parties wish to securely compute some joint function of their inputs. In the stand-alone case, it has been shown that every efficient function can be securely computed. However, in the setting of concurrent composition, broad impossibility results have been proven for the case of no honest majority and no trusted setup phase. These results hold both for the case of general composition (where a secure protocol is run many times concurrently with arbitrary other protocols) and self composition (where a single secure protocol is run many times concurrently). In this paper, we investigate the feasibility of obtaining security in the concurrent setting, assuming that each party has a local clock and that these clocks proceed at approximately the same rate. We show that under this mild timing assumption, it is possible to securely compute any multiparty functionality under concurrent self composition. Loosely speaking, we also show that it is possible to securely compute any multiparty functionality under concurrent general composition, as long as the secure protocol is run only with protocols whose messages are delayed by a specified amount of time. On the negative side, we show that it is impossible to achieve security under concurrent general composition with no restrictions whatsoever on the network (like the aforementioned delays), even in the timing model.

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Lower Bounds and Impossibility Results for Concurrent Self Composition.

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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.

•Jan 1, 2004•0 citations

Concurrent general composition of secure protocols in the timing model

Yael Tauman Kalai, Yehuda Lindell, Manoj Prabhakaran

In the setting of secure multiparty computation, a set of mutually distrustful parties wish to jointly compute some function of their input (i.e., they wish to securely carry out some distributed task). %The joint computation should be such that even In the stand-alone case, it has been shown that every efficient function can be securely computed. However, in the setting of concurrent composition, broad impossibility results have been proven for the case where there is no honest majority (or trusted setup).In this paper, we investigate the feasibility of obtaining secure multiparty protocols in a network where certain time bounds are assumed. Specifically, the security of our protocols rely on the very reasonable assumption that local clocks do not "drift" too much (i.e., it is assumed that they proceed at approximately the same rate). We show that under this mild timing assumption, it is possible to securely compute any functionality under concurrent general composition (as long as messages from the arbitrary other protocols are delayed for a specified amount of time).

ACM Symposium on Theory of Computing (STOC)•May 22, 2005•45 citations
In the setting of secure multiparty computation, a set of mutually distrustful parties wish to securely compute some joint function of their inputs. In the stand-alone case, it has been shown that every efficient function can be securely computed. However, in the setting of concurrent composition, broad impossibility results have been proven for the case of no honest majority and no trusted setup phase. These results hold both for the case of general composition (where a secure protocol is run many times concurrently with arbitrary other protocols) and self composition (where a single secure protocol is run many times concurrently). In this paper, we investigate the feasibility of obtaining security in the concurrent setting, assuming that each party has a local clock and that these clocks proceed at approximately the same rate. We show that under this mild timing assumption, it is possible to securely compute any multiparty functionality under concurrent self composition. Loosely speaking, we also show that it is possible to securely compute any multiparty functionality under concurrent general composition, as long as the secure protocol is run only with protocols whose messages are delayed by a specified amount of time. On the negative side, we show that it is impossible to achieve security under concurrent general composition with no restrictions whatsoever on the network (like the aforementioned delays), even in the timing model.
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.
In the setting of secure multiparty computation, a set of mutually distrustful parties wish to jointly compute some function of their input (i.e., they wish to securely carry out some distributed task). %The joint computation should be such that even In the stand-alone case, it has been shown that every efficient function can be securely computed. However, in the setting of concurrent composition, broad impossibility results have been proven for the case where there is no honest majority (or trusted setup).In this paper, we investigate the feasibility of obtaining secure multiparty protocols in a network where certain time bounds are assumed. Specifically, the security of our protocols rely on the very reasonable assumption that local clocks do not "drift" too much (i.e., it is assumed that they proceed at approximately the same rate). We show that under this mild timing assumption, it is possible to securely compute any functionality under concurrent general composition (as long as messages from the arbitrary other protocols are delayed for a specified amount of time).