Existing Results Sample Clauses

Existing Results. We consider a computationally unbounded, threshold ad- versary may have non-terminating runs, where the (usual) ex- pected running time will be infinite. Thus, our measure of ERT, also followed in [8, 7], is with respect to the ex- ecutions where the parties terminate (more on this later). Based on the above parameters, the best known ABA proto- cols are summarized in Table 1. Ref. Type Resilience CC ERT (R) [6] AST t < n/3 O(2n) O(2n) [12, 13] AST t < n/4 poly(n) O(1) [1] AST t < n/3 poly(n) O(n2) Table 1 Summary of the best known ABA protocols; poly(x) stands for polynomial in x and AST stands for almost-surely terminating. Adv, who can corrupt any t parties out of the n − − parties in a Byzantine1 fashion. It was shown in [23] that a BA (and an ABA) protocol tolerating Adv is possible if and only if t < n/3. Thus, an ABA protocol designed with exactly n = 3t + 1 parties is called an optimally-resilient ABA protocol. Xxxxxx, Xxxxx and Xxxxxxxx’x seminal im- possibility result on deterministic ABA protocols [14] im- plies that any (randomized) ABA protocol must have non- terminating runs, where some honest2 party(ies) may not output any value and thus may not terminate at all. An ABA protocol is called (1 s)-terminating [8, 7], if the honest par- ties terminate the protocol with probability3 at least (1 s), where s > 0. On the other hand, an ABA protocol is called almost-surely terminating [1], if the probability of the occur- rence of a non-terminating execution is asymptotically zero. The important parameters of an ABA protocol are: – Resilience: The maximum number of corruptions t, that the protocol can tolerate. – Communication Complexity (CC): The total number of bits communicated by the honest parties in the proto- col. The communication complexity has two parts: the private communication which is done over the point- to-point secure channels4 and the broadcast communi- cation which is done in order to send a message (pub- licly) to everyone. The broadcast primitive in the asyn- chronous setting is implemented using Bracha’s asyn- chronous broadcast protocol [6] (see Section 2.6). – Expected Running Time (ERT): We consider the ex- pected running time (ERT) R of an ABA protocol, con- ditioned on the event that all the (honest) parties termi- nate; this notion of expectancy is weaker than the usual notion of expectation, where the expectancy is over all possible events. An (1 − s)-terminating ABA protocol 1 A Byzantine corrupted party can behave in an...
Sample 1
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Existing Results. − − We consider a computationally unbounded threshold adver- xxxx Xxx, who can corrupt any t parties out of the n par- ties in a Byzantine1 fashion. From [26], a BA (and hence an ABA) protocol tolerating Adv is possible if and only if t < n/3. Thus, an ABA protocol designed with exactly n = 3t + 1 parties is called an optimally resilient proto- col. Xxxxxx, Xxxxx and Xxxxxxxx’x impossibility result on de- terministic ABA protocols [17] implies that any (random- ized) ABA protocol must have non-terminating runs, where some honest party(ies) may not output any value and thus may not terminate at all. An ABA protocol is called (1 ϵ)- terminating [9, 8]), if the honest parties terminate the pro- tocol with probability2 at least (1 ϵ), where ϵ > 0. On the other hand, an ABA protocol is called almost-surely ter- minating [1], if the probability of the occurrence of a non- terminating execution is asymptotically zero. The important parameters of an ABA protocol are: – Resilience: it is the maximum number of corruptions (t) that the protocol can tolerate. – Communication Complexity (CC): it is the total number of bits communicated by the honest parties in the proto- col. The communication complexity has two parts: the
Sample 1

Related to Existing Results

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  • - OWNERSHIP/USE OF THE RESULTS II.3.1 Unless stipulated otherwise in this agreement, ownership of the results of the action, including industrial and intellectual property rights, and of the reports and other documents relating to it shall be vested in the beneficiary.

  • Evaluation Results A. Evaluation results shall be used:

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