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by Matthew Franklin, Juan A. Garay, Moti Yung
http://www.bell-labs.com/user/garay/self-test.ps
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Abstract:
Abstract. In this paper we suggest the notion of self-testing/correcting protocols. The work initiates the merge of distributed computing and the area of "program checking " introduced by Blum, and specifically employs extended notions from the work of Blum, Luby and Rubinfeld. In this setting, given a protocol P (a collection of programs on a network of n processors) which allegedly implements a distributed function f, a selftester for f is a (simpler) protocol which makes calls to P to estimate the probability that P when executed in a given environment is faulty (i.e., P and f differ in some of the outputs). A self-correcting protocol is another protocol which allows for the computation of f correctly on every input (with high probability) as long as P in the same type of environment is not too faulty. We first consider self-testing/correcting under a basic form of environmental malfunction, that of crash failures, and design a self-tester/corrector pair for protocols implementing the agreement "function. " Many distributed protocols can be designed "on top " of this primitive, and can be self tested/corrected whenever it can be. We then consider self-testing/ correcting under gossiping failures, and present a generic self-testing/ correcting pair that is privacy-preserving. The notion is basic in protocols where secrecy is an issue. A self-corrector for P is privacy-preserving if it is private (with overwhelming probability) whenever P is private (with overwhelming probability). In the process of our study, we identify the basic components of a protocol self-testing "utility library, " which allows for the safe bootstrapping of the self-testing/correcting process. 1
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