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标题：Input locality and hardness amplification
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作者：Andrej Bogdanov ; Alon Rosen
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2011
卷号：2011
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We establish new hardness amplification results for one-way functions in which each input bit influences only a small number of output bits (a.k.a. input-local functions). Our transformations differ from previous ones in that they approximately preserve input locality and at the same time retain the input size of the original function. Let f:01n01m be a one-way function with input locality d, and suppose that f cannot be inverted in time exp(O(nd)) on an -fraction of inputs. Our main results can be summarized as follows: 1. If f is injective then it is equally hard to invert f on a (1−)-fraction of inputs. 2. If f is regular then there is a function g:01n01m+O(n) that~is d+O(log3n) input local and is equally hard to invert on a (1−)-fraction of inputs. A natural candidate for a function with small input locality and for which no sub-exponential time attacks are known is Goldreich's one-way function. To make our results applicable to this function, we prove that when its input locality is set to be d=O(logn) certain variants of the function are (almost) regular with high probability. In some cases, our techniques are applicable even when the input locality is not small. We demonstrate this by extending our first main result to one-way functions of the "parity with noise" type.
关键词：hardness amplification, input locality, one-way function, parity with noise