NDLI: Input Locality and Hardness Amplification

Content Provider	Springer Nature Link
Author	Bogdav, Andrej Rosen, Alon
Copyright Year	2011
Abstract	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:{0,1} n →{0,1} m be a one-way function with input locality d, and suppose that f cannot be inverted in time $\exp(\tilde{O}(\sqrt{n}\cdot d))$ on an ε-fraction of inputs. Our main results can be summarized as follows: If f is injective then it is equally hard to invert f on a (1−ε)-fraction of inputs. If f is regular then there is a function g:{0,1} n →{0,1} m+O(n) that is d+O(log3 n) input local and is equally hard to invert on a (1−ε)-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.
Starting Page	144
Ending Page	171
Page Count	28
File Format	PDF
ISSN	09332790
Journal	Journal of Cryptology
Volume Number	26
Issue Number	1
e-ISSN	14321378
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-12-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	One-way function Input locality Hardness amplification Parity with noise Coding and Information Theory Computational Mathematics and Numerical Analysis Combinatorics Probability Theory and Stochastic Processes Communications Engineering, Networks
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications Software

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