Book ChapterDOI
Lower bound on average-case complexity of inversion of goldreich’s function by drunken backtracking algorithms
Dmitry Itsykson
- Vol. 6072, pp 204-215
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It is proved an exponential lower bound on the average time of inverting Goldreich’s function by drunken [AHI05] backtracking algorithms; therefore the open question stated in [CEMT09] is resolved.Abstract:
We prove an exponential lower bound on the average time of inverting Goldreich’s function by drunken [AHI05] backtracking algorithms; therefore we resolve the open question stated in [CEMT09]. The Goldreich’s function [Gol00] has n binary inputs and n binary outputs. Every output depends on d inputs and is computed from them by the fixed predicate of arity d. Our Goldreich’s function is based on an expander graph and on the nonliniar predicates of a special type. Drunken algorithm is a backtracking algorithm that somehow chooses a variable for splitting and randomly chooses the value for the variable to be investigated at first. Our proof technique significantly simplifies the one used in [AHI05] and in [CEMT09].read more
Citations
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Journal Article
Pseudorandom Generators with Long Stretch and Low locality from Random Local One-Way Functions.
TL;DR: The existence of locally computable pseudorandom generators with small sublinear stretch was shown to be possible in this article, where it is known that such generators are likely to exist for the case of small sub-linear stretch.
Journal ArticleDOI
Cryptographic Hardness of Random Local Functions
TL;DR: This work will survey known attacks and hardness results, discuss different flavors of hardness (one-wayness, pseudorandomness, collision resistance, public-key encryption, and mention applications to other problems in cryptography and computational complexity, with the hope to develop a systematic study of the cryptographic hardness of local functions.
Proceedings ArticleDOI
Pseudorandom generators with long stretch and low locality from random local one-way functions
TL;DR: This work constructs collections of PRGs that each of their outputs depend on a small number of d input bits based on the one-wayness of "random" local functions, and shows that these constructions give rise to strong inapproximability results for the densest-subgraph problem in d-uniform hypergraphs for constant d.
Book ChapterDOI
A dichotomy for local small-bias generators
TL;DR: Evidence in support of the view that small bias is a good measure of pseudorandomness for local functions with large stretch is given, by demonstrating that resilience to linear distinguishers implies resilience to a larger class of attacks for such functions.
Book ChapterDOI
Lower bounds for splittings by linear combinations
Dmitry Itsykson,Dmitry Sokolov +1 more
TL;DR: This paper considers an extension of the DPLL paradigm that can split by an arbitrary linear combination of variables modulo two and quickly solve formulas that explicitly encode linear systems moduloTwo.
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