One-way functions with optimal output locality

Benny Applebaum

doi:10.1007/978-3-642-17367-7_6

One-way functions with optimal output locality

Benny Applebaum^*

^*Corresponding author for this work

School of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In Chap. 4 it was shown that, under relatively mild assumptions, there exist one-way functions (OWFs) in NC⁰₄. This result is not far from optimal as there is no OWF in NC⁰₂. In this chapter we partially close this gap by providing an evidence for the existence of OWF in NC⁰₃. This is done in two steps: (1) we describe a new variant of randomized encoding that allows us to obtain a OWF in NC⁰₃ from a “robust” OWF which remains hard to invert even when some information on the preimage x is leaked; (2) we show how to construct a robust OWF assuming that a random function of (arbitrarily large) constant locality is one-way. (A similar assumption was previously made by Goldreich in Electron. Colloq. Comput. Complex. 7:090, 2000.)

Original language	English
Title of host publication	Information Security and Cryptography
Publisher	Springer International Publishing
Pages	107-121
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-642-17367-7_6
State	Published - 2014

Publication series

Name	Information Security and Cryptography
Volume	19
ISSN (Print)	1619-7100
ISSN (Electronic)	2197-845X

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One-way functions with optimal output locality

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