**The Cryptographic Hardness of Random Local Functions -- Survey**

*Benny Applebaum*

**Abstract: **Constant parallel-time cryptography allows to perform complex cryptographic tasks at an ultimate level of parallelism, namely, by local functions
that each of their output bits depend on a constant number of input bits. A natural way to obtain local cryptographic constructions is to use \emph{random local functions} in which each output bit is computed by applying some fixed $d$-ary predicate $P$ to a randomly chosen $d$-size subset of the input bits.

In this work, we will study the cryptographic hardness of random local functions. In particular, we 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. We also present some open questions with the hope to develop a systematic study of the cryptographic hardness of local functions.

**Category / Keywords: **foundations / local cryptography, constant-depth circuits, NC0, one-way functions, pseudorandom generators, hash functions, public-key encryption

**Original Publication**** (with major differences): **IACR-TCC-2013

**Date: **received 26 Feb 2015

**Contact author: **benny applebaum at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20150227:222106 (All versions of this report)

**Short URL: **ia.cr/2015/165

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