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The Cryptographic Hardness of Random Local Functions (Survey)
, 2015
"... Constant paralleltime 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 random local ..."
Abstract

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Constant paralleltime 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 random local functions in which each output bit is computed by applying some fixed dary predicate P to a randomly chosen dsize 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 (onewayness, pseudorandomness, collision resistance, publickey 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