Cryptography with constant input locality

Benny Applebaum*, Yuval Ishai, Eyal Kushilevitz

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study the following natural question: Which cryptographic primitives (if any) can be realized by functions with constant input locality, namely functions in which every bit of the input influences only a constant number of bits of the output? This continues the study of cryptography in low complexity classes. It was recently shown (Applebaum et al., FOCS 2004) that, under standard cryptographic assumptions, most cryptographic primitives can be realized by functions with constant output locality, namely ones in which every bit of the output is influenced by a constant number of bits from the input. We (almost) characterize what cryptographic tasks can be performed with constant input locality. On the negative side, we show that primitives which require some form of non-malleability (such as digital signatures, message authentication, or non-malleable encryption) cannot be realized with constant input locality. On the positive side, assuming the intractability of certain problems from the domain of error correcting codes (namely, hardness of decoding a random linear code or the security of the McEliece cryptosystem), we obtain new constructions of one-way functions, pseudorandom generators, commitments, and semantically-secure public-key encryption schemes whose input locality is constant. Moreover, these constructions also enjoy constant output locality. Therefore, they give rise to cryptographic hardware that has constant-depth, constant fan-in and constant fan-out. As a byproduct, we obtain a pseudorandom generator whose output and input locality are both optimal (namely, 3).

Original languageEnglish
Title of host publicationAdvances in Cryptology - CRYPTO 2007 - 27th Annual International Cryptology Conference, Proceedings
PublisherSpringer Verlag
Number of pages19
ISBN (Print)9783540741428
StatePublished - 2007
Externally publishedYes
Event27th Annual International Cryptology Conference, CRYPTO 2007 - Santa Barbara, CA, United States
Duration: 19 Aug 200723 Aug 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4622 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th Annual International Cryptology Conference, CRYPTO 2007
Country/TerritoryUnited States
CitySanta Barbara, CA


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