 
Summary: Cryptography with Constant Input Locality #
Benny Applebaum + Yuval Ishai # Eyal Kushilevitz §
March 10, 2009
Abstract
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 lo
cality. On the negative side, we show that primitives which require some form of nonmalleability
(such as digital signatures, message authentication, or nonmalleable encryption) cannot be re
alized 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
binary linear code or the security of the McEliece cryptosystem), we obtain new construc
tions of oneway functions, pseudorandom generators, commitments, and semanticallysecure
publickey encryption schemes whose input locality is constant. Moreover, these constructions
also enjoy constant output locality and thus they give rise to cryptographic hardware that has
