 
Summary: Cryptography with Constant Input Locality
(extended abstract)
Benny Applebaum, Yuval Ishai , and Eyal Kushilevitz
Computer Science Department, Technion, Haifa 32000, Israel
{abenny,yuvali,eyalk}@cs.technion.ac.il
Abstract. We study the following natural question: Which cryptographic
primitives (if any) can be realized by functions with constant input lo
cality, namely functions in which every bit of the input influences only a
constant number of bits of the output? This continues the study of cryp
tography 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 out
put 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 prim
itives which require some form of nonmalleability (such as digital sig
natures, message authentication, or nonmalleable encryption) cannot
be realized with constant input locality. On the positive side, assuming
the intractability of certain problems from the domain of error correcting
