TY - JOUR

T1 - Cryptography with constant input locality

AU - Applebaum, Benny

AU - Ishai, Yuval

AU - Kushilevitz, Eyal

N1 - Funding Information:
Supported by NSF grants CNS-0627526, CCF-0426582 and CCF-0832797. Most of this work done while studying in the Technion.
Funding Information:
Supported by BSF grant 2004361 and NSF grants 0205594, 0430254, 0456717, 0627781, 0716389.
Funding Information:
Research supported by grant 1310/06 from the Israel Science Foundation.

PY - 2009/10

Y1 - 2009/10

N2 - 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 by 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 binary 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 and thus 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).

AB - 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 by 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 binary 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 and thus 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).

KW - Cryptography with low complexity

KW - Hardness of decoding random linear code

KW - Input locality

KW - NC

UR - http://www.scopus.com/inward/record.url?scp=68549121004&partnerID=8YFLogxK

U2 - 10.1007/s00145-009-9039-0

DO - 10.1007/s00145-009-9039-0

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AN - SCOPUS:68549121004

SN - 0933-2790

VL - 22

SP - 429

EP - 469

JO - Journal of Cryptology

JF - Journal of Cryptology

IS - 4

ER -