TY - GEN

T1 - Cryptography with constant input locality

AU - Applebaum, Benny

AU - Ishai, Yuval

AU - Kushilevitz, Eyal

PY - 2007

Y1 - 2007

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 (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).

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 (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).

UR - http://www.scopus.com/inward/record.url?scp=38049158077&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-74143-5_6

DO - 10.1007/978-3-540-74143-5_6

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:38049158077

SN - 9783540741428

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 92

EP - 110

BT - Advances in Cryptology - CRYPTO 2007 - 27th Annual International Cryptology Conference, Proceedings

PB - Springer Verlag

T2 - 27th Annual International Cryptology Conference, CRYPTO 2007

Y2 - 19 August 2007 through 23 August 2007

ER -