Verifying proofs in constant depth
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
A dichotomy for local small-bias generators
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Commitments and efficient zero-knowledge proofs from learning parity with noise
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Verifying proofs in constant depth
ACM Transactions on Computation Theory (TOCT)
Robust pseudorandom generators
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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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).