Abstract
We consider the problem of constructing efficient locally decodable codes in the presence of a computationally bounded adversary. Assuming the existence of one-way functions, we construct efficient locally decodable codes with positive information rate and low (almost optimal) query complexity which can correctly decode any given bit of the message from constant channel error rate ρ. This compares favorably to our state of knowledge locally-decodable codes without cryptographic assumptions. For all our constructions, the probability for any polynomial-time adversary, that the decoding algorithm incorrectly decodes any bit of the message is negligible in the security parameter.
Part of this work was done when all the authors were at IPAM. The first author is supported in part by NSF Cybertrust grant No. 0430254, Xerox Innovation group Award and IBM Faculty Award. The second and third authors were supported in part from grants from the NSF ITR and Cybertrust programs (including grants 0627781, 0456717, and 0205594), a subgrant from SRI as part of the Army Cyber-TA program, an equipment grant from Intel, and an Alfred P. Sloan Foundation Research Fellowship.
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Ostrovsky, R., Pandey, O., Sahai, A. (2007). Private Locally Decodable Codes. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_35
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DOI: https://doi.org/10.1007/978-3-540-73420-8_35
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