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AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
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APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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Wireless Personal Communications: An International Journal
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In this paper we introduce the notion of a Public-Key Encryption Scheme that is also a Locally-Decodable Error-Correcting Code (PKLDC). In particular, we allow any polynomial-time adversary to read the entire ciphertext, and corrupt a constant fraction of the bits of the entireciphertext. Nevertheless, the decoding algorithm can recover any bit of the plaintext with all but negligible probability by reading only a sublinear number of bits of the (corrupted) ciphertext.We give a general construction of a PKLDC from any Semantically-Secure Public Key Encryption (SS-PKE) and any Private Information Retrieval (PIR) protocol. Since Homomorphic encryption implies PIR, we also show a reduction from any Homomorphic encryption protocol to PKLDC.Applying our construction to the best known PIR protocol (that of Gentry and Ramzan), we obtain a PKLDC, which for messages of size nand security parameter kachieves ciphertexts of size $\mathcal{O}(n)$, public key of size $\mathcal{O}(n+k)$, and locality of size $\mathcal{O}(k^2)$. This means that for messages of length n= 茂戮驴(k2 + 茂戮驴), we can decode a bit of the plaintext from a corrupted ciphertext while doing computation sublinear in n.