Public-Key Locally-Decodable Codes

  • Brett Hemenway
  • Rafail Ostrovsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5157)

Abstract

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 entire ciphertext. 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 n and security parameter k achieves 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 = ω(k2 + ε), we can decode a bit of the plaintext from a corrupted ciphertext while doing computation sublinear in n.

Keywords

Public Key Cryptography Locally Decodable Codes Error Correcting Codes Bounded Channel Model Chinese Remainder Theorem Private Information Retrieval 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Brett Hemenway
    • 1
  • Rafail Ostrovsky
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaLos Angeles
  2. 2.Department of Computer Science and Department of MathematicsUniversity of CaliforniaLos Angeles

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