Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Efficient checking of polynomials and proofs and the hardness of approximation problems
Efficient checking of polynomials and proofs and the hardness of approximation problems
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A New Approach To Information Theory
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Public-Key Locally-Decodable Codes
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
3-query locally decodable codes of subexponential length
Proceedings of the forty-first annual ACM symposium on Theory of computing
Computationally private information retrieval with polylogarithmic communication
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Codes for Computationally Simple Channels: Explicit Constructions with Optimal Rate
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
High-rate codes with sublinear-time decoding
Proceedings of the forty-third annual ACM symposium on Theory of computing
Optimal error correction against computationally bounded noise
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Locally Decodable Codes
Private locally decodable codes
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Hi-index | 0.00 |
This work considers locally decodable codes in the computationally bounded channel model. The computationally bounded channel model, introduced by Lipton in 1994, views the channel as an adversary which is restricted to polynomial-time computation. Assuming the existence of IND-CPA secure public-key encryption, we present a construction of public-key locally decodable codes, with constant codeword expansion, tolerating constant error rate, with locality O(λ), and negligible probability of decoding failure, for security parameter λ. Hemenway and Ostrovsky gave a construction of locally decodable codes in the public-key model with constant codeword expansion and locality O(λ2), but their construction had two major drawbacks. The keys in their scheme were proportional to n, the length of the message, and their schemes were based on the F-hiding assumption. Our keys are of length proportional to the security parameter instead of the message, and our construction relies only on the existence of IND-CPA secure encryption rather than on specific number-theoretic assumptions. Our scheme also decreases the locality from O(λ2) to O(λ). Our construction can be modified to give a generic transformation of any private-key locally decodable code to a public-key locally decodable code based only on the existence of an IND-CPA secure public-key encryption scheme.