Design theory
Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Designing programs that check their work
Journal of the ACM (JACM)
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Designs, Codes and Cryptography - Special issue containing papers presented at the Second Upper Michigan Combinatorics Workshop on Designs, Codes and Geometries
Computationally private information retrieval (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Improved upper bounds on information-theoretic private information retrieval (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Linear Perfect Codes and a Characterization of the ClassicalDesigns
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
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
Communications of the ACM
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Breaking the O(n1/(2k-1)) Barrier for Information-Theoretic Private Information Retrieval
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Information-Theoretic Private Information Retrieval: A Unified Construction
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Upper Bound on Communication Complexity of Private Information Retrieval
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Hiding Instances in Multioracle Queries
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Efficient Checking of Computations
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Replication is not needed: single database, computationally-private information retrieval
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
A Geometric Approach to Information-Theoretic Private Information Retrieval
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
General constructions for information-theoretic private information retrieval
Journal of Computer and System Sciences
Towards 3-query locally decodable codes of subexponential length
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Improved lower bounds for locally decodable codes and private information retrieval
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Proceedings of the forty-third annual ACM symposium on Theory of computing
SIAM Journal on Computing
Communication-efficient distributed oblivious transfer
Journal of Computer and System Sciences
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A k-query locally decodable code(LDC) allows to probabilistically decode any bit of an encoded message by probing only kbits of its corrupted encoding. A stronger and desirable property is that of self-correction, allowing to efficiently recover not only bits of the message but also arbitrary bits of its encoding. In contrast to the initial constructions of LDCs, the recent and most efficient constructions are not known to be self-correctable. The existence of self-correctable codes of comparable efficiency remains open.A closely related problem with a very different motivation is that of private information retrieval(PIR). A k-server PIR protocol allows a user to retrieve the i-th bit of a database, which is replicated among kservers, without revealing information about ito any individualserver. A natural generalization is t-private PIR, which keeps ihidden from any tcolluding servers. In contrast to the initial PIR protocols, it is not known how to generalize the recent and most efficient protocols to yield t-private protocols of comparable efficiency.In this work we study both of the above questions, showing that they are in fact related. We start by presenting a general transformation of any 1-private PIR protocol (equivalently, LDC) into a t-private protocol with a similar amount of communication per server. Combined with the recent result of Yekhanin (STOC 2007), this yields a significant improvement over previous t-private PIR protocols. A major weakness of our transformation is that the number of servers in the resulting t-private protocols grows exponentially with t. We show that if the underlying LDC satisfies the stronger self-correctionproperty, then there is a similar transformation in which the number of servers grows only linearlywith t, which is the best one can hope for. Finally, we study the question of closing the current gap between the complexity of the best known LDC and that of self-correctable codes, and relate this question to a conjecture of Hamada concerning the algebraic rank of combinatorial designs.