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
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
Upper Bound on Communication Complexity of Private Information Retrieval
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Optimal Lower Bounds for 2-Query Locally Decodable Linear Codes
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Lower Bounds for Linear Locally Decodable Codes and Private Information Retrieval
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Better Lower Bounds for Locally Decodable Codes
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
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
A tight lower bound for restricted PIR protocols
Computational Complexity
An \Omega(n^1/3 ) Lower Bound for Bilinear Group Based Private Information Retrieval
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Improved lower bounds for locally decodable codes and private information retrieval
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Public-Key Locally-Decodable Codes
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
The Complexity of Local List Decoding
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
On Locally Decodable Codes, Self-correctable Codes, and t-Private PIR
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Short locally testable codes and proofs: a survey in two parts
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Short locally testable codes and proofs
Studies in complexity and cryptography
Three-Query Locally Decodable Codes with Higher Correctness Require Exponential Length
ACM Transactions on Computation Theory (TOCT)
Communication-efficient distributed oblivious transfer
Journal of Computer and System Sciences
Nearly private information retrieval
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Private locally decodable codes
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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A q-query Locally Decodable Code (LDC) encodes an n-bitmessage x as an n-bit codeword C(x), such that one canprobabilistically recover any bit xi of the message by queryingonly q bits of the codeword C(x), even after some constantfraction of codeword bits has been corrupted.We give new constructions of three query LDCs of vastly shorterlength than that of previous constructions. Specifically, givenany Mersenne prime p = 2t - 1, we design three query LDCs of length N=(n1/t), for every n. Based on thelargest known Mersenne prime, this translates to a length of less than exp(n10-7), compared to exp(n1/2) in the previous constructions. It hasoften been conjectured that there are infinitely many Mersenneprimes. Under this conjecture, our constructions yield three querylocally decodable codes of length N=exp(nO(1/(log log n))) forinfinitely many n. We also obtain analogous improvements for Private InformationRetrieval (PIR) schemes. We give 3-server PIR schemes withcommunication complexity of O(n10-7) to accessan n-bit database, compared to the previous best scheme withcomplexity O(n1/5.25). Assuming again that there areinfinitely many Mersenne primes, we get 3-server PIR schemes ofcommunication complexity nO(1/(log log n))for infinitely many n. Previous families of LDCs and PIR schemes were based on theproperties of low-degree multivariate polynomials over finitefields. Our constructions are completely different and areobtained by constructing a large number of vectors in a smalldimensional vector space whose inner products are restricted tolie in an algebraically nice set.