Privacy amplification by public discussion
SIAM Journal on Computing - Special issue on cryptography
Elements of information theory
Elements of information theory
Interactive communication of balanced distributions and of correlated files
SIAM Journal on Discrete Mathematics
Secret-key reconciliation by public discussion
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Chernoff-Hoeffding Bounds for Applications with Limited Independence
SIAM Journal on Discrete Mathematics
CCS '99 Proceedings of the 6th ACM conference on Computer and communications security
List decoding algorithms for certain concatenated codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Communication complexity of document exchange
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Introduction to Coding Theory
A New Approach To Information Theory
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Private Codes or Succinct Random Codes That Are (Almost) Perfect
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Correcting errors without leaking partial information
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Explicit capacity-achieving list-decodable codes
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
New shielding functions to enhance privacy and prevent misuse of biometric templates
AVBPA'03 Proceedings of the 4th international conference on Audio- and video-based biometric person authentication
Simple and tight bounds for information reconciliation and privacy amplification
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Derandomized constructions of k-wise (almost) independent permutations
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Optimal error correction against computationally bounded noise
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Error correction in the bounded storage model
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Generalized privacy amplification
IEEE Transactions on Information Theory - Part 2
Combinatorial bounds for list decoding
IEEE Transactions on Information Theory
Set reconciliation with nearly optimal communication complexity
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Private locally decodable codes
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Communicating over a noisy channel is typically much easier when errors are drawn from a fixed, known distribution than when they are chosen adversarially. This paper looks at how one can use schemes designed for random errors in an adversarial context, at the cost of few additional random bits and without relying on unproven computational assumptions. The basic approach is to permute the positions of a bit string using a permutation drawn from a t-wise independent family, where t = o(n). This leads to several new results: • We show that concatenated codes can correct errors up to the Shannon capacity even when the errors are only slightly random --- it is sufficient that they be t-wise independently distributed, for t roughly ω(log n). • We construct computationally efficient information reconciliation protocols correcting pn adversarial binary Hamming errors with optimal communication complexity and entropy loss n(h(p) + o(1)) bits, where n is the length of the strings and h() is the binary entropy function. Information reconciliation protocols allow cooperating parties to correct errors in a shared string. They are important tools in two applications: first, for dealing with noisy secrets in cryptography; second, for synchronizing remote copies of large files. Entropy loss measures how much information is leaked to an eavesdropper listening in on the protocol. • We improve the randomness complexity (key length) of efficiently decodable capacity-approaching private codes from Θ(n log n) to n + o(n). We also present a simplified proof of an existential result on private codes due to Langberg (FOCS '04).