The complexity of finite functions
Handbook of theoretical computer science (vol. A)
The computational complexity of universal hashing
Theoretical Computer Science - Special issue on structure in complexity theory
Cryptographic primitives based on hard learning problems
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
On sharing secrets and Reed-Solomon codes
Communications of the ACM
Communications of the ACM
The Complexity of Computing
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
LFSR-based Hashing and Authentication
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Secure Human Identification Protocols
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Noise-tolerant learning, the parity problem, and the statistical query model
Journal of the ACM (JACM)
Randomness Conductors and Constant-Degree Lossless Expanders
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Expander-Based Constructions of Efficiently Decodable Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Efficiently decodable codes meeting Gilbert-Varshamov bound for low rates
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
List Decoding of Error-Correcting Codes: Winning Thesis of the 2002 ACM Doctoral Dissertation Competition (Lecture Notes in Computer Science)
Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Cryptography with constant computational overhead
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Secure Computation from Random Error Correcting Codes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
How to Encrypt with the LPN Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
On lattices, learning with errors, random linear codes, and cryptography
Journal of the ACM (JACM)
Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
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
Parallel and concurrent security of the HB and HB+ protocols
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Cryptography from learning parity with noise
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
IEEE Transactions on Information Theory - Part 1
Linear-time encodable and decodable error-correcting codes
IEEE Transactions on Information Theory - Part 1
Class of constructive asymptotically good algebraic codes
IEEE Transactions on Information Theory
Linear-time encodable/decodable codes with near-optimal rate
IEEE Transactions on Information Theory
Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs
IEEE Transactions on Information Theory - Part 2
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A random linear code has good minimal distance with high probability. The conjectured intractability of decoding random linear codes has recently found many applications in cryptography. One disadvantage of random linear codes is that their encoding complexity grows quadratically with the message length. Motivated by this disadvantage, we present a randomized construction of linear error-correcting codes which can be encoded in linear time and yet enjoy several useful features of random linear codes. Our construction is based on a linear-time computable hash function due to Ishai, Kushilevitz, Ostrovsky and Sahai [25]. We demonstrate the usefulness of these new codes by presenting several applications in coding theory and cryptography. These include the first family of linear-time encodable codes meeting the Gilbert-Varshamov bound, the first nontrivial linear-time secret sharing schemes, and plausible candidates for symmetric encryption and identification schemes which can be conjectured to achieve better asymptotic efficiency/security tradeoffs than all current candidates.