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List-decoding reed-muller codes over small fields
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Decodability of group homomorphisms beyond the johnson bound
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Learning unions of ω(1)-dimensional rectangles
Theoretical Computer Science
Making Cryptographic Primitives Harder
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The Security of All Bits Using List Decoding
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Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding
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Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions
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List Decoding Tensor Products and Interleaved Codes
SIAM Journal on Computing
Learning unions of ω(1)-dimensional rectangles
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Quantum hardcore functions by complexity-theoretical quantum list decoding
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Combinatorial algorithms for compressed sensing
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On related-secret pseudorandomness
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Computational complexity since 1980
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Nearly optimal sparse fourier transform
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We introduce a unifying framework for proving that predicate P is hard-core for a one-way function f, and apply it to a broad family of functions and predicates, reproving old results in an entirely different way as well as showing new hard-core predicates for well known one-way function cadidates.Our framework extends the list-coding method of Goldreich and Levin for showing hard-core predicates. Namely, a predicate will correspond to some error correcting code, predicting a predicate will correspond to access to a corrupted codeword, and the task of inverting one-way functions will correspond to the task of list decoding a corrupted codeword.A characteristic of the error correcting codes which emerge and are addressed by our framework, is that codewords can be approximated by a small number of heavy coefficients in their Fourier representation. Moreover, as long as corrupted words are close enough to legal codewords, they will share a heavy Fourier coefficient. We list decodes, by devising a learning algorithm applied to corrupted codewords for learning heavy Fourier coefficients.For codes defined over {0, 1}n domain, a learning algorithm by Kushilevitz and Mansour already exists. For codes defined over ZN, which are the codes which emerge for predicates based on number theoretic one-way functions such as the RSA and Exponentiation modulo primes, we develop a new learning algorithm. This latter algorithm may be of independent interest outside the realm of hard-core predicates.