Communications of the ACM
Solving low-density subset sum problems
Journal of the ACM (JACM)
How to construct random functions
Journal of the ACM (JACM)
Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Crytographic limitations on learning Boolean formulae and finite automata
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
When won't membership queries help?
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
An O(nlog log n) learning algorithm for DNF under the uniform distribution
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Cryptographic hardness of distribution-specific learning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Hardness Results for Learning First-Order Representations and Programming by Demonstration
Machine Learning - Special issue on the ninth annual conference on computational theory (COLT '96)
A tamper-proof and lightweight authentication scheme
Pervasive and Mobile Computing
Cryptographic limitations on learning one-clause logic programs
AAAI'93 Proceedings of the eleventh national conference on Artificial intelligence
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We investigate cryptographic lower bounds on the number of samples and on computational resources required to learn several classes of boolean circuits on the uniform distribution. Under the assumption that solving n x n1+&egr; subset sum is hard, we construct (using the results of Impagliazzo and Naor [IN89] and Goldreich, Goldwasser, and Micali[GGM86] a pseudo-random function generator that can be computed by shallow boolean circuits. From this we conclude that learning AC1 circuits on the uniform distribution requires &OHgr;(nlog log n) different samples, or, alternatively, that learning AC1 circuits on the uniform distribution with a polynomial number of samples is as hard as solving n x n1+&egr; subset sum. We also show that no algorithm can learn NC1 circuits on the uniform distribution with a polynomial number of samples. Using the weaker assumption that solving n x (1+&egr;)nsubset sum is hard, we show that the class of NC circuits can not be learned with nlogcn samples for any c.