On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh 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
On Pseudorandom Generators with Linear Stretch in NC0
Computational Complexity
On lattices, learning with errors, random linear codes, and cryptography
Journal of the ACM (JACM)
Deterministic Approximation Algorithms for the Nearest Codeword Problem
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Complexity Lower Bounds using Linear Algebra
Foundations and Trends® in Theoretical Computer Science
Cryptography with constant input locality
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
Propagation connectivity of random hypergraphs
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
Better key sizes (and attacks) for LWE-based encryption
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
New algorithms for learning in presence of errors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Cryptography in constant parallel time
Cryptography in constant parallel time
SIAM Journal on Computing
Some results on average-case hardness within the polynomial hierarchy
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Public-key cryptographic primitives provably as secure as subset sum
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
On pseudorandom generators with linear stretch in NC0
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Cryptography from learning parity with noise
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Pseudorandom generators with long stretch and low locality from random local one-way functions
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
A dichotomy for local small-bias generators
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Decoding random binary linear codes in 2n/20: how 1 + 1 = 0 improves information set decoding
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
IND-CCA secure cryptography based on a variant of the LPN problem
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
When homomorphism becomes a liability
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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We consider the problem to determine the maximal number of satisfiable equations in a linear system chosen at random. We make several plausible conjectures about the average case hardness of this problem for some natural distributions on the instances, and relate them to several interesting questions in the theory of approximation algorithms and in cryptography.Namely we show that our conjectures imply the following facts:Feige's hypothesis about the hardness of refuting a random 3CNF is true, which in turn implies inapproximability within a constant for several combinatorial problems, for which no NP-hardness of approximation is known.It is hard to approximate the NEAREST CODEWORD within factor n^{1 - \varepsilon}.It is hard to estimate the rigidity of a matrix. More exactly, it is hard to distinguish between matrices of low rigidity and random ones.There exists a secure public-key (probabilistic) cryptosystem, based on the intractability of decoding of random binary codes.Our conjectures are strong in that they assume cryptographic hardness: no polynomial algorithm can solve the problem on any non-negligible fraction of inputs. Nevertheless, to the best of our knowledge no efficient algorithms are currently known that refute any of our hardness conjectures.